#ABCMIZ_0
G1 2
GAdjectiveStr
mc#1#2; \langle #1,#2 \rangle
G2 5
GTA-structure
mc#1#2#3#4#5; \langle #1,#2,#3,#4,#5 \rangle
G3 6
GTAS-structure
mc#1#2#3#4#5#6; \langle #1,#2,#3,#4,#5,#6 \rangle
J1 1
GAdjectiveStr
hol#1; adjective structure of #1
J2 1
GTA-structure
hol#1; {\it TA}-structure of #1
J3 1
GTAS-structure
hol#1; {\it TAS}-structure of #1
L1 0
GAdjectiveStr
hn adjective structure #0
adjective structures #0
L2 0
GTA-structure
ha {\it TA}-structure #0
{\it TA}-structures #0
L3 0
GTAS-structure
ha {\it TAS}-structure #0
{\it TAS}-structures #0
M1 1
Madjective
hn adjective #0 of #1
adjectives #0 of #1
O1 0 1
Onon-
mol; \mathop{\rm non} #1
O2 0 1
Oadjs
mol; \mathop{\rm adjs} #1
O3 0 1
Otypes
mol; \mathop{\rm types} #1
O4 0 1
Oast
mow#1; \ast_{#1}
O4 1 1
Oast
moi@6; #1 \ast #2
O5 0 1
Osub
mol; \mathop{\rm sub} #1
O6 1 0
O@-->
mow/1k; {{\circ}\!{\to}}_{#1}
O7 0 1
Oradix
mol; \mathop{\rm radix} #1
R1 1 1
Ris_applicable_to
iy applicable to #2
not applicable to #2
R2 1 1
Ris_properly_applicable_to
iy properly applicable to #2
not properly applicable to #2
U1 1
Uadjectives
hosl#1; set of adjectives of #1
set of adjectives
U2 1
Unon-op
honl#1; operation non of #1
operation non
U3 1
Uadj-map
honl#1; adjective map of #1
adjective map
U4 1
Usub-map
hosl#1; subject map of #1
subject map
V1 1
VMizar-widening-like
a Mizar-widening-like
V2 1
Vwithout_fixpoints
a without fixpoints
V3 1
Vconsistent
a consistent
V4 1
Vadj-structured
w structured adjectives
V5 1
Vadjs-typed
w typed adjectives
V6 1
Vnon-absorbing
n absorbing non
V7 1
Vsubjected
a subjected
#ABCMIZ_1
M1 0
Mvariable
ha variable #0
variables #0
M2 0
Mquasi-loci
ha quasi-locus sequence #0
quasi-loci #0
M3 0
MConstructorSignature
ha% constructor signature #0
constructor signatures #0
M4 0
Mexpression
ha expression #0
expressions #0
M4 1
Mexpression
hn expression #0 of #1
expressions #0 of #1
M4 2
Mexpression
hn expression #0 of #1 from #2
expressions #0 of #1 from #2
M5 0
Mquasi-term
ha quasi-term #0
quasi-terms #0
M5 1
Mquasi-term
ha quasi-term #0 of #1
quasi-terms #0 of #1
M6 0
Mquasi-adjective
ha quasi-adjective #0
quasi-adjectives #0
M6 1
Mquasi-adjective
ha quasi-adjective #0 of #1
quasi-adjectives #0 of #1
M7 0
Mquasi-type
ha quasi-type #0
quasi-types #0
M7 1
Mquasi-type
ha quasi-type #0 of #1
quasi-types #0 of #1
M8 2
Mterm-transformation
ha transformation #0 of #1-terms over #2
transformations #0 of #1-terms over #2
M9 0
Mvaluation
ha valuation #0
valuations #0
M9 1
Mvaluation
ha valuation #0 of #1
valuations #0 of #1
O1 0 1
Ovarcl
mol; \mathop{\rm varcl} #1
O2 0 1
Ovars
mol#1; \mathop{\rm vars}(#1)
O3 0 0
OQuasiLoci
mol; \mathop{\rm QuasiLoci}
O4 0 0
Oa_Type
mcsl; \mathop{\bf type}
O4 0 1
Oa_Type
mosw#1; \mathop{\bf type}_{#1}
O5 0 0
Oan_Adj
mcnl; \mathop{\bf adj}
O5 0 1
Oan_Adj
monw#1; \mathop{\bf adj}_{#1}
O6 0 0
Oa_Term
mcsl; \mathop{\bf term}
O6 0 1
Oa_Term
mosw#1; \mathop{\bf term}_{#1}
O7 0 0
Onon_op
mcl; \mathop{\bf non}
O7 0 1
Onon_op
mow#1; \mathop{\bf non}_{#1}
O8 0 0
OMinConstrSign
mol; \mathop{\rm MinConstrSign}
O9 0 0
OModes
mol; \mathop{\rm Modes}
O10 0 0
OAttrs
mol; \mathop{\rm Attrs}
O11 0 0
OConstructors
mol; \mathop{\rm Constructors}
O12 0 1
Okind_of
hol; kind of #1
O13 0 1
Oloci_of
hol; loci of #1
O14 0 1
Oindex_of
hol; index of #1
O15 0 0
OMaxConstrSign
mol; \mathop{\rm MaxConstrSign}
O16 0 1
OMSVars
mol; \mathop{\rm Vars} #1
O17 0 0
OQuasiTerms
mol; \mathop{\rm QuasiTerms}
O17 0 1
OQuasiTerms
mol; \mathop{\rm QuasiTerms} #1
O18 1 1
O-trm
mor#2; #1\vec{~}(#2)
O19 0 1
ONon
mol; \mathop{\rm non} #1
O20 0 0
OQuasiAdjs
mol; \mathop{\rm QuasiAdjs}
O20 0 1
OQuasiAdjs
mol; \mathop{\rm QuasiAdjs} #1
O21 0 0
OQuasiTypes
mol; \mathop{\rm QuasiTypes}
O21 0 1
OQuasiTypes
mol; \mathop{\rm QuasiTypes} #1
O22 0 1
Othe_base_of
hol; base of #1
O23 0 0
OVarPoset
mol; \mathop{\rm VarPoset}
O24 0 1
Ovars-function
mol; \mathop{\rm vars\hbox{-}function} #1
O25 1 1
Oidval
mol#1; \mathop{\rm idval}_{#1}#2
O26 1 1
Oat
mor#2; #1[#2]
V1 1
Vconstructor
a constructor
V2 1
Vinitialized
n initialized
V3 1
Vground
a ground
V4 1
Vcompound
a compound
V5 1
Vpure
a pure
V6 1
Vwith_an_operation_for_each_sort
x an operation for each sort
V7 1
Vwith_missing_variables
x missing variables
V8 1
Vsubstitution
b substitution
V9 1
Virrelevant
n irrelevant
V10 1
Vrelevant
a relevant
#ABCMIZ_A
M1 1
Msubexpression
ha subexpression #0 of #1
subexpressions #0 of #1
M2 1
Mtype-distribution
ha type-distribution #0 for #1
type-distributions #0 for #1
O1 0 1
Oconstrs
mol; \mathop{\rm constrs} #1
O2 0 1
Omain-constr
mol; \mathop{\rm main\hbox{-}constr} #1
O3 0 1
Oargs
mol; \mathop{\rm args} #1
O4 0 1
Obase_exp_of
hol; base expression of #1
O5 0 0
Oset-constr
mol; \mathop{\rm set\hbox{-}constr}
O6 0 0
Oset-type
mol; \mathop{\rm set\hbox{-}type}
R1 1 1
Rmatches_with
h #1 matches #2
#1 does not matche #2
R2 1 2
Runifies
h #1 unifies #2 with #3
#1 does not unify #2 with #3
R3 2 0
Rare_unifiable
h #1 and #2 are unifiable
#1 and #2 are not unifiable
R4 2 0
Rare_weakly-unifiable
h #1 and #2 are weakly-unifiable
#1 and #2 are not weakly-unifiable
R5 1 2
Ris_a_unification_of
i a unification of #2 and #3
not a unification of #2 and #3
R6 1 2
Ris_a_general-unification_of
i a general-unification of #2 and #3
not a general-unification of #2 and #3
V1 1
Vstandardized
a standardized
V2 1
Varity-rich
n arity-rich
#ABIAN
O1 0 1
O=_
mow#1; #1_\equiv
R1 1 1
Ris_a_fixpoint_of
i a fixpoint of #2
not a fixpoint of #2
R2 1 0
Rhas_a_fixpoint
j a fixpoint
no fixpoint
R3 1 0
Rhas_no_fixpoint
j no fixpoint
a fixpoint
V1 1
Veven
n even
V2 1
Vodd
n odd
V3 1
Vcovering
a covering
#ABSVALUE
O1 0 1
Osgn
mol@s; \mathop{\rm sgn} #1
O1 0 2
Osgn
mol#1#2; \mathop{\rm sgn}(#1,#2)
#AFF_1
V1 1
Vbeing_line
b line
#AFF_2
V1 1
Vsatisfying_PPAP
s {\bf PPAP}
V2 1
VPappian
a Pappian
V3 1
Vsatisfying_PAP_1
s ${\bf PAP}_1$
V4 1
VDesarguesian
a Desarguesian
V5 1
Vsatisfying_DES_1
s ${\bf DES}_1$
V6 1
Vsatisfying_DES_2
s ${\bf DES}_2$
V7 1
VMoufangian
a Moufangian
V8 1
Vsatisfying_TDES_1
s ${\bf TDES}_1$
V9 1
Vsatisfying_TDES_2
s ${\bf TDES}_2$
V10 1
Vsatisfying_TDES_3
s ${\bf TDES}_3$
V11 1
Vtranslational
a translational
V12 1
Vsatisfying_des_1
s ${\bf des}_1$
V13 1
Vsatisfying_pap
s pap
V14 1
Vsatisfying_pap_1
s ${\bf pap}_1$
#AFF_3
V1 1
Vsatisfying_DES1
s {\bf DES1}
V2 1
Vsatisfying_DES1_1
s ${\bf DES1}_1$
V3 1
Vsatisfying_DES1_2
s ${\bf DES1}_2$
V4 1
Vsatisfying_DES1_3
s ${\bf DES1}_3$
V5 1
Vsatisfying_DES2
s {\bf DES2}
V6 1
Vsatisfying_DES2_1
s ${\bf DES2}_1$
V7 1
Vsatisfying_DES2_2
s ${\bf DES2}_2$
V8 1
Vsatisfying_DES2_3
s ${\bf DES2}_3$
#AFF_4
R1 3 0
Ris_coplanar
h #1, #2, #3 are coplanar
#1, #2, #3 are not coplanar
V1 1
Vbeing_plane
b plane
#AFINSQ_1
K1 1 L1 vAFINSQ_1
K<%
L%>
mc#1; \langle #1\rangle
K1 2 L1 vAFINSQ_1
K<%
L%>
mc#1#2; \langle #1,#2 \rangle
K1 3 L1 vAFINSQ_1
K<%
L%>
mc#1#2#3; \langle #1,#2,#3 \rangle
M1 0
MXFinSequence
ha finite 0-sequence #0
finite 0-sequences #0
M1 1
MXFinSequence
ha finite 0-sequence #0 of #1
finite 0-sequences #0 of #1
O1 0 1
O<%>
mow#1; {\langle\rangle}_{#1}
O2 1 0
O^omega
moq; #1^\omega
O3 0 3
OReplace
mol#1#2#3; \mathop{\rm Replace}(#1,#2,#3)
#AFINSQ_2
O1 0 1
OSgm0
mol; \mathop{\rm Sgm}_0 #1
O2 0 2
OSubXFinS
hol/2r@s#1#2; #2-subsequence of #1
R1 1 1
R<N<
m #1 < #2
#1 \not< #2
R2 1 1
R<N=
m #1 \leq #2
#1 \not\leq #2
#AFPROJ
O1 0 1
OAfLines
hol; lines of #1
O2 0 1
OAfPlanes
hol; planes of #1
O3 0 1
OLinesParallelity
hol; parallelity of lines of #1
O4 0 1
OPlanesParallelity
hol; parallelity of planes of #1
O5 0 1
OLDir
hol; direction of #1
O6 0 1
OPDir
hol; direction of #1
O7 0 1
ODir_of_Lines
hol; directions of lines of #1
O8 0 1
ODir_of_Planes
hol; directions of planes of #1
O9 0 1
OInc_of_Dir
hol; incidence of directions of #1
O10 0 1
OProjHorizon
hol; projective horizon of #1
#AFVECT0
M1 0
MWeakAffVect
ha weak affine vector space #0
weak affine vector spaces #0
M2 0
MProper_Uniquely_Two_Divisible_Group
ha proper uniquely two divisible group #0
proper uniquely two divisible groups #0
O1 0 2
OPSym
mcl@s#1#2; \mathop{\rm PSym}(#1,#2)
O2 0 1
OPadd
mol@s; \mathop{\rm Padd} #1
O2 0 3
OPadd
mcl@s#1#2#3; \mathop{\rm Padd}(#1,#2,#3)
O3 0 1
OPcom
mol@s; \mathop{\rm Pcom} #1
O3 0 2
OPcom
mcl@s#1#2; \mathop{\rm Pcom}(#1,#2)
O4 0 2
OGroupVect
mcl@s#1#2; \mathop{\rm GroupVect}(#1,#2)
R1 0 2
RMDist
h #1, #2 are in a maximal distance
#1, #2 are not in a maximal distance
R2 1 2
Ris_Iso_of
i an isomorphism of #2 and #3
not an isomorphism of #2 and #3
R3 2 0
Rare_Iso
h #1, #2 are isomorph
#1, #2 are not isomorph
V1 1
VWeakAffVect-like
a weak affine vector space-like
#AFVECT01
M1 0
MWeakAffSegm
ha weak segment-congruence space #0
weak segment-congruence spaces #0
V1 1
VWeakAffSegm-like
a weak segment-congruence space-like
#ALGSEQ_1
M1 1
MAlgSequence
hn algebraic sequence #0 of #1
algebraic sequences #0 of #1
R1 1 1
Ris_at_least_length_of
h the length of #2 is at most #1
the length of #2 is not at most #1
V1 1
Vfinite-Support
a finite-Support
#ALGSPEC1
M1 1
Mrng-retract
ha rng-retraction #0 of #1
rng-retractions #0 of #1
M2 1
MExtension
hn extension #0 of #1
extensions #0 of #1
O1 1 1
O-indexing
moi; #1 \mathop{\rm\hbox{-}indexing} #2
R1 2 1
Rform_a_replacement_in
h #1 and #2 form a replacement in #3
#1 and #2 does not form a replacement in #3
#ALGSTR_0
G1 2
GaddMagma
mc#1#2; \langle #1,#2 \rangle
G2 3
GaddLoopStr
mc#1#2#3; \langle #1,#2,#3 \rangle
G3 2
GmultMagma
mc#1#2; \langle #1,#2 \rangle
G4 3
GmultLoopStr
mc#1#2#3; \langle #1,\allowbreak #2,\allowbreak #3\rangle
G5 4
GmultLoopStr_0
mc#1#2#3#4; \langle #1,\allowbreak #2,\allowbreak #3,\allowbreak #4\rangle
G6 5
GdoubleLoopStr
mc#1#2#3#4#5; \langle #1,\allowbreak #2,\allowbreak #3,\allowbreak #4,\allowbreak #5\rangle
J1 1
GaddMagma
hol#1; additive magma of #1
J2 1
GaddLoopStr
hol#1; additive loop structure of #1
J3 1
GmultMagma
hol#1; multiplicative magma of #1
J4 1
GmultLoopStr
hol#1; multiplicative loop structure of #1
J5 1
GmultLoopStr_0
hol#1; multiplicative loop with zero structure of #1
J6 1
GdoubleLoopStr
hol#1; double loop structure of #1
L1 0
GaddMagma
hn additive magma #0
additive magmas #0
L2 0
GaddLoopStr
hn additive loop structure #0
additive loop structures #0
L3 0
GmultMagma
ha multiplicative magma #0
multiplicative magmas #0
L4 0
GmultLoopStr
ha multiplicative loop structure #0
multiplicative loop structures #0
L5 0
GmultLoopStr_0
ha multiplicative loop with zero structure #0
multiplicative loop with zero structures #0
L6 0
GdoubleLoopStr
ha double loop structure #0
double loop structures #0
O1 0 0
OTrivial-addMagma
mol; \mathop{\rm Trivial\hbox{-}addMagma}
O2 0 0
OTrivial-addLoopStr
mol; \mathop{\rm Trivial\hbox{-}addLoopStr}
O3 0 0
OTrivial-multMagma
mol; \mathop{\rm Trivial\hbox{-}multMagma}
O4 0 0
OTrivial-multLoopStr
mol; \mathop{\rm Trivial\hbox{-}multLoopStr}
O5 0 0
OTrivial-multLoopStr_0
mow{}; \mathop{\rm Trivial\hbox{-}multLoopStr}_0
O6 0 0
OTrivial-doubleLoopStr
mol; \mathop{\rm Trivial\hbox{-}doubleLoopStr}
U1 1
UaddF
hosl#1; addition of #1
addition
U2 1
UmultF
hosl#1; multiplication of #1
multiplication
V1 1
Vleft_add-cancelable
a left add-cancelable
V2 1
Vright_add-cancelable
a right add-cancelable
V3 1
Vadd-cancelable
n add-cancelable
V4 1
Vleft_complementable
a left complementable
V5 1
Vright_complementable
a right complementable
V6 1
Vcomplementable
a complementable
V7 1
Vleft_mult-cancelable
a left mult-cancelable
V8 1
Vright_mult-cancelable
a right mult-cancelable
V9 1
Vmult-cancelable
a mult-cancelable
V10 1
Vleft_invertible
a left invertible
V11 1
Vright_invertible
a right invertible
V12 1
Vinvertible
n invertible
V13 1
Valmost_left_cancelable
n almost left cancelable
V14 1
Valmost_right_cancelable
n almost right cancelable
V15 1
Valmost_cancelable
n almost cancelable
V16 1
Valmost_left_invertible
n almost left invertible
V17 1
Valmost_right_invertible
n almost right invertible
V18 1
Valmost_invertible
n almost invertible
#ALGSTR_1
M1 0
MLoop
ha loop #0
loops #0
M1 1
MLoop
ha loop #0 of #1
loops #0 of #1
M2 0
MmultLoop
ha multiplicative loop #0
multiplicative loops #0
M3 0
MmultGroup
ha multiplicative group #0
multiplicative groups #0
M4 0
MmultLoop_0
ha multiplicative loop #0 with zero
multiplicative loops #0 with zero
M5 0
MmultGroup_0
ha multiplicative group #0 with zero
multiplicative groups #0 with zero
O1 0 1
OExtract
mcl@s#1; {\rm Extract}(#1)
O2 0 0
OmultEX_0
hc; trivial multiplicative loop\zero
V1 1
Vleft_zeroed
a left zeroed
V2 1
Vadd-left-invertible
n add-left-invertible
V3 1
Vadd-right-invertible
n add-right-invertible
V4 1
VLoop-like
a loop-like
V5 1
Vcancelable
a cancelable
V6 1
VmultLoop_0-like
a multiplicative loop with zero-like
#ALGSTR_2
M1 0
MdoubleLoop
ha double loop #0
double loops #0
M2 0
MleftQuasi-Field
ha left quasi-field #0
left quasi-fields #0
M3 0
MrightQuasi-Field
ha right quasi-field #0
right quasi-fields #0
M4 0
MdoublesidedQuasi-Field
ha double sided quasi-field #0
double sided quasi-fields #0
M5 0
M_Skew-Field
ha skew field #0
skew fields #0
M6 0
M_Field
ha field #0
fields #0
#ALGSTR_3
G1 4
GTernaryFieldStr
mc#1#2#3#4; \langle #1, #2, #3, #4\rangle
J1 1
GTernaryFieldStr
hol#1; ternary field structure of #1
L1 0
GTernaryFieldStr
ha ternary field structure #0
ternary field structures #0
M1 0
MTernary-Field
ha ternary field #0
ternary fields #0
O1 0 3
OTern
mcl@s#1#2#3; \mathop{\rm T}(#1,#2,#3)
O2 0 0
Oternaryreal
mow; \mathop{{\rm T}_{\mathbb R}}
O3 0 0
OTernaryFieldEx
mow; \mathop{{\mathbb R}_{\rm t}}
O4 0 3
Otern
mcl@s#1#2#3; \mathop{{\rm T}^e}(#1,#2,#3)
U1 1
UTernOp
hosl#1; tern operation of #1
tern operation
V1 1
VTernary-Field-like
a ternary field-like
#ALGSTR_4
M1 1
MRelators
ha relators #0 of #1
relators #0 of #1
M2 1
MmultSubmagma
ha submagma #0 of #1
submagmas #0 of #1
O1 0 2
OIFXFinSequence
hol; 0-sequence$\mathop{_{#2}}(#1)$
O2 0 1
OClassOp
mo@0; \mathop{\circ_{#1}} 
O3 0 1
Oequ_rel
hol; equivalence relation of #1
O4 0 1
Oequ_kernel
hol; equivalence kernel of #1
O5 0 1
Othe_mult_induced_by
hol; multiplication induced by #1
O6 0 1
Othe_submagma_generated_by
hol; submagma generated by #1
O7 0 1
Ofree_magma_seq
hol; free magma sequence of #1
O8 0 1
Ofree_magma
mol#1; \mathop{\rm M}(#1)
O8 0 2
Ofree_magma
mol#1#2; \mathop{\rm M_{#2}}(#1)
O9 0 1
Ofree_magma_carrier
hol; carrier of free magma on #1
O10 0 1
Ofree_magma_mult
hol; multiplication of free magma on #1
O11 0 1
Olength
mol; \mathop{\rm length} #1
O12 0 2
Ocanon_image
hol#1#2; $#2$-canonical image of #1
O13 0 1
Ofree_magmaF
mol#1; \mathop{\bf M}(#1)
R1 1 1
Rextends
hy #1 extends #2
#1 not extends #2
#ALG_1
M1 1
MCongruence
ha congruence #0 of #1
congruences #0 of #1
O1 0 1
OExtendRel
moq; #1^\hash
O2 0 2
OQuotOp
mow#2; #1_{/#2}
O3 0 2
OQuotOpSeq
mow#1#2; \mathop{\rm Opers}(#1)_{/#2}
O4 0 2
OQuotUnivAlg
mow#2; #1_{/#2}
O5 0 2
ONat_Hom
hol; natural homomorphism of #1 w.r.t. #2
O6 0 1
OCng
mcl#1; \mathop{\rm Cng}(#1)
O7 0 1
OHomQuot
mob#1; \overline{#1}
R1 1 1
Ris_representatives_FS
i a finite sequence of representatives of #2
not a finite sequence of representatives of #2
#ALI2
M1 1
Mcontraction
ha contraction #0 of #1
contractions #0 of #1
#ALTCAT_1
G1 2
GAltGraph
mc#1#2; \langle #1,#2 \rangle
G2 3
GAltCatStr
mc#1#2#3; \langle #1,#2,#3 \rangle
J1 1
GAltGraph
hol#1; graph of #1
J2 1
GAltCatStr
hol#1; category structure of #1
K1 2 L1 vALTCAT_1
K<^
L^>
mo; \langle #1,#2 \rangle
K2 1 L2 vALTCAT_1
K{|
L|}
mo; \{\!| #1 |\!\}
K2 2 L2 vALTCAT_1
K{|
L|}
mo; \{\!| #1,#2 |\!\}
L1 0
GAltGraph
ha graph #0
graphs #0
L2 0
GAltCatStr
ha category structure #0
category structures #0
M1 1
Mobject
hn object #0 of #1
objects #0 of #1
M2 1
MBinComp
ha binary composition #0 of #1
binary compositions #0 of #1
M3 0
Mcategory
ha category #0
categories #0
M4 0
Mdiscrete_category
ha discrete category #0
discrete categories #0
O1 0 2
OFuncComp
mol#1#2; \mathop{\rm FuncComp}(#1,#2)
O2 0 1
OEnsCat
mow#1; \mathop{\rm Ens}_{#1}
O3 0 1
Oidm
mow#1; \mathop{\rm id}_{#1}
O4 0 1
ODiscrCat
mol#1; \mathop{\rm DiscrCat}(#1)
U1 1
UArrows
hopl#1; arrows of #1
arrows
V1 1
Vwith_right_units
x right units
V2 1
Vwith_left_units
x left units
V3 1
Vcompositional
a compositional
V4 1
Vquasi-functional
a quasi-functional
V5 1
Vsemi-functional
a semi-functional
V6 1
Vpseudo-functional
a pseudo-functional
V7 1
Vwith_units
x units
V8 1
Vquasi-discrete
a quasi-discrete
V9 1
Vpseudo-discrete
a pseudo-discrete
#ALTCAT_2
M1 1
MSubCatStr
ha substructure #0 of #1
substructures #0 of #1
M2 1
Msubcategory
ha subcategory #0 of #1
subcategories #0 of #1
O1 0 1
Othe_hom_sets_of
mow#1; \mathop{\rm HomSets}_{#1}
O2 0 1
Othe_comps_of
mow#1; \mathop{\rm Composition}_{#1}
O3 0 1
OAlter
mol#1; \mathop{\rm Alter}(#1)
O4 0 0
Othe_empty_category
mow; \emptyset_{\it CAT}
O5 0 1
OObCat
moi(1,1); \square{\restriction}#1
R1 1 1
Rcc=
m #1 \mathrel{\dot\subseteq} #2
#1 \dot\nsubseteq #2
V1 1
Vid-inheriting
n id-inheriting
#ALTCAT_3
R1 1 1
Ris_left_inverse_of
i left inverse of #2
not left inverse of #2
R2 1 1
Ris_right_inverse_of
i right inverse of #2
not right inverse of #2
R3 2 0
Rare_iso
h #1,#2 are iso
#1,#2 are not iso
V1 1
Viso
n iso
V2 1
Vmono
a mono
V3 1
V_zero
a  zero
#ALTCAT_4
O1 0 1
OAllMono
mol#1; \mathop{\rm AllMono} #1
O2 0 1
OAllEpi
mol#1; \mathop{\rm AllEpi} #1
O3 0 1
OAllRetr
mol#1; \mathop{\rm AllRetr} #1
O4 0 1
OAllCoretr
mol#1; \mathop{\rm AllCoretr} #1
O5 0 1
OAllIso
mol#1; \mathop{\rm AllIso} #1
#AMISTD_1
M2 1
Mpre-Macro
ha pre-Macro #0 of #1
pre-Macros #0 of #1
O1 0 2
ONIC
mol#1#2; \mathop{\rm NIC}(#1,#2)
O2 0 1
OJUMP
mol#1; \mathop{\rm JUMP} (#1)
O3 0 2
OSUCC
mol#1#2; \mathop{\rm SUCC}(#1,#2)
O4 0 1
OSTC
mol#1; \mathop{\rm STC} (#1)
O5 0 2
Oil.
mol#1#2; \mathop{\rm il}_{#1} (#2)
O6 0 2
Olocnum
mol#1#2; \mathop{\rm locnum}(#1,#2)
O7 0 2
ONextLoc
mol#1#2; \mathop{\rm NextLoc}(#1,#2)
O8 0 1
OLastLoc
mol#1; \mathop{\rm LastLoc} #1
V1 1
Vjump-only
a jump-only
V2 1
VInsLoc-antisymmetric
n InsLoc-antisymmetric
V3 1
Vreally-closed
a really-closed
V4 1
Vpara-closed
a para-closed
V5 1
Vhalt-ending
a halt-ending
V6 1
Vunique-halt
a unique-halt
#AMISTD_2
O1 0 1
OJumpParts
mol; \mathop{\rm JumpParts} #1
O2 0 1
OAddressParts
mol#1; \mathop{\rm AddressParts} #1
O3 0 1
OStop
mol#1; \mathop{\rm Stop} #1
O4 0 2
OIncAddr
mol#1#2; \mathop{\rm IncAddr}(#1,#2)
O5 0 1
OCutLastLoc
mol#1; \mathop{\rm CutLastLoc} #1
O6 0 2
ORelocated
mol#1#2; \mathop{\rm Relocated}(#1,#2)
V1 1
Vwith_explicit_jumps
x explicit jumps
V3 1
Vins-loc-free
n instruction location free
V4 1
VIC-relocable
n IC-relocable
V5 1
Vrelocable
a relocable
V6 1
VExec-preserving
n Exec-preserving
V7 1
VJ/A-independent
a J/A-independent
#AMISTD_3
O1 0 0
OTrivialInfiniteTree
mol; \mathop{\rm TrivialInfiniteTree}
O2 0 1
OFirstLoc
mol#1; \mathop{\rm FirstLoc}(#1)
O4 0 2
OLocSeq
mol#1#2; \mathop{\rm LocSeq}(#1,#2)
O5 0 1
OExecTree
mol#1; \mathop{\rm ExecTree}(#1)
#AMISTD_5
V1 1
VIC-recognized
n IC-recognized
V2 1
VCurIns-recognized
a CurIns-recognized
V3 1
Vrelocable1
a relocable1
V4 1
Vrelocable2
a relocable2
#AMI_1
G1 6
GAMI-Struct
mc#1#2#3#4#5#6; \langle #1,#2,#3,#4,#5,#6 \rangle
J1 1
GAMI-Struct
hol#1; AMI of #1
L1 1
GAMI-Struct
hn AMI #0 over #1
AMI's #0 over #1
M2 1
MInstruction
hn instruction #0 of #1
instructions #0 of #1
M3 1
MPartState
ha part state #0 of #1
part states #0 of #1
M4 1
MFinPartState
ha finite partial state #0 of #1
finite partial states #0 of #1
M6 1
MProgram
ha program #0 of #1
programs #0 of #1
M7 1
MInsType
hn instruction type #0 of #1
instruction types #0 of #1
O1 0 1
OTrivial-AMI
mo; {\bf AMI}_{\rm t}
O2 0 1
OIC
mow#1; {\bf IC}_{#1}
O3 0 1
OObjectKind
mol@s#1; {\rm ObjectKind}(#1)
O4 0 2
OExec
mol@s#1#2; {\rm Exec}(#1,#2)
O5 0 1
Ohalt
mow#1; {\bf halt}_{#1}
O6 0 2
OCurInstr
mol#1#2; \mathop{\rm CurInstr}(#1,#2)
O7 0 1
OProgramPart
mol#1; \mathop{\rm ProgramPart}(#1)
O8 0 1
OFinPartSt
mol@s#1; {\rm FinPartSt}(#1)
O9 0 1
OData-Locations
mol; \mathop{\rm Data Locations} #1
O10 0 1
OInsCode
mol#1; \mathop{\rm InsCode}(#1)
O11 0 1
OAddressPart
mol#1; \mathop{\rm AddressPart} (#1)
O12 0 1
OJumpPart
mol; \mathop{\rm JumpPart} #1
O13 0 1
OInsCodes
mol; \mathop{\rm InsCodes} #1
O14 0 2
OStart-At
mol#1#2; \mathop{\rm Start At}(#1,#2)
O15 0 1
ODataPart
mol#1; \mathop{\rm DataPart}(#1)
R1 1 1
Rhalts_on
h #1 is halting on #2
#1 is not halting on #2
R4 1 1
Rhalts_at
h #1 halts at #2
#1 does not halt at #2
U1 1
UInstruction-Counter
honl#1; instruction counter of #1
instruction counter
U2 1
UInstructions
hopl#1; instructions of #1
instructions
U3 1
UObject-Kind
hosl#1; object kind of #1
object kind
U4 1
UExecution
hosl#1; execution of #1
execution
V1 1
Vstored program
a stored program
V2 1
VIC-Ins-separated
n IC-Ins-separated
V3 1
Vsteady-programmed
a steady-programmed
V4 1
Vdefinite
a definite
V5 1
Vrealistic
a realistic
V6 1
Vautonomic
n autonomic
V10 1
Vstandard ins
a standard ins
V11 1
Vdata-only
a data-only
V12 1
Vhalt-free
a halt-free
V14 2
V-started
a #1 -started
#AMI_2
M1 0
MSCM-State
ha \SCM-state #0
\SCM-states #0
M1 1
MSCM-State
hn \SCM-state #0 over #1
\SCM-states #0 over #1
O1 0 0
OSCM-Halt
mow; {\rm Halt}_{\rm SCM}
O2 0 0
OSCM-Data-Loc
mow; {\rm Data\hbox{-}Loc}_{\rm SCM}
O3 0 0
OSCM-Memory
mol; \mathop{\rm SCM-Memory}
O4 0 0
OSCM-Instr
mow; {\rm Instr}_{\rm SCM}
O4 0 1
OSCM-Instr
mol#1; {\rm Instr}_{\rm SCM}(#1)
O5 0 0
OSCM-OK
mow; {\rm OK}_{\rm SCM}
O5 0 1
OSCM-OK
mol#1; {\rm OK}_{\rm SCM}(#1)
O6 0 2
OSCM-Chg
mol@s#1#2; {\rm Chg}_{\rm SCM}(#1,#2)
O6 0 3
OSCM-Chg
mol@s#1#2#3; {\rm Chg}_{\rm SCM}(#1,#2,#3)
O7 1 0
Oaddress_1
mor@s; #1 \mathop{\rm address}_1
O8 1 0
Oaddress_2
mor@s; #1 \mathop{\rm address}_2
O9 0 2
Ojump_address
mol#1#2; \mathop{\rm jump\_address}(#1,#2)
O9 1 0
Ojump_address
mor@s; #1 \mathop{\rm address}_{\rm j}
O10 1 0
Ocjump_address
mor@s; #1 \mathop{\rm address}_{\rm j}
O11 1 0
Ocond_address
mor@s; #1 \mathop{\rm address}_{\rm c}
O12 0 2
OSCM-Exec-Res
mol@s#1#2; {\rm Exec\hbox{-}Res}_{\rm SCM}(#1,#2)
O13 0 0
OSCM-Exec
mow; {\rm Exec}_{\rm SCM}
O13 0 1
OSCM-Exec
mol#1; {\rm Exec}_{\rm SCM}(#1)
#AMI_3
M1 0
MData-Location
ha data-location #0
data-locations #0
M1 1
MData-Location
ha Data-Location #0 of #1
Data-Locations #0 of #1
O1 0 0
OSCM
mc; {\bf SCM}
O1 0 1
OSCM
mol#1; {\bf SCM}(#1)
O2 0 2
OAddTo
mol@s#1#2; {\rm AddTo}(#1,#2)
O2 0 3
OAddTo
mol#1#2#3; \mathop{\rm AddTo}(#1,#2,#3)
O2 0 4
OAddTo
mol#1#2#3#4; \mathop{\rm AddTo}(#1,#2,#3,#4)
O3 0 2
OSubFrom
mol@s#1#2; {\rm SubFrom}(#1,#2)
O3 0 4
OSubFrom
mol#1#2#3#4; \mathop{\rm SubFrom}(#1,#2,#3,#4)
O4 0 2
OMultBy
mol@s#1#2; {\rm MultBy}(#1,#2)
O4 0 4
OMultBy
mol#1#2#3#4; \mathop{\rm MultBy}(#1,#2,#3,#4)
O5 0 2
ODivide
mol@s#1#2; {\rm Divide}(#1,#2)
O5 0 4
ODivide
mol#1#2#3#4; \mathop{\rm Divide}(#1,#2,#3,#4)
O6 0 1
Ogoto
mol@s; {\rm goto\ } #1
O6 0 2
Ogoto
mol#1#2; \mathop{\rm goto}(#1,#2)
O7 0 1
OSCM-goto
mol; \mathop{\rm SCM-goto} #1
O8 1 1
O=0_goto
mo#1; {\bf if\ } #1=0 {\bf \ goto\ } #2
O9 1 1
O>0_goto
mo#1; {\bf if\ } #1>0 {\bf \ goto\ } #2
O10 0 1
Odl.
mow#1; {\bf d}_{#1}
O10 0 2
Odl.
mol#1#2; \mathop{\rm dl}_{#1} (#2)
#AMI_4
O1 0 0
OEuclide-Algorithm
hos@a; Euclid's algorithm
O2 0 0
OEuclide-Function
hos@a; Euclid's function
#AMI_7
O1 0 1
OOut_\_Inp
mol; \mathop{\rm IODiff} #1
O2 0 1
OOut_U_Inp
mol; \mathop{\rm IOSum} #1
V1 1
Vwith_non_trivial_Instructions
x non trivial instruction set
V2 1
Vwith_non_trivial_ObjectKinds
x non trivial ObjectKinds
#AMI_WSTD
V1 1
Vweakly_standard
a weakly standard
#ANALMETR
G1 3
GParOrtStr
mc#1#2#3; \langle #1, #2, #3\rangle
J1 1
GParOrtStr
hol#1; metric-affine structure of #1
L1 0
GParOrtStr
ha metric-affine structure #0
metric affine structures #0
M1 0
MOrtAfSp
ha metric affine space #0
metric affine spaces #0
M2 0
MOrtAfPl
ha metric affine plane #0
metric affine planes #0
O1 0 3
OOrthogonality
ho#2#3; orthogonality determined by #2, #3 in #1
O2 0 3
OAMSpace
mcl@s#1#2#3; {\bf AMSp}(#1,#2,#3)
O3 0 1
OAf
hol; affine reduct of #1
R1 0 2
RGen
h #1, #2 span the space
#1, #2 do not span the space
R2 2 2
Rare_Ort_wrt
h #1, #2 are orthogonal w.r.t. #3, #4
#1, #2 are not orthogonal w.r.t. #3, #4
R2 4 2
Rare_Ort_wrt
h #1, #2, #3 and #4 are orthogonal w.r.t. #5, #6
#1, #2, #3 and #4 are not orthogonal w.r.t. #5, #6
U1 1
Uorthogonality
honl#1; orthogonality of #1
orthogonality
V1 1
VOrtAfSp-like
a metric affine space-like
V2 1
VOrtAfPl-like
a metric affine plane-like
#ANALOAF
G1 2
GAffinStruct
mc#1#2; \langle #1, #2\rangle
J1 1
GAffinStruct
hol#1; affine structure of #1
L1 0
GAffinStruct
hn affine structure #0
affine structures #0
M1 0
MOAffinSpace
hn ordered affine space #0
ordered affine spaces #0
M2 0
MOAffinPlane
hn ordered affine plane #0
ordered affine planes #0
O1 0 1
ODirPar
mow/1k#1; {\upharpoonleft\!\upharpoonright}_{#1}
O2 0 1
OOASpace
mol@s; \mathop{\rm OASpace} #1
R1 1 1
R//
m #1 \parallel #2
#1 \nparallel #2
R1 2 1
R//
m #1,#2 \parallel #3
#1,#2 \nparallel #3
R1 2 2
R//
m #1,#2 \upupharpoons #3, #4
#1,#2 \nupupharpoons #3, #4
U1 1
UCONGR
hosl#1; congruence of #1
congruence
V1 1
VOAffinSpace-like
n ordered affine space-like
V2 1
V2-dimensional
a 2-dimensional
#ANALORT
O1 0 3
OOrtm
ml@s#1#2#3; \rho^{\rm M}_{#1,#2}(#3)
O2 0 3
OOrte
ml@s#1#2#3; \rho^{\rm E}_{#1,#2}(#3)
O3 0 3
OCORTE
ho; Euclidean oriented orthogonality defined over #1,#2,#3
O4 0 3
OCORTM
ho; Minkowskian oriented orthogonality defined over #1,#2,#3
O5 0 3
OCESpace
mol@s#1#2#3; \mathop{\rm CESpace}(#1,#2,#3)
O6 0 3
OCMSpace
mol@s#1#2#3; \mathop{\rm CMSpace}(#1,#2,#3)
R1 4 2
Rare_COrte_wrt
h the segments #1, #2 and #3, #4 are E-coherently orthogonal in the basis #5, #6
the segments #1, #2 and #3, #4 are not E-coherently orthogonal in the basis #5, #6
R2 4 2
Rare_COrtm_wrt
h the segments #1, #2 and #3, #4 are M-coherently orthogonal in the basis #5, #6
the segments #1, #2 and #3, #4 are not M-coherently orthogonal in the basis #5, #6
#ANPROJ_1
O1 0 1
OProportionality_as_EqRel_of
hol; proportionality in #1
O2 0 1
ODir
hol; direction of #1
O3 0 1
OProjectivePoints
hol; \projectpoint #1
O4 0 1
OProjectiveCollinearity
hol; \projectcoll #1
O5 0 1
OProjectiveSpace
hol; projective space over #1
R1 0 2
Rare_Prop
h #1 and #2 are proportional
#1 and #2 are not proportional
R2 3 0
Rare_LinDep
h #1, #2 and #3 are lineary dependent
#1, #2 and #3 are not lineary dependent
#ANPROJ_2
M1 0
MCollProjectiveSpace
ha projective space #0 defined in terms of collinearity
projective spaces #0 defined in terms of collinearity
M2 0
MCollProjectivePlane
ha projective plane #0 defined in terms of collinearity
projective planes #0 defined in terms of collinearity
R1 3 0
Rare_Prop_Vect
h #1, #2 and #3 are proper vectors
#1, #2 and #3 are not proper vectors
R2 6 0
Rlie_on_a_triangle
h #1, #2, #3, #4, #5, and #6 lie on a triangle
#1, #2, #3, #4, #5, and #6 do not lie on a triangle
R3 7 0
Rare_perspective
h #1, #2, #3, #4, #5, #6, and #7 are perspective
#1, #2, #3, #4, #5, #6, and #7 are not perspective
R4 7 0
Rlie_on_an_angle
h #1, #2, #3, #4, #5, #6, and #7 lie on an angle
h #1, #2, #3, #4, #5, #6, and #7 do not lie on an angle
R5 7 0
Rare_half_mutually_not_Prop
h #1, #2, #3, #4, #5, #6, #7 are half-mutually not proportional
#1, #2, #3, #4, #5, #6, #7 are not half-mutually not proportional
V1 1
VVebleian
a Vebleian
V2 1
Vat_least_3rank
n at least 3 rank
V3 1
Vat_most-3-dimensional
n at most 3 dimensional
#AOFA_000
M1 0
MpreIfWhileAlgebra
ha pre-if-while algebra #0
pre-if-while algebras #0
M2 1
MAlgorithm
hn algorithm #0 of #1
algorithms #0 of #1
M3 0
MIfWhileAlgebra
hn if-while algebra #0
if-while algebras #0
M4 3
MExecutionFunction
hn execution function #0 of #1 over #2 and #3
execution functions #0 of #1 over #2 and #3
O1 1 1
Oorbit
moi#2; #1{\rm\hbox{-}orbit}(#2)
O2 0 1
OGenerators
mol; \mathop{\rm Generators} #1
O3 0 1
OEmptyIns
mow{}#1; \mathop{\rm EmptyIns}_{#1}
O4 1 1
O\;
moi; #1;#2
O5 0 3
Oif-then-else
mol#1#2; \mathop{\rm if} #1 \mathbin{\rm then} #2 \mathbin{\rm else} #3
O6 0 2
Oif-then
mol#1; \mathop{\rm if} #1 \mathbin{\rm then} #2
O7 0 2
Owhile
mol#1; \mathop{\rm while} #1 \mathbin{\rm do} #2
O8 0 4
Ofor-do
mol#1#2#3; \mathop{\rm for} #1 \mathbin{\rm until} #2 \mathbin{\rm step} #3 \mathbin{\rm do} #4
O9 0 1
OElementaryInstructions
mow{}#1; \mathop{\rm ElementaryInstructions}_{#1}
O10 0 0
OECIW-signature
mol; \mathop{\rm ECIW\hbox{-}signature}
O11 0 3
Oiteration-degree
mol#1#2#3; \mathop{\rm termination\hbox{-}degree}(#1,#2,#3)
O12 0 4
OTerminatingPrograms
mol#1#2#3#4; \mathop{\rm TerminatingPrograms}(#1,#2,#3,#4)
R1 1 1
Rnin
mn #1 \not\in #2
#1 \in #2
R2 1 1
Rcomplies_with_if_wrt
hy #1 complies with {\bf if} w.r.t. #2
#1 does not comply with {\bf if} w.r.t. #2
R3 1 1
Rcomplies_with_while_wrt
hy #1 complies with {\bf while} w.r.t. #2
#1 does not complies with {\bf while} w.r.t. #2
R4 1 2
Riteration_terminates_for
hy iteration of #1 started in #2 terminates w.r.t. #3
iteration of #1 started in #2 does not terminate w.r.t. #3
R5 1 1
Ris_terminating_wrt
i terminating w.r.t. #2
not terminating w.r.t. #2
R5 1 2
Ris_terminating_wrt
i terminating w.r.t. #2 and #3
not terminating w.r.t. #2 and #3
R6 1 2
Ris_invariant_wrt
i invariant w.r.t. #2 and #3
not invariant w.r.t. #2 and #3
V1 1
Vwith_empty-instruction
x empty-instruction
V2 1
Vwith_catenation
x catenation
V3 1
Vwith_if-instruction
x if-instruction
V4 1
Vwith_while-instruction
x while-instruction
V5 1
VECIW-strict
n E.C.I.W.-strict
V6 1
Vcomplying_with_empty-instruction
a complying-with-empty-instruction
V7 1
Vcomplying_with_catenation
a complying-with-catenation
V8 1
Vabsolutely-terminating
n absolutely-terminating
#AOFA_I00
M1 1
MEnumeration
hn enumeration #0 of #1
enumerations #0 of #1
M2 1
MDenumeration
ha denumeration #0 of #1
denumerations #0 of #1
M3 1
MINT-Variable
ha $\mathbb Z$-variable #0 of #1
$\mathbb Z$-variables #0 of #1
M3 2
MINT-Variable
ha $\mathbb Z$-variable #0 of #1 w.r.t. #2
$\mathbb Z$-variables #0 of #1 w.r.t. #2
M4 1
MINT-Expression
ha $\mathbb Z$-expression #0 of #1
$\mathbb Z$-expressions #0 of #1
M4 2
MINT-Expression
ha $\mathbb Z$-expression #0 of #1 w.r.t. #2
$\mathbb Z$-expressions #0 of #1 w.r.t. #2
M5 1
MINT-Array
ha $\mathbb Z$-array #0 of #1
$\mathbb Z$-arrays #0 of #1
M6 0
MINT-Exec
ha $\mathbb Z$-execution #0
$\mathbb Z$-executions #0
M6 1
MINT-Exec
ha $\mathbb Z$-execution #0 with #1
$\mathbb Z$-executions #0 with #1
M6 2
MINT-Exec
ha $\mathbb Z$-execution #0 with #1 over #2
$\mathbb Z$-executions #0 with #1 over #2
O1 0 2
Oleq
mol#1#2; \mathop{\rm leq}(#1,#2)
O1 1 1
Oleq
moi; #1 \mathop{\rm leq} #2
O2 0 2
Ogt
mol#1#2; \mathop{\rm gt}(#1,#2)
O2 1 1
Ogt
moi; #1 \mathop{\rm gt} #2
O3 0 2
Oeq
mol#1#2; \mathop{\rm eq}(#1,#2)
O3 1 1
Oeq
moi; #1 \mathop{\rm eq} #2
O4 0 0
OINT-ElemIns
mol; \mathop{\rm{\mathbb Z}\hbox{-}ElemIns}
O4 0 1
OINT-ElemIns
mol; \mathop{\rm{\mathbb Z}\hbox{-}ElemIns} #1
O5 1 1
O+=
moi@s; #1{\verb|+=|\,} #2
O6 1 1
O*=
moi@s; #1{\verb|*=|\,}#2
O7 0 2
Oswap
mol#1#2; \mathop{\rm swap}(#1,#2)
O7 0 3
Oswap
mol#1#2#3; \mathop{\rm swap}(#1,#2,#3)
O8 1 1
O%=
moi@s; #1{\verb|%=|\,} #2
O9 1 1
O/=
moi@s; #1{\verb|/=|\,} #2
O10 1 0
Ois_odd
Hor; #1 is odd
O11 1 0
Ois_even
Hor; #1 is even
O12 1 1
Ogeq
moi; #1 \mathop{\rm geq} #2
O13 1 1
Olt
moi; #1 \mathop{\rm lt} #2
R1 1 3
Ris_assignment_wrt
i an assignment w.r.t. #2, #3, and #4
not an assignment w.r.t. #2, #3, and #4
R2 2 1
Rform_assignment_wrt
h #1 and #2 form an assignment w.r.t. #3
#1 and #2 does not form an assignment w.r.t. #3
#ARMSTRNG
G1 3
GDB-Rel
mc#1#2#3; \langle #1,#2,#3 \rangle
J1 1
GDB-Rel
hol#1; DB-relationship of #1
L1 0
GDB-Rel
ha DB-relationship #0
DB-relationships #0
M1 1
MSubset-Relation
ha relation #0 on subsets of #1
relations #0 on subsets of #1
M2 1
MDependency-set
ha dependency set #0 of #1
dependency sets #0 of #1
M3 1
MDependency
ha dependency #0 of #1
dependencies #0 of #1
M4 1
MFull-family
ha Full family #0 of #1
Full families #0 of #1
O1 1 1
OMaximal_in
moi#1#2; \mathop{{\rm Maximals}_{#1}} (#2)
O2 0 1
O/\-IRR
mol#1; \cap{\rm\hbox{-}Irreducibles} (#1)
O3 0 1
ODependencies
mol#1; \mathop{\rm dependencies} (#1)
O4 0 1
ODependency-str
mol#1; \mathop{\rm dependency\hbox{-}structure} (#1)
O5 0 1
ODependencies-Order
mol#1; \mathop{\rm Dependencies\hbox{-}Order} #1
O6 0 1
OMaximal_wrt
mol#1; \mathop{\rm Maximals} (#1)
O7 0 1
Osaturated-subsets
mol#1; \mathop{\rm saturated\hbox{-}subsets} (#1)
O8 0 1
Oclosed_attribute_subset
mol#1; \mathop{\rm closed\hbox{-}attribute\hbox{-}subset} (#1)
O9 1 1
Odeps_encl_by
mol#1#2; (#2)\hbox{-enclosed in\ } #1
O10 0 1
Oenclosure_of
mol#1; (#1)\hbox{-enclosure}
O11 0 1
ODependency-closure
mol#1; \mathop{\rm dependency\hbox{-}closure} (#1)
O12 0 1
Ocandidate-keys
mol#1; \mathop{\rm candidate\hbox{-}keys} (#1)
O13 0 1
Ocharact_set
mol#1; \mathop{\rm characteristic} (#1)
R1 1 1
Ris_/\-irreducible_in
i $\cap$-irreducible in #2
not $\cap$-irreducible in #2
R2 1 1
Ris_/\-reducible_in
i $\cap$-reducible in #2
not $\cap$-reducible in #2
R3 1 2
R>|>
m #1 \rightarrow_{#3} #2
#1 \not\rightarrow_{#3} #2
R4 2 1
Rholds_in
h $(#1,#2)$ holds in #3
$(#1,#2)$ does not hold in #3
R5 1 1
Ris_at_least_as_informative_as
i at least as informative as #2
not at least as informative as #2
R6 1 2
R^|^
m #1 \nearrow_{#3} #2
#1 \not\nearrow_{#3} #2
R7 1 1
Ris_generator-set_of
i generator set of #2
not generator set of #2
R8 1 1
Ris_p_i_w_ncv_of
i prime implicant of #2 with no complemented variables
not prime implicant of #2 with no complemented variables
U1 1
UAttributes
hopl#1; attributes of #1
attributes
U2 1
UDomains
hopl#1; domains of #1
domains
U3 1
URelationship
hosl#1; relationship of #1
relationship
V1 1
V(B1)
a (B1)
V2 1
V(B2)
a (B2)
V3 1
V(F2)
a (F2)
V4 1
V(DC1)
a (DC1)
V5 1
V(F1)
a (F1)
V6 1
V(DC2)
a (DC2)
V7 1
V(F3)
a (F3)
V8 1
V(F4)
a (F4)
V9 1
Vfull_family
a full family
V10 1
V(DC3)
a (DC3)
V11 1
V(M1)
a (M1)
V12 1
V(M2)
a (M2)
V13 1
V(M3)
a (M3)
V14 1
V(C1)
a (C1)
V15 1
Vwithout_proper_subsets
a without proper subsets
V16 1
V(C2)
a (C2)
V17 1
V(DC4)
a (DC4)
V18 1
V(DC5)
a (DC5)
V19 1
V(DC6)
a (DC6)
#ARROW
O1 0 1
OLinPreorders
mol; \mathop{\rm LinPreorders} #1
O2 0 1
OLinOrders
mol; \mathop{\rm LinOrders} #1
R1 1 2
R<=_
m #1 \leq_{#2} #3
#1 \not\leq_{#2} #3
R2 1 2
R>=_
m #1 \geq_{#2} #3
#1 \not\geq_{#2} #3
R3 1 2
R<_
m #1 <_{#2} #3
#1 \not<_{#2} #3
R4 1 2
R>_
m #1 >_{#2} #3
#1 \not>_{#2} #3
#ARYTM_0
K1 2 L1 vARYTM_0
K[*
L*]
moi@a/2r@m; #1+#2i
K1 4 L1 vARYTM_0
K[*
L*]
mc#1#2#3#4; \langle #1,#2,#3,#4\rangle_{\mathbb H}
O1 0 1
Oopp
mok@s; {}^{\rm op}#1
O1 1 0
Oopp
moq; {#1^{\rm op}}
O2 0 1
Oinv
mol; \mathop{\rm inv} #1
#ARYTM_1
O1 1 1
O-'
moi@a; #1 \mathbin{{-}'} #2
O1 1 2
O-'
moi#2#3; #1 \mathbin{{-}'}(#2,#3)
O2 0 1
O-
mol@4; {\mathopen{-} #1}
O2 0 2
O-
mol(1)@s#2; (-1)^{{\rm sgn}(#2)}#1
O2 1 0
O-
moq; #1^-
O2 1 1
O-
moi@a; #1-#2
#ARYTM_2
O1 0 0
ODEDEKIND_CUTS
mol; \mathop{\rm DedekindCuts}
O2 0 0
OREAL+
mol; {\mathbb R_+}
O3 0 1
ODEDEKIND_CUT
mol; \mathop{\rm DedekindCut}\,#1
O4 0 1
OGLUED
mol; \mathop{\rm Glued}\,#1
#ARYTM_3
O1 0 0
Oone
mc; {\bf 1}
O2 0 2
Olcm
mcl@s#1#2; \mathop{\rm lcm}(#1,#2)
O2 1 1
Olcm
mcl@s#1#2; \mathop{\rm lcm}(#1,#2)
O3 1 1
Ohcf
mcl@s#1#2; \mathop{\rm gcd}(#1,#2)
O4 0 2
ORED
mol#1#2; \mathop{\rm RED}(#1,#2)
O5 0 0
ORAT+
mol; {\mathbb Q_+}
O6 0 1
Onumerator
mol@s; \mathop{\rm num} #1
O7 0 1
Odenominator
mol@s; \mathop{\rm den} #1
O8 0 1
O/
mo{kmqw}@s#1; {1\over #1}
O8 1 1
O/
mo{kmqw}@s#1#2; {{#1} \over {#2}}
O8 1 2
O/
mor(1)@s#2#3; #1({{#2} \over {#3}})
O9 0 2
Oquotient
mol#1#2; \mathop{\rm quotient}(#1,#2)
O10 0 2
O+
mol#1#2; \mathopen{+} (#1,#2)
O10 0 3
O+
mol#1#2#3; +(#1,#2,#3)
O10 1 0
O+
mor; {#1}^+
O10 1 1
O+
moi@a; #1+#2
O10 1 2
O+
moi#2#3; #1 +(#2,#3)
O11 0 1
O*'
mok@s; {}^\ast #1
O11 0 2
O*'
mol@s#1#2; \ast(#1,#2)
O11 1 0
O*'
mct#1; \overline{\kern1pt #1 \kern1pt}
O11 1 1
O*'
moi@m; #1 \ast #2
R1 2 0
Rare_relative_prime
h #1 and #2 are relative prime
#1 and #2 are not relative prime
R2 1 1
Rdivides
m #1 \mid #2
#1 \nmid #2
R3 1 1
R<='
m #1 \leq #2
#1 \nleq #2
R4 1 1
R<
m #1 < #2
#1 \not< #2
R4 1 2
R<
m #1 <_{#3} #2
#1 \not<_{#3} #2
#ASYMPT_0
O1 0 1
OBig_Oh
mol#1; O(#1)
O1 0 2
OBig_Oh
mol#1#2; O(#1|#2)
O2 0 1
OBig_Omega
mol#1; \Omega(#1)
O2 0 2
OBig_Omega
mol#1#2; \Omega(#1|#2)
O3 0 1
OBig_Theta
mol#1; \Theta(#1)
O3 0 2
OBig_Theta
mol#1#2; \Theta(#1|#2)
O4 1 1
Otaken_every
mow#2; {#1}_{#2}
R1 1 1
Rmajorizes
h #1 majorizes #2
#1 does not majorize #2
R2 1 1
Ris_smooth_wrt
i smooth w.r.t. #2
not smooth w.r.t. #2
V1 1
Vlogbase
a logbase
V2 1
Veventually-nonnegative
n eventually-nonnegative
V3 1
Veventually-positive
n eventually-positive
V4 1
Veventually-nonzero
n eventually-nonzero
V5 1
Veventually-nondecreasing
n eventually-nondecreasing
V6 1
Vsmooth
a smooth
#ASYMPT_1
O1 0 3
Oseq_a^
mol#1#2#3; \{{#1}^{#2\cdot n+#3)}\}_{n\in\mathbb N}
O2 0 0
Oseq_logn
mow; \{\log_2 n\}_{n\in\mathbb N}
O3 0 1
Oseq_n^
mow1; \{n^{#1}\}_{n\in\mathbb N}
O4 0 1
Oseq_const
mol#1; \{#1\}_{n\in\mathbb N}
O5 0 1
Oseq_n!
mow#1; \{(n+#1)!\}_{n\in\mathbb N}
O6 0 0
OPOWEROF2SET
mol; \{2^n: n\in\mathbb N\}
O7 0 1
OStep1
mor#1; #1\hbox{!`}
#AUTALG_1
M1 2
MMSFunctionSet
ha set #0 of many sorted functions from  #1 into #2
sets #0 of many sorted functions from  #1 into #2
O1 0 1
OUAAut
mol#1; \mathop{\rm UAAut}(#1)
O2 0 1
OUAAutComp
mol#1; \mathop{\rm UAAutComp}(#1)
O3 0 1
OUAAutGroup
mol#1; \mathop{\rm UAAutGroup}(#1)
O4 0 1
OMSAAut
mol#1; \mathop{\rm MSAAut}(#1)
O5 0 1
OMSAAutComp
mol#1; \mathop{\rm MSAAutComp}(#1)
O6 0 1
OMSAAutGroup
mol#1; \mathop{\rm MSAAutGroup}(#1)
#AUTGROUP
O1 0 1
OAut
mol#1; \mathop{\rm Aut}(#1)
O2 0 1
OAutComp
mol#1; \mathop{\rm AutComp}(#1)
O3 0 1
OAutGroup
mol#1; \mathop{\rm AutGroup}(#1)
O4 0 1
OInnAut
mol#1; \mathop{\rm InnAut}(#1)
O5 0 1
OInnAutGroup
mol#1; \mathop{\rm InnAutGroup}(#1)
O6 0 1
OConjugate
mol#1; \mathop{\rm Conjugate}(#1)
#BAGORDER
M1 1
MTermOrder
ha term order #0 of #1
term orders #0 of #1
O1 0 1
OTotDegree
mol; \mathop{\rm TotDegree} #1
O2 0 1
OLexOrder
mol#1; \mathop{\rm LexOrder} #1
O3 0 1
OInvLexOrder
mol#1; \mathop{\rm InvLexOrder} #1
O4 0 1
OGraded
mol#1; \mathop{\rm Graded} #1
O5 0 1
OGrLexOrder
mol#1; \mathop{\rm GrLexOrder} #1
O6 0 1
OGrInvLexOrder
mol#1; \mathop{\rm GrInvLexOrder} #1
O7 0 4
OBlockOrder
mol#1#2#3#4; \mathop{\rm BlockOrder}(#1,#2,#3,#4)
O8 0 1
ONaivelyOrderedBags
mol#1; \mathop{\rm NaivelyOrderedBags} #1
O9 0 1
OPosetMin
mol#1; \mathop{\rm PosetMin} #1
O10 0 1
OPosetMax
mol#1; \mathop{\rm PosetMax} #1
O11 0 1
OFinOrd-Approx
mol#1; \mathop{\rm FinOrd\hbox{-}Approx} #1
O12 0 1
OFinOrd
mol#1; \mathop{\rm FinOrd} #1
O13 0 1
OFinPoset
mol#1; \mathop{\rm FinPoset} #1
O14 0 2
OMinElement
mol#1#2; \mathop{\rm MinElement}(#1,#2)
V1 1
Vadmissible
n admissible
#BCIALG_1
G1 2
GBCIStr
mc#1#2; \langle #1,#2 \rangle
G2 3
GBCIStr_0
mc#1#2#3; \langle #1,#2,#3 \rangle
J1 1
GBCIStr
hol#1; BCI structure of #1
J2 1
GBCIStr_0
hol#1; BCI structure with 0 of #1
L1 0
GBCIStr
ha BCI structure #0
BCI structures #0
L2 0
GBCIStr_0
ha BCI structure #0 with 0
BCI structures #0 with 0
M1 0
MBCI-algebra
ha BCI-algebra #0
BCI-algebras #0
M1 4
MBCI-algebra
ha BCI-algebra #0 commutating with #1, #2 and #3, #4
BCI-algebras #0 commutating with #1, #2 and #3, #4
M2 0
MBCK-algebra
ha BCK-algebra #0
BCK-algebras #0
M2 4
MBCK-algebra
ha BCK-algebra #0 commutating with #1, #2 and #3, #4
BCK-algebras #0 commutating with #1, #2 and #3, #4
O1 0 0
OBCI-EXAMPLE
mol; \mathop{\rm BCI\hbox{-}EXAMPLE}
O2 0 1
OBCK-part
mol; \mathop{\rm BCK\hbox{-}part} #1
O3 0 1
OAtomSet
mol; \mathop{\rm AtomSet} #1
O4 0 1
OBranchV
mol; \mathop{\rm BranchV} #1
U1 1
UInternalDiff
hosl#1; internal diff of #1
internal diff
V1 1
Vbeing_B
b B
V2 1
Vbeing_C
b C
V3 1
Vbeing_I
b I
V4 1
Vbeing_K
b K
V5 1
Vbeing_BCI-4
b BCI-4
V6 1
Vbeing_BCK-5
b BCK-5
V7 1
Vgenerated_by_atom
a generated by atom
V8 1
Vquasi-associative
a quasi-associative
V9 1
Vpositive-implicative
a positive-implicative
V10 1
Vweakly-positive-implicative
a weakly-positive-implicative
V11 1
Vweakly-implicative
a weakly-implicative
V12 1
Vp-Semisimple
a {\it p}-semisimple
V13 1
Valternative
n alternative
#BCIALG_2
M1 1
ML-congruence
hn L-congruence #0 of #1
L-congruences #0 of #1
M2 1
MR-congruence
hn R-congruence #0 of #1
R-congruences #0 of #1
M3 2
MI-congruence
hn I-congruence #0 of #1 by #2
I-congruences #0 of #1 by #2
O1 0 1
OIConSet
mol; \mathop{\rm IConSet} #1
O2 0 1
OConSet
mol; \mathop{\rm ConSet} #1
O3 0 1
OLConSet
mol; \mathop{\rm LConSet} #1
O4 0 1
ORConSet
mol; \mathop{\rm RConSet} #1
O5 0 1
OEqClaOp
mol; \mathop{\rm EqClaOp} #1
O6 0 1
OzeroEqC
mol; \mathop{\rm zeroEqC} #1
V1 1
Vleast
a least
V2 1
Vgreatest
a greatest
V3 1
Vnilpotent
a nilpotent
#BCIALG_3
M1 1
MCommutative-Ideal
ha commutative-ideal #0 of #1
commutative-ideals #0 of #1
V1 1
Vbeing_greatest
b greatest
V2 1
Vbeing_positive
b positive
V3 1
VBCI-commutative
a BCI-commutative
V4 1
VBCI-weakly-commutative
a BCI-weakly-commutative
V5 1
Vinvolutory
n involutory
V6 1
Vbeing_Iseki
n Iseki
V7 1
VIseki_extension
n Iseki-extension
V8 1
VBCK-positive-implicative
a BCK-positive-implicative
V9 1
VBCK-implicative
a BCK-implicative
#BCIALG_4
G1 4
GBCIStr_1
mc#1#2#3#4; \langle #1,#2,#3,#4 \rangle
J1 1
GBCIStr_1
hol#1; BCI structure with complements of #1
L1 0
GBCIStr_1
ha BCI structure #0 with complements
BCI stuctures #0 with complements
M1 0
MBCI-Algebra_with_Condition(S)
ha BCI-algebra #0 with condition (S)
BCI-algebras #0 with condition (S)
M2 0
MBCK-Algebra_with_Condition(S)
ha BCK-algebra #0 with condition (S)
BCK-algebra #0 with condition (S)
M3 0
Msemi-Brouwerian-algebra
ha semi-Brouwerian algebra #0
semi-Brouwerian algebras #0
O1 0 0
OBCI_S-EXAMPLE
hol; BCI S-example
O2 0 2
OCondition_S
mol#1#2; \mathop{\rm ConditionS}(#1,#2)
O3 0 1
OAdjoint_pGroup
hol; adjoint p-group of #1
O4 0 1
OProduct_S
mol#1; \mathop{\rm ProductS}(#1)
O5 0 1
OInitial_section
hol; initial section of #1
U1 1
UExternalDiff
honl#1; external complement of #1
external complement
V1 1
Vwith_condition_S
s condition (S)
V2 1
Vbeing_SB-1
b SB-1
V3 1
Vbeing_SB-2
b SB-2
V4 1
Vbeing_SB-4
b SB-4
#BCIALG_5
O1 0 1
Op-Semisimple-part
mol; \mathop{p\rm\hbox{-}Semisimple\hbox{-}part} #1
V1 1
Vquasi-commutative
a quasi-commutative
#BCIALG_6
M1 2
MBCI-homomorphism
ha BCI-homomorphism #0 from #1 to #2
BCI-homomorphisms #0 from #1 to #2
O1 0 1
OBCI-power
mol; \mathop{\rm BCI\hbox{-}power} #1
O2 0 2
OHKOp
mol#1#2; \mathop{\rm HKOp}(#1,#2)
O3 0 2
OzeroHK
mol#1#2; \mathop{\rm zeroHK}(#1,#2)
O4 0 2
OHK
mol#1#2; \mathop{\rm HK}(#1,#2)
V1 1
Vfinite-period
a finite-period
V2 1
Visotonic
n isotonic
#BCIIDEAL
M1 1
Massociative-ideal
hn associative-ideal #0 of #1
associative-ideals #0 of #1
M2 1
Mp-ideal
ha $p$-ideal #0 of #1
$p$-ideals #0 of #1
M3 1
Mimplicative-ideal
hn implicative-ideal #0 of #1
implicative-ideals #0 of #1
M4 1
Mpositive-implicative-ideal
ha positive-implicative-ideal #0 of #1
positive-implicative-ideals #0 of #1
O1 0 1
Oinitial_section
hol; initial section of #1
#BHSP_1
G1 5
GUNITSTR
mc#1#2#3#4#5; \langle #1, #2, #3, #4, #5\rangle
J1 1
GUNITSTR
hol#1; unitary space structure of #1
L1 0
GUNITSTR
ha unitary space structure #0
unitary space structures #0
M1 0
MRealUnitarySpace
ha real unitary space #0
real unitary spaces #0
U1 1
Uscalar
hosl#1; scalar product of #1
scalar product
V1 1
VRealUnitarySpace-like
a real unitary space-like
#BHSP_3
R1 1 1
Ris_compared_to
i compared to #2
not compared to #2
V1 1
VCauchy
a Cauchy
#BHSP_5
M1 1
MOrthogonalFamily
hn orthogonal family #0 of #1
orthogonal families #0 of #1
M2 1
MOrthonormalFamily
hn orthonormal family #0 of #1
orthonormal families #0 of #1
O1 0 2
Osetop_SUM
mol#1#2; \mathop{\rm SetopSum}(#1,#2)
O2 0 2
OFunc_Seq
mol#1#2; \mathop{\rm FuncSeq}(#1,#2)
O3 0 5
Osetopfunc
mol#1#2#3#4#5; \mathop{\rm setopfunc}(#1,#2,#3,#4,#5)
O4 0 3
Osetop_xPre_PROD
mol#1#2#3; \mathop{\rm SetopPreProd}(#1,#2,#3)
O5 0 3
Osetop_xPROD
mol#1#2#3; \mathop{\rm SetopProd}(#1,#2,#3)
#BHSP_6
O1 0 1
Osetsum
mol#1; \mathop{\rm Setsum}(#1)
O2 0 2
Osum_byfunc
mol#1#2; \mathop{\rm SumByfunc}(#1,#2)
R1 1 1
Ris_summable_set_by
i summable set by #2
not summable set by #2
V1 1
Vsummable_set
a summable\_set
V2 1
Vweakly_summable_set
a weakly summable\_set
#BILINEAR
M1 2
MForm
ha form #0 of #1,#2
forms #0 of #1,#2
M2 2
Mbilinear-Form
ha bilinear form #0 of #1,#2
bilinear forms #0 of #1,#2
O1 0 2
ONulForm
mol#1#2; \mathop{\rm NulForm}(#1,#2)
O2 0 2
OFunctionalFAF
mol@s#2; #1(#2,\cdot)
O3 0 2
OFunctionalSAF
mol@s#2; #1(\cdot,#2)
O4 0 2
OFormFunctional
moq; #1 \otimes #2
O5 0 1
Oleftker
moq; \mathop{\rm leftker} #1
O6 0 1
Orightker
moq; \mathop{\rm rightker} #1
O7 0 1
Odiagker
moq; \mathop{\rm diagker} #1
O8 0 1
OLKer
moq; \mathop{\rm LKer} #1
O9 0 1
ORKer
moq; \mathop{\rm RKer} #1
O10 0 1
OLQForm
mol#1; \mathop{\rm LQForm} (#1)
O11 0 1
ORQForm
mol#1; \mathop{\rm RQForm} (#1)
O12 0 1
OQForm
mol#1; \mathop{\rm QForm} (#1)
V1 1
VadditiveFAF
n additive w.r.t. second argument
V2 1
VadditiveSAF
n additive w.r.t. first argument
V3 1
VhomogeneousFAF
a homogeneous w.r.t. second argument
V4 1
VhomogeneousSAF
a homogeneous w.r.t. first argument
V5 1
Vdegenerated-on-left
a degenerated on left
V6 1
Vdegenerated-on-right
a degenerated on right
#BINARITH
O1 0 2
Ocarry
mol#1#2; \mathop{\rm carry}(#1,#2)
O2 0 1
OBinary
mol#1; \mathop{\rm Binary}(#1)
O3 0 1
OAbsval
mol#1; \mathop{\rm Absval}(#1)
O4 0 2
Oadd_ovfl
mol#1#2; \mathop{\rm add\_ovfl}(#1,#2)
R1 2 0
Rare_summable
h #1 and #2 are summable
#1 and #2 are not summable
#BINARI_2
O1 0 1
OBin1
mol#1; \mathop{\rm Bin1}(#1)
O2 0 1
ONeg2
mol#1; \mathop{\rm Neg2}(#1)
O3 0 1
OIntval
mol#1; \mathop{\rm Intval}(#1)
O4 0 2
OInt_add_ovfl
mol#1#2; \mathop{\rm Int\_add\_ovfl}(#1,#2)
O5 0 2
OInt_add_udfl
mol#1#2; \mathop{\rm Int\_add\_udfl}(#1,#2)
#BINARI_3
O1 1 1
O-BinarySequence
moi@a#2; #1\mathop{\rm\hbox{-}BinarySequence}(#2)
#BINARI_4
O1 0 2
OMajP
mol#1#2; \mathop{\rm MajP}(#1,#2)
O2 0 2
O2sComplement
mol#1#2; \mathop{\rm 2sComplement}(#1,#2)
#BINOM
O1 0 1
ONat-mult-left
mol#1; \mathop{\rm Nat\hbox{-}mult\hbox{-}left} #1
O2 0 1
ONat-mult-right
mol#1; \mathop{\rm Nat\hbox{-}mult\hbox{-}right} #1
#BINOP_1
M1 1
MUnOp
ha unary operation #0 on #1
unary operations #0 on #1
M1 2
MUnOp
ha unary #2-congruent operation #0 on #1
unary #2-congruent operations #0 on #1
M2 1
MBinOp
ha binary operation #0 on #1
binary operations #0 on #1
M2 2
MBinOp
ha binary #2-congruent operation #0 on #1
binary #2-congruent operations #0 on #1
O1 0 1
Othe_unity_wrt
mow/1k#1; \mathop{\bf 1}_{#1}
R1 1 1
Ris_a_left_unity_wrt
i a left unity w.r.t. #2
not a left unity w.r.t. #2
R2 1 1
Ris_a_right_unity_wrt
i a right unity w.r.t. #2
not a right unity w.r.t. #2
R3 1 1
Ris_a_unity_wrt
i a unity w.r.t. #2
not a unity w.r.t. #2
R4 1 1
Ris_left_distributive_wrt
i left distributive w.r.t. #2
not left distributive w.r.t. #2
R5 1 1
Ris_right_distributive_wrt
i right distributive w.r.t. #2
not right distributive w.r.t. #2
R6 1 1
Ris_distributive_wrt
i distributive w.r.t. #2
not distributive w.r.t. #2
V1 1
Vcommutative
a commutative
V2 1
Vassociative
n associative
V3 1
Vidempotent
n idempotent
#BINOP_2
O1 0 0
Ocompcomplex
mow; {-}_{\mathbb C}
O2 0 0
Oinvcomplex
mow;  \mathop{{}^{-1}_{\mathbb C}}
O3 0 0
Oaddcomplex
mow; {+}_{\mathbb C}
O4 0 0
Odiffcomplex
mow; {-}_{\mathbb C}
O5 0 0
Omultcomplex
mow; {\cdot}_{\mathbb C}
O5 1 0
Omultcomplex
mow/1m#1; \mathop{{\cdot}_{\mathbb C}^{#1}}
O6 0 0
Odivcomplex
mow;  \mathop{/_{\mathbb C}}
O7 0 0
Ocompreal
mow; -_{\mathbb R}
O8 0 0
Oinvreal
mow;  \mathop{{}^{-1}_{\mathbb R}}
O9 0 0
Oaddreal
mow; +_{\mathbb R}
O10 0 0
Odiffreal
mow; \mathop{{-}_{\mathbb R}}
O11 0 0
Omultreal
mow; \cdot_{\mathbb R}
O11 1 0
Omultreal
mcr@s/1m#1; \mathop{{\cdot}_{\mathbb R}^{#1}}
O12 0 0
Odivreal
mow;  \mathop{/_{\mathbb R}}
O13 0 0
Ocomprat
mow;  \mathop{{-}_{\mathbb Q}}
O14 0 0
Oinvrat
mo;  \mathop{{}^{-1}_{\mathbb Q}}
O15 0 0
Oaddrat
mow;  \mathop{+_{\mathbb Q}}
O16 0 0
Odiffrat
mow;  \mathop{-_{\mathbb Q}}
O17 0 0
Omultrat
mow;  \mathop{{\cdot}_{\mathbb Q}}
O18 0 0
Odivrat
mow;  \mathop{/_{\mathbb Q}}
O19 0 0
Ocompint
mol; \mathop{\rm compint}
O19 0 1
Ocompint
mol#1; \mathop{\rm compint} #1
O20 0 0
Oaddint
mo; +_{\mathbb Z}
O20 0 1
Oaddint
mow#1; +_{#1}
O21 0 0
Odiffint
mow;  \mathop{-_{\mathbb Z}}
O22 0 0
Omultint
mow; \cdot_{\mathbb Z}
O22 0 1
Omultint
mow#1; \cdot_{{\mathbb Z}_{#1}}
O23 0 0
Oaddnat
mow; {+}_{\mathbb N}
O24 0 0
Omultnat
mow; {\cdot}_{\mathbb N}
#BINTREE1
O1 0 1
Oroot-label
hosl#1; root label of #1
V1 1
Vbinary
a binary
#BINTREE2
O1 0 2
ONumberOnLevel
mol#1#2; \mathop{\rm NumberOnLevel}(#1,#2)
O2 0 2
OFinSeqLevel
mol#1#2; \mathop{\rm FinSeqLevel}(#1,#2)
#BIRKHOFF
O1 1 0
O-hash
moq; #1^\hash
#BOOLMARK
M1 1
MBoolean_marking
ha Boolean marking #0 of #1
Boolean marking #0 of #1
O1 0 1
OBool_marks_of
mol; \mathop{\rm Bool\_marks\_of} #1
O2 0 2
OFiring
mol#1#2; \mathop{\rm Firing}(#1,#2)
R1 1 1
Ris_firable_on
i firable on #2
not firable on #2
R2 1 1
Ris_not_firable_on
in not firable on #2
firable on #2
#BORSUK_1
M1 1
Mu.s.c._decomposition
hn upper semi-continuous decomposition #0 of #1
upper semi-continuous decompositions #0 of #1
M2 1
MDECOMPOSITION
hn upper semi-continuous decomposition #0 into compacta of #1
upper semi-continuous decompositions #0 into compacta of #1
O1 0 1
OBase-Appr
mc#1; \mathop{\rm BaseAppr}(#1)
O2 0 1
OPr1
mol@s; \pi_1\!\cdot #1
O2 0 2
OPr1
mc#1#2; \pi_{1}(#1,#2)
O3 0 1
OPr2
mol@s; \pi_2\!\cdot #1
O3 0 2
OPr2
mc#1#2; \pi_{2}(#1,#2)
O4 0 1
OTrivDecomp
hol; trivial decomposition of #1
O5 0 1
Ospace
hol; decomposition space of #1
O6 0 1
OProj
hol; projection onto #1
O6 0 2
OProj
mol#1#2; \mathop{\rm Proj}(#1,#2)
O7 0 1
OTrivExt
hol; trivial extension of #1
O8 0 0
OI[01]
mc; {\mathbb I}
O9 0 0
O0[01]
mc; 0_{\mathbb I}
O10 0 0
O1[01]
mc; 1_{\mathbb I}
R1 1 1
Ris_a_retract_of
i a retract of #2
not a retract of #2
R2 1 1
Ris_an_SDR_of
i a strong deformation retract of #2
not a strong deformation retract of #2
V1 1
VDECOMPOSITION-like
n upper semi-continuous decomposition-like
V2 1
Vbeing_a_retraction
b a retraction
#BORSUK_2
R1 2 0
Rare_connected
h #1, #2 are connected
#1, #2 are not connected
R2 2 0
Rare_homotopic
h #1,#2 are homotopic
#1,#2 are not homotopic
V1 1
Varcwise_connected
n arcwise connected
V2 1
Vpathwise_connected
a pathwise connected
#BORSUK_4
O1 0 0
OI(01)
mol; I(01)
#BORSUK_5
O1 0 0
OIRRAT
mc; {\mathbb I\mathbb Q}
O1 0 2
OIRRAT
mol#1#2; \rbrack #1,#2\lbrack{}_{\mathbb I\mathbb Q}
#BORSUK_6
M1 2
MHomotopy
ha homotopy #0 between #1 and #2
homotopies #0 between #1 and #2
O1 0 2
ORePar
mol#1#2; \mathop{\rm RePar}(#1,#2)
O2 0 0
O1RP
mol; \mathop{\rm 1^{st}RP}
O3 0 0
O2RP
mol; \mathop{\rm 2^{nd}RP}
O4 0 0
O3RP
mol; \mathop{\rm 3^{rd}RP}
O5 0 0
OLowerLeftUnitTriangle
mol; \mathop{\rm LowerLeftUnitTriangle}
O6 0 0
OIAA
mol; \mathop{\rm IAA}
O7 0 0
OUpperUnitTriangle
mol; \mathop{\rm UpperUnitTriangle}
O8 0 0
OIBB
mol; \mathop{\rm IBB}
O9 0 0
OLowerRightUnitTriangle
mol; \mathop{\rm LowerRightUnitTriangle}
O10 0 0
OICC
mol; \mathop{\rm ICC}
#BROUWER
O1 0 2
ODiffElems
mol#1#2; \mathop{\rm DiffElems}(#1,#2)
O2 0 2
OTdisk
mol#1#2; \mathop{\rm Tdisk}(#1,#2)
O3 0 2
OHC
mol#1#2; \mathop{\rm HC}(#1,#2)
O3 0 4
OHC
mol#1#2#3#4; \mathop{\rm HC}(#1,#2,#3,#4)
O4 0 1
OBR-map
mol; \mathop{\rm BR\hbox{-}map} #1
#BSPACE
O1 0 0
OZ_2
mow; {\mathbf Z}_2
O2 1 1
O\*\
moi; #1 \cdot #2
O3 0 1
Obspace-sum
mow#1; \Sigma_{#1}
O4 0 1
Obspace-scalar-mult
mow#1; \cdot_{#1}
O5 0 1
Obspace
mow#1; B_{#1}
O6 0 1
Osingletons
mow; S_{#1}
V1 1
VSingleton
a singleton
#BVFUNC_1
O1 1 1
O'imp'
moi#1#2; #1 \Rightarrow #2
O2 1 1
O'eqv'
moi#1#2; #1 \Leftrightarrow #2
O3 0 1
OO_el
mol#1; \mathop{\it false}(#1)
O4 0 1
OI_el
mol#1; \mathop{\it true}(#1)
O5 0 1
OB_INF
mol; \mathop{\rm INF} #1
O5 0 2
OB_INF
mol#1#2; \mathop{\rm INF}(#1,#2)
O6 0 1
OB_SUP
mol; \mathop{\rm SUP} #1
O6 0 2
OB_SUP
mol#1#2; \mathop{\rm SUP}(#1,#2)
O7 0 1
OGPart
mol#1; \mathop{\rm GPart} #1
R1 1 1
Ris_dependent_of
h #1 is dependent of #2
#1 is not dependent of #2
#BVFUNC_2
O1 0 2
OCompF
mol#1#2; \mathop{\rm CompF}(#1,#2)
O2 0 2
OAll
mol(2)@s/1k#1; {\forall_{#1}} #2
O2 0 3
OAll
mol(3)@s/1k#1#2; {\forall_{#1,#2}} #3
O2 0 4
OAll
mol(4)@s/1k#1#2#3; {\forall_{#1,#2,#3}} #4
O3 0 2
OEx
mol(2)@s/1k#1; {\exists_{#1}} #2
O3 0 3
OEx
mol(3)@s/1k#1#2; {\exists_{#1,#2}} #3
O3 0 4
OEx
mol(4)@s/1k#1#2#3; {\exists_{#1,#2,#3}} #4
R1 1 1
Ris_upper_min_depend_of
h #1 is upper min depend of #2
#1 is not upper min depend of #2
R2 1 0
Ris_a_coordinate
h #1 is a coordinate
#1 is not a coordinate 
R3 1 2
Ris_independent_of
h #1 is independent of #2,#3
#1 is not independent of #2,#3
V1 1
Vgenerating
a generating
V2 1
Vindependent
n independent
#C0SP1
M1 1
MSubring
ha subring #0 of #1
subrings #0 of #1
O1 0 2
Omult_
mol#1#2; \mathop{\rm mult}(#1,#2)
O2 0 2
OOne_
mol#1#2; \mathop{\rm One}(#1,#2)
O3 0 1
OR_Algebra_of_BoundedFunctions
hol; \mbR-algebra of bounded functions on #1
O4 0 1
OR_Normed_Algebra_of_BoundedFunctions
hol; \mbR-normed algebra of bounded functions on #1
V1 1
Vhaving-inverse
x inverse
V2 1
Vadditively-closed
n additively-closed
V3 1
Vmultiplicatively-closed
a multiplicatively-closed
V4 1
Vadditively-linearly-closed
n additively-linearly-closed
V5 1
Vscalar-mult-cancelable
a scalar-multiplcation-cancelable
#C0SP2
O1 0 1
OContinuousFunctions
mol#1; \mathop{\rm C ( #1 ; \mathbb R) }
O2 0 1
OR_Algebra_of_ContinuousFunctions
mol#1; \mathop{\rm C ( #1 ; \mathbb R)}
O3 0 1
OContinuousFunctionsNorm
mol#1; || \cdot ||_{C(#1 ;\mathbb R )}
O4 0 1
OR_Normed_Algebra_of_ContinuousFunctions
mol#1; \mathop{\rm C ( #1 ; \mathbb R)}
#CALCUL_1
O1 0 1
OAnt
mol#1; \mathop{\rm Ant}(#1)
O2 0 1
OSuc
mol#1; \mathop{\rm Suc}(#1)
O3 0 0
Oset_of_CQC-WFF-seq
hol; set of CQC-WFF-sequences
R1 1 1
Ris_tail_of
iy a tail of #2
not a tail of #2
R2 1 1
Ris_Subsequence_of
iy a subsequence of #2
not a subsequence of #2
R3 2 0
Ris_a_correct_step
hy step #2 in #1 is correct
step #2 in #1 is not correct
R4 1 1
Ris_formal_provable_from
iy formally provable from #2
not formally provable from #2
V1 1
Va_proof
b a formal proof
#CALCUL_2
O1 0 2
Oseq
mol#1#2; \mathop{\rm seq}(#1,#2)
O2 0 1
OPer
mol; \mathop{\rm Per} #1
O2 0 2
OPer
mol#1#2; \mathop{\rm Per}(#1,#2)
O3 0 1
OBegin
mol; \mathop{\rm Begin}(#1)
O4 0 1
OImpl
mol; \mathop{\rm Impl}(#1)
O5 0 2
OIdFinS
mol#1#2; \mathop{\rm IdFinS}(#1,#2)
#CANTOR_1
M1 1
Mprebasis
ha prebasis #0 of #1
prebases #0 of #1
O1 0 1
OUniCl
mol#1; \mathop{\rm UniCl}(#1)
O2 0 1
OFinMeetCl
mol#1; \mathop{\rm FinMeetCl}(#1)
O3 0 0
Othe_Cantor_set
hol; Cantor set
V1 1
Vquasi_basis
a quasi basis
V2 1
Vquasi_prebasis
a quasi-prebasis
#CARDFIN2
O1 0 1
Oderangements
mol; \mathop{\rm derangements} #1
O2 0 1
Oround
mol; \mathop{\rm round} #1
O3 0 0
Oder_seq
hol; der seq
O4 0 2
Onot-one-to-one
mol#1#2; \mathop{\rm not\hbox{-}one\hbox{-}to\hbox{-}one}(#1,#2)
#CARD_1
M1 0
MCardinal
ha cardinal number #0
cardinal numbers #0
O1 0 0
O0
mc; 0
O2 0 1
Ocard
mct#1; \overline{\overline{\kern1pt #1 \kern1pt}}
O3 0 1
Onextcard
moq; {#1}^+
O4 0 1
Oalef
mow/1k#1; \aleph_{#1}
O5 0 1
OSegm
mow#1; {\mathbb Z}_{#1}
O5 0 2
OSegm
mol#1#2; \mathop{\rm Segm}(#1,#2)
O5 0 3
OSegm
mol#1#2#3; \mathop{\rm Segm}(#1,#2,#3)
V1 1
Vcardinal
a cardinal
V2 1
Vlimit_cardinal
a limit cardinal
V3 2
V-element
a #1-element
#CARD_2
O1 1 1
O+`
moi@a; #1+#2
O2 1 1
O*`
moi@m; #1 \cdot #2
#CARD_3
M1 0
MCardinal-Function
ha function #0 yielding cardinal numbers
functions #0 yielding cardinal numbers
O1 0 1
OCard
mol@s; \mathop{\rm Card} #1
O2 0 1
Odisjoin
mol@s; \mathop{\rm disjoint} #1
O3 0 1
OUnion
mol; \bigcup #1
O3 0 2
OUnion
mol#1#2; \mathop{\rm Union}(#1,#2)
O4 0 1
Oproduct
mol@s; \prod #1
O4 0 2
Oproduct
mol(1)@s#2; \pi^{#2}#1
O5 0 1
Opi
mol@s; \prod #1
O5 0 2
Opi
mol@s/2k/1m#2; \pi_{#2}#1
O5 0 3
Opi
mol#1#2#3; \pi(#1,#2,#3)
O6 0 1
OSum
mol@s; \sum #1
O6 0 2
OSum
mol@s#2; \sum_{\kappa=0}^{#2}#1(\kappa)
O6 0 3
OSum
mol@s#2#3; \sum_{\kappa=#2+1}^{#3}#1(\kappa)
O7 0 1
OProduct
mol@s; \prod #1
O7 0 2
OProduct
mol#1#2; \mathop{\rm Product}(#1,#2)
O8 0 1
Osproduct
mol@s; \prod^{\cdot} #1
O9 0 0
ODOM
mol; \mathop{\rm DOM}
O9 0 1
ODOM
mol#1; \mathop{\rm DOM}(#1)
O10 0 1
Oproduct"
mol#1; \mathop{\rm product}(#1)
O11 0 1
Oproj
ho; projection onto #1
O11 0 2
Oproj
mol#1#2; \mathop{\rm proj}(#1,#2)
O11 1 1
Oproj
mol/1k#1#2; \mathop{\rm proj}_{#1}(#2)
V1 1
VCardinal-yielding
a cardinal yielding
V2 1
Vwith_common_domain
x common domain
V3 1
Vproduct-like
a product-like
V4 1
Vcountable
a countable
V5 1
Vdenumerable
a denumerable
#CARD_5
M1 0
MAleph
hn aleph #0
alephs #0
O1 0 1
Ocf
mol@s; \mathop{\rm cf} #1
O2 1 1
O-powerfunc_of
mow#1#2; (\alpha\mapsto\alpha^{#1})_{\alpha\in #2}
V1 1
Vregular
a regular
V2 1
Virregular
n irregular
#CARD_FIL
M1 1
MFilter
ha filter #0 of #1
filters #0 of #1
M2 1
MIdeal
hn ideal #0 of #1
ideals #0 of #1
M3 3
MInf_Matrix
hn Inf Matrix #0 of #1,#2,#3
Inf Matrices #0 of #1,#2,#3
O1 0 1
Odual
mol#1; \mathop{\rm dual} #1
O2 0 2
OExtend_Filter
mol#1#2; \mathop{\rm Extend\_Filter}(#1,#2)
O3 0 1
OFilters
mol#1; \mathop{\rm Filters} #1
O4 0 1
OFrechet_Filter
mol#1; \mathop{\rm Frechet\_Filter} #1
O5 0 1
OFrechet_Ideal
mol#1; \mathop{\rm Frechet\_Ideal} #1
O6 0 1
Opredecessor
mol#1; \mathop{\rm predecessor} #1
R1 1 1
Ris_multiplicative_with
h #1 is multiplicative with #2
#1 is not multiplicative with #2
R2 1 1
Ris_additive_with
h #1 is additive with #2
#1 is not additive with #2
R3 1 1
Ris_complete_with
h #1 is complete with #2
#1 is not complete with #2
R4 0 0
RGCH
h Generalized Continuum Hypothesis holds
Generalized Continuum Hypothesis does not hold
R5 1 1
Ris_Ulam_Matrix_of
h #1 is Ulam Matrix of #2
#1 is not Ulam Matrix of #2
V1 1
Vuniform
n uniform
V2 1
Vprincipal
a principal
V3 1
Vbeing_ultrafilter
b an ultrafilter
V4 1
Vinaccessible
n inaccessible
V5 1
Vstrong_limit
a strong limit
V6 1
Vstrongly_inaccessible
a strongly inaccessible
V7 1
Vmeasurable
a measurable
#CARD_FIN
O1 0 4
OChoose
mol#1#2#3#4; \mathop{\rm Choose}(#1,#2,#3,#4)
O2 0 2
OCard_Intersection
hol#1#2; card intersection of #1 w.r.t. #2
#CARD_LAR
O1 0 2
OLBound
mol#1#2; \mathop{\rm LBound}(#1,#2)
O2 0 1
Olimpoints
mol#1; \mathop{\rm limpoints} #1
R1 1 1
Ris_unbounded_in
h #1 is unbounded in #2
#1 is not unbounded in #2
R2 1 1
Ris_closed_in
h #1 is closed in #2
#1 is not closed in #2
R3 1 1
Ris_club_in
h #1 is club in #2
#1 is not club in #2
R4 1 1
Ris_stationary_in
h #1 is stationary in #2
#1 is not stationary in #2
V1 1
Vunbounded
n unbounded
V2 1
Vstationary
a stationary
V3 1
VMahlo
a Mahlo
V4 1
Vstrongly_Mahlo
a strongly Mahlo
#CATALAN1
O1 0 1
OCatalan
mol#1; \mathop{\rm Catalan}(#1)
#CATALAN2
M1 1
MOMEGA
ha set #0 of $\omega$-sequences of #1
sets #0 of $\omega$-sequences of #1
O1 0 2
ODomin_0
mol#1#2; \mathop{\rm Domin}_0(#1,#2)
O2 1 1
O(##)
moi; #1 \mathop{(\hash)} #2
V1 1
Vdominated_by_0
a dominated by 0
#CATALG_1
M1 0
MSignature
ha@ signature #0
signatures #0
M1 1
MSignature
ha signature #0 over #1
signatures #0 over #1
M2 0
MCatSignature
ha cat-signature #0
cat-signatures #0
M2 1
MCatSignature
ha cat-signature #0 of #1
cat-signatures #0 of #1
O1 1 2
O-MSF
moi(1,3)@m#2; #1{\upharpoonright}_{#2}#3
O2 0 1
OCatSign
mol#1; \mathop{\rm CatSign}(#1)
O3 0 1
Ounderlay
mol#1; \mathop{\rm underlay} #1
O4 0 1
Oidsym
mol#1; \mathop{\rm idsym} #1
O5 0 2
Ohomsym
mol#1#2; \mathop{\rm homsym}(#1,#2)
O6 0 3
Ocompsym
mol#1#2#3; \mathop{\rm compsym}(#1,#2,#3)
O7 0 1
OUpsilon
mow#1; \Upsilon_{#1}
O8 0 1
OPsi
mow#1; \Psi_{#1}
V1 1
Vdelta-concrete
a $\delta$-concrete
#CAT_1
G1 6
GCatStr
mc#1#2#3#4#5#6; \langle #1,\allowbreak #2,\allowbreak #3,\allowbreak #4,\allowbreak #5,\allowbreak #6\rangle
J1 1
GCatStr
hol#1; category structure of #1
L1 0
GCatStr
ha category structure #0
category structures #0
M1 1
MObject
hn object #0 of #1
objects #0 of #1
M2 1
MMorphism
ha morphism #0 of #1
morphisms #0 of #1
M2 2
MMorphism
ha morphism #0 from #1 to #2
morphisms #0 from #1 to #2
M3 0
MCategory
ha category #0
categories #0
M4 2
MFunctor
ha functor #0 from #1 to #2
functors #0 from #1 to #2
O1 0 1
OHom
mol@s#1; \mathop{\rm Hom}(#1)
O1 0 2
OHom
mcl@s#1#2; \mathop{\rm hom}(#1,#2)
O1 1 0
OHom
mol@s#1; \mathop{\rm hom}(#1,\square)
O2 0 1
O1Cat
mcl@s#1#2; \mathop{\dot\circlearrowright}(#1)
O2 0 2
O1Cat
mcl@s#1#2; \mathop{\dot\circlearrowright}(#1,#2)
O3 0 1
OObj
mol@s; \mathop{\rm Obj} #1
O4 0 2
Ohom
mol@s#1#2; \mathop{\rm hom}(#1,#2)
O4 0 3
Ohom
mow(1)/2k#2#3; #1_{#2,#3}
O4 0 5
Ohom
mol#1#2#3#4#5; \mathop{\rm hom}(#1,#2,#3,#4,#5)
U1 1
UComp
hosl#1; composition of #1
composition
U2 1
UId
honl#1; id\hbox{-}map of #1
id\hbox{-}map
V1 1
VCategory-like
a category-like
V2 1
Vmonic
a monic
V3 1
Vepi
n epi
V4 1
Vterminal
a terminal
V5 1
Vinitial
n initial
V6 1
Visomorphic
n isomorphic
V7 1
Vfull
a full
V8 1
Vfaithful
a faithful
#CAT_2
M1 2
MFUNCTOR-DOMAIN
ha non empty set #0 of functors from #1 into #2
non empty sets #0 of functors from #1 into #2
M2 1
MSubcategory
ha subcategory #0 of #1
subcategories #0 of #1
O1 0 2
OFunct
mol@s#1#2; \mathop{\rm Funct}(#1,#2)
O2 1 1
O?-
mor(1)@s#2; #1(#2, {-})
O3 1 1
O-?
mor@s#2; #1({-}, #2)
R1 1 1
Ris_full_subcategory_of
i full subcategory of #2
not full subcategory of #2
#CAT_3
M1 2
MProjections_family
ha projections family #0 from #1 onto #2
projections families #0 from #1 onto #2
M2 2
MInjections_family
hn injections family #0 into #1 on #2
injections families #0 into #1 on #2
O1 0 1
Ocods
mo@a/1r; \mathop{\rm cod}_\kappa #1(\kappa)
O2 0 1
Oterm
mol#1; \mathop{\rm term} #1
O2 0 2
Oterm
mol(2)@s#1; \bfvert^{#1}#2
O2 1 0
Oterm
mow; #1_{\rm t}
O2 1 1
Oterm
mor#2; #1(#2)
O2 1 2
Oterm
mor#2#3; #1(#2, #3)
O3 0 1
Oinit
mol#1; \mathop{\rm init} #1
O3 0 2
Oinit
mol#1#2; \mathop{\rm init}(#1,#2)
R1 1 1
Ris_a_product_wrt
i a product w.r.t. #2
not a product w.r.t. #2
R1 1 2
Ris_a_product_wrt
i a product w.r.t. #2 and #3
not a product w.r.t. #2 and #3
R2 1 1
Ris_a_coproduct_wrt
i a coproduct w.r.t. #2
not a coproduct w.r.t. #2
R2 1 2
Ris_a_coproduct_wrt
i a coproduct w.r.t. #2 and #3
not a coproduct w.r.t. #2 and #3
V1 1
Vretraction
a retraction
V2 1
Vcoretraction
a coretraction
#CAT_4
G1 10
GProdCatStr
mc#1#2#3#4#5#6#7#8#9#10; \langle #1, #2, #3, #4, #5, #6, #7, #8, #9, #10\rangle
G2 10
GCoprodCatStr
mc#1#2#3#4#5#6#7#8#9#10; \langle #1, #2, #3, #4, #5, #6, #7, #8, #9, #10\rangle
J1 1
GProdCatStr
hol#1; Cartesian category structure of #1
J2 1
GCoprodCatStr
hol#1; cocartesian category structure of #1
K1 2 L1 vCAT_4
K[$
L$]
mc#1#2; \langle #1,#2\rangle
L1 0
GProdCatStr
ha Cartesian category structure #0
Cartesian category structures #0
L2 0
GCoprodCatStr
ha cocartesian category structure #0
cocartesian category structures #0
M1 0
MCartesian_category
ha Cartesian category #0
Cartesian categories #0
M2 0
MCocartesian_category
ha cocartesian category #0
cocartesian categories #0
O1 0 1
O[1]
mow#1; {\bf 1}_{#1}
O2 1 1
O[x]
moi@m; #1\times #2
O3 0 2
Oc1Cat
mcl@s#1#2; \mathop{\dot\circlearrowright}_{\rm c}(#1,#2)
O4 0 1
Olambda'
mol@s#1; \lambda^{-1}(#1)
O5 0 1
Orho
mol@s#1; \rho(#1)
O6 0 1
Orho'
mol@s#1; \rho^{-1}(#1)
O7 0 2
OSwitch
mol@s#1; \mathop{\rm Switch}(#1)
O8 0 1
ODelta
mol@s#1; \Delta(#1)
O9 0 3
OAlpha
mol@s#1#2#3; \alpha((#1,#2),#3)
O10 0 3
OAlpha'
mol@s#1#2#3; \alpha(#1,(#2,#3))
O11 0 2
Oin1
mol@s/1l@a/2r@a#1#2; \mathop{\rm in}_1(#1+#2)
O12 0 2
Oin2
mol@s/1l@a/2r@a#1#2; \mathop{\rm in}_2(#1+#2)
O13 0 2
Oc1Cat*
mcl@s#1#2; \mathop{\dot\circlearrowright}^{\rm op}_{\rm c}(#1,#2)
U1 1
UTerminalObj
hosl#1; terminal of #1
terminal
U2 1
UCatProd
hosl#1; product of #1
product
U3 1
UProj1
hosl#1; 1st-projection of #1
1st-projection
U4 1
UProj2
hosl#1; 2nd-projection of #1
2nd-projection
U5 1
UInitial
hosl#1; initial of #1
initial
U6 1
UCoproduct
hosl#1; coproduct of #1
coproduct
U7 1
UIncl1
hosl#1; 1st-coprojection of #1
1st-coprojection
U8 1
UIncl2
hosl#1; 2nd-coprojection of #1
2nd-coprojection
V1 1
Vwith_finite_product
x finite product
V2 1
VCartesian
a Cartesian
V3 1
Vwith_finite_coproduct
x finite coproduct
V4 1
VCocartesian
a cocartesian
#CAT_5
O1 1 1
O-SliceCat
mol#1#2; \mathop{\rm SliceCat}(#1,#2)
O2 0 1
OSliceFunctor
mol#1; \mathop{\rm SliceFunctor}(#1)
O3 0 1
OSliceContraFunctor
mol#1; \mathop{\rm SliceContraFunctor}(#1)
V1 1
Vwith_triple-like_morphisms
x triple-like morphisms
V2 1
Vcategorial
a categorial
V3 1
VCategorial
a categorial
#CFCONT_1
R1 1 1
Ris_continuous_on
i continuous on #2
not continuous on #2
#CFDIFF_1
M1 0
MC_REST
ha rest_{\mathbb C} #0
rests_{\mathbb C} #0
M2 0
MC_LINEAR
ha complex linear function #0
complex linear functions #0
O1 0 1
OInvShift
mol; \mathop{\rm InvShift} #1
#CFUNCDOM
G1 6
GComplexAlgebraStr
mc#1#2#3#4#5#6; \langle #1, #2, #3, #4, #5, #6\rangle
J1 1
GComplexAlgebraStr
hol#1; complex algebra structure of #1
L1 0
GComplexAlgebraStr
ha complex algebra structure #0
complex algebra structures #0
M1 0
MComplexAlgebra
ha complex algebra #0
complex algebras #0
O1 0 1
OComplexFuncAdd
mow/1m#1; +_{{\mathbb C}^{#1}}
O2 0 1
OComplexFuncMult
mow/1m#1; \cdot_{{\mathbb C}^{#1}}
O3 0 1
OComplexFuncExtMult
mcr@s/1m#1; \cdot^{\mathbb C}_{{\mathbb C}^{#1}}
O4 0 1
OComplexFuncZero
mow/1m#1; {\bf 0}_{{\mathbb C}^{#1}}
O5 0 1
OComplexFuncUnit
mow/1m#1; {\bf 1}_{{\mathbb C}^{#1}}
O6 0 1
OCRing
mol@s#1; \mathop{\rm CRing}(#1)
O7 0 1
OCAlgebra
mol@s#1; \mathop{\rm CAlgebra}(#1)
#CFUNCT_1
M1 0
MComplex
ha complex number #0
complex numbers #0
#CHAIN_1
M1 1
MGrating
ha #1-dimensional grating #0
#1-dimensional gratings #0
M2 1
MGap
ha gap #0 of #1
gaps #0 of #1
M3 2
MCell
ha #1-cell #0 of #2
#1-cells #0 of #2
M4 2
MGrChain
ha #1-grchain #0 of #2
#1-grchains #0 of #2
O1 0 2
Ocells
mol#2; #1\hbox{-}\mathop{\rm cells}(#2)
O2 0 1
Oinfinite-cell
hol; infinite cell of #1
O3 0 1
Ostar
mol#1; #1^{\star}
O4 0 1
Odel
mol; \partial #1
O4 0 2
Odel
mcl#1#2; \partial
R1 1 1
Rbounds
h #1 bounds #2
#1 does not bound #2
#CHORD
M1 2
MAdjGraph
hn adjacency graph #0 of #2 in #1
adjacency graphs #0 of #2 in #1
M2 2
MVertexSeparator
ha vertex separator #0 of #1 and #2
vertex separators #0 of #1 and #2
M3 1
MVertexScheme
ha vertex scheme #0 of #1
vertex schemes #0 of #1
O1 1 1
O.followSet
moi#2; #1\mathclose{\rm .followSet}(#2)
O2 1 1
O.AdjacentSet
moi#2; #1\mathclose{\rm .adjacentSet}(#2)
R1 2 0
Rare_adjacent
h #1 and #2 are adjacent
#1 and #2 are not adjacent
V1 1
Vminlength
a minimum length
V2 1
Vsimplicial
a simplicial
V3 1
Vminimal
a minimal
V4 1
Vchordal
a chordal
V5 1
Vchordless
a chordless
#CIRCCMB3
O1 0 1
Ostabilization-time
hosl#1; stabilization time of #1
V1 1
Vstabilizing
a stabilizing
V2 1
Vwith_stabilization-limit
x a stabilization limit
V3 1
Vone-gate
n one-gate
V4 1
Vwith_nonpair_inputs
x nonpair inputs
#CIRCCOMB
M1 1
MGate
ha gate #0 of #1
gates #0 of #1
M2 1
MFinSeqLen
ha finite sequence #0 with length #1
finite sequences #0 with length #1
O1 0 2
O1GateCircStr
mol#1#2; \mathop{\rm 1GateCircStr}(#1,#2)
O1 0 3
O1GateCircStr
mol#1#2#3; \mathop{\rm 1GateCircStr}(#1,#2,#3)
O2 0 2
O1GateCircuit
mol#1#2; \mathop{\rm 1GateCircuit}(#1,#2)
O2 0 3
O1GateCircuit
mol#1#2#3; \mathop{\rm 1GateCircuit}(#1,#2,#3)
O2 0 4
O1GateCircuit
mol#1#2#3#4; \mathop{\rm 1GateCircuit}(#1,#2,#3,#4)
V1 1
Vunsplit
n unsplit
V2 1
Vgate`1=arity
x arity held in gates
V3 1
Vgate`2isBoolean
x Boolean denotation held in gates
V4 1
Vgate`2=den
x denotation held in gates
#CIRCLED1
M1 1
Mcircled_Combination
ha circled combination #0 of #1
circled combinations #0 of #1
O1 0 1
OCircled-Family
mol; \mathop{\rm Circled\hbox{-}Family} #1
O2 0 1
OCir
mol; \mathop{\rm Cir} #1
O3 0 1
OcircledComb
mol; \mathop{\rm circledComb} #1
#CIRCTRM1
M1 1
MCompatibleValuation
ha valuation #0 compatible with #1
valuations #0 compatible with #1
M2 3
MSortMap
ha sort map #0 from #1 and #2 into #3
sort maps #0 from #1 and #2 into #3
M3 4
MOperMap
hn operation map #0 from #1 and #2 into #3 obeying #4
operation maps #0 from #1 and #2 into #3 obeying #4
O1 1 0
O-CircuitStr
moi; #1{\rm\hbox{-}CircuitStr}
O2 0 2
Othe_action_of
hosl#1#2; action of #1 w.r.t. #2
O3 1 1
O-CircuitSorts
moi#2; #1{\rm\hbox{-}CircuitSorts} (#2)
O4 1 1
O-CircuitCharact
moi#2; #1{\rm\hbox{-}CircuitCharact} (#2)
O5 1 1
O-Circuit
moi#2; #1{\rm\hbox{-}Circuit} (#2)
R1 2 1
Rare_equivalent_wrt
h #1 and #2 are equivalent w.r.t. #3
#1 and #2 are not equivalent w.r.t. #3
R1 2 2
Rare_equivalent_wrt
h #1 and #2 are equivalent w.r.t. #3 and #4
#1 and #2 are not equivalent w.r.t. #3 and #4
R2 1 2
Rpreserves_inputs_of
h #1 preserves inputs of #2 in #3
#1 does not preserve inputs of #2 in #3
R3 2 2
Rform_embedding_of
h #1 and #2 form embedding of #3 into #4
#1 and #2 do not form embedding of #3 into #4
R4 2 2
Rare_similar_wrt
h #1 and #2 are similar w.r.t. #3 and #4
#1 and #2 are not similar w.r.t. #3 and #4
R5 1 2
Rcalculates
h #1 calculates #2 in #3
#1 does not calculate #2 in #3
R6 2 1
Rspecifies
h #1 and #2 specify #3
#1 and #2 do not specify #3
#CIRCUIT1
M1 1
MCircuit
ha circuit #0 of #1
circuits #0 of #1
M1 2
MCircuit
ha circuit #0 over #1 and #2
circuits #0 over #1 and #2
M2 1
MInputFuncs
hn input function #0 of #1
input functions #0 of #1
O1 0 1
OSet-Constants
mol#1; \mathop{\rm Set\hbox{-}Constants}(#1)
O2 1 1
O-th_InputValues
moi#2; #1{\it\hbox{-}th\rm\hbox{-}input}(#2)
O3 1 1
Odepends_on_in
moi; #1\mathop{\rm depends\hbox{-}on\hbox{-}in} #2
O4 0 2
Osize
mol#1#2; \mathop{\rm size}(#1,#2)
#CIRCUIT2
O1 0 1
OFix_inp
mol#1; \mathop{\rm FixInput}(#1)
O2 0 1
OFix_inp_ext
mol#1; \mathop{\rm FixInputExt}(#1)
O3 0 2
OIGTree
mol#1#2; \mathop{\rm InputGenTree}(#1,#2)
O4 0 2
OIGValue
mol#1#2; \mathop{\rm InputGenValue}(#1,#2)
O5 0 1
OFollowing
mol@s#1; {\rm Following}(#1)
O5 0 2
OFollowing
mol#1#2; \mathop{\rm Following}(#1,#2)
O6 0 2
OInitialComp
mol#1#2; \mathop{\rm InitialComp}(#1,#2)
O7 0 1
OComputation
mol@s#1; {\rm Computation}(#1)
O7 0 2
OComputation
mol#1#2; \mathop{\rm Computation}(#1,#2)
V1 1
Vstable
a stable
#CLASSES1
O1 0 1
OTarski-Class
mcl@s#1; {\bf T}(#1)
O1 0 2
OTarski-Class
mcl@s/2k#1#2; {\bf T}_{#2}(#1)
O2 0 1
ORank
mow/1k#1; {\bf R}_{#1}
O3 0 1
Othe_transitive-closure_of
moq; #1^{\ast_{\in}}
O4 0 1
Othe_rank_of
mcl@s#1; \mathop{\rm rk}(#1)
R1 1 1
Ris_Tarski-Class_of
i a Tarski class of #2
not a Tarski class of #2
R2 2 0
Rare_fiberwise_equipotent
h #1 and #2 are fiberwise equipotent
#1 and #2 are not fiberwise equipotent
V1 1
Vsubset-closed
a subset-closed
V2 1
VTarski
a Tarski
#CLASSES2
M1 0
MUniverse
ha universal class #0
universal classes #0
M2 0
MFinSet
ha set #0 of a finite rank
sets #0 of finite ranks
M3 0
MSet
ha {\it Set} #0
{\it Sets} #0
O1 0 0
OFinSETS
mcw; {\bf U}_0
O2 0 0
OSETS
mcw; {\bf U}_1
O3 0 1
OUniverse_closure
mol#1; \mathop{\rm Universe\_closure}(#1)
O4 0 1
OUNIVERSE
mow/1k#1; {\bf U}_{#1}
V1 1
Vuniversal
a universal
#CLOPBAN1
M1 0
MComplexBanachSpace
ha complex Banach space #0
complex Banach spaces #0
O1 0 1
OComplexVectSpace
mol@s#1; \mathop{\rm ComplexVectSpace}(#1)
O1 0 2
OComplexVectSpace
mol@s#1#2; \mathop{\rm ComplexVectSpace}(#1,#2)
O2 0 2
OC_VectorSpace_of_LinearOperators
mol@s#1#2; \mathop{\rm CVSpLinOps}(#1,#2)
O3 0 2
OC_VectorSpace_of_BoundedLinearOperators
mol@s#1#2; \mathop{\rm CVSpBdLinOps}(#1,#2)
O4 0 2
OC_NormSpace_of_BoundedLinearOperators
mol@s#1#2; \mathop{\rm CNSpBdLinOps}(#1,#2)
#CLOPBAN2
G1 7
GNormed_Complex_AlgebraStr
mc#1#2#3#4#5#6#7; \langle #1, #2, #3, #4, #5,#6,#7\rangle
J1 1
GNormed_Complex_AlgebraStr
hol#1; normed complex algebra structure of #1
L1 0
GNormed_Complex_AlgebraStr
ha normed complex algebra structure #0
normed complex algebra structures #0
M1 0
MComplexBLAlgebra
ha complex BL algebra
complex BL algebras
M2 0
MNormed_Complex_Algebra
ha normed complex algebra
normed complex algebras
M3 0
MComplex_Banach_Algebra
ha complex Banach algebra
complex Banach algebras
O1 0 1
OC_Algebra_of_BoundedLinearOperators
mol#1; \mathop{\rm CAlgBdLinOps}(#1)
O2 0 1
OC_Normed_Algebra_of_BoundedLinearOperators
mol#1; \mathop{\rm CNAlgBdLinOps}(#1)
#CLOSURE1
G1 2
GMSClosureStr
mc#1#2; \langle #1, #2 \rangle
J1 1
GMSClosureStr
hol#1; many sorted closure system structure of #1
L1 1
GMSClosureStr
ha many sorted closure system structure #0 over #1
many sorted closure system structures #0 over #1
M1 1
MMSSetOp
ha set many sorted operation #0 in #1
set many sorted operations #0 in #1
M2 1
MMSClosureSystem
ha many sorted closure system #0 of #1
many sorted closure systems #0 of #1
M3 1
MMSClosureOperator
ha many sorted closure operator #0 of #1
many sorted closure operators #0 of #1
O1 0 1
OMSFull
mol#1; \mathop{\rm MSFull}(#1)
O2 0 1
OMSFixPoints
mol#1; \mathop{\rm FixPoints}(#1)
#CLOSURE2
G1 2
GClosureStr
mc#1#2; \langle #1,#2 \rangle
J1 1
GClosureStr
hol#1; closure system structure of #1
L1 1
GClosureStr
ha closure system structure #0 over #1
closure system structures #0 over #1
M1 1
MSubsetFamily
ha family #0 of many sorted subsets indexed by #1
families #0 of many sorted subsets indexed by #1
M2 1
MSetOp
ha set operation #0 in #1
set operations #0 in #1
M3 1
MClosureSystem
ha closure system #0 of #1
closure systems #0 of #1
M4 1
MClosureOperator
ha closure operator #0 of #1
closure operators #0 of #1
O1 0 1
OBool
mol#1; \mathop{\rm Bool}(#1)
O2 0 1
OFull
mol#1; \mathop{\rm Full}(#1)
O3 0 1
OClOp->ClSys
mol#1; \mathop{\rm ClSys}(#1)
O4 0 1
OClSys->ClOp
mol#1; \mathop{\rm ClOp}(#1)
R1 1 1
Rin'
mn #1 \in #2
#1 \nin #2
R2 1 1
Rc='
mn #1 \subseteq #2
#1 \not\subseteq #2
U1 1
UFamily
hosl#1; family of #1
family
#CLOSURE3
O1 0 1
Osupp
mol#1; \mathop{\rm supp}(#1)
O2 0 1
OMSUnion
mol#1; \mathop{\rm MSUnion}(#1)
O3 0 1
OSubAlgCl
mol#1; \mathop{\rm SubAlgCl}(#1)
#CLVECT_1
G1 4
GCLSStruct
mc#1#2#3#4; \langle #1, #2, #3, #4\rangle
G2 5
GCNORMSTR
mc#1#2#3#4#5; \langle #1, #2, #3, #4,#5\rangle
J1 1
GCLSStruct
hol#1; CLS structure of #1
J2 1
GCNORMSTR
hol#1; complex normed space structure of #1
L1 0
GCLSStruct
ha CLS structure #0
CLS structures #0
L2 0
GCNORMSTR
ha complex normed space structure #0
complex normed space structures #0
M1 0
MComplexLinearSpace
ha complex linear space #0
complex linear spaces #0
M2 0
MComplexNormSpace
ha complex normed space #0
complex normed spaces #0
O1 0 0
OTrivial-CLSStruct
mol; \mathop{\rm Trivial\hbox{-}CLSStruct}
V2 1
VComplexNormSpace-like
a complex normed space-like
#COHSP_1
O1 0 1
OFlatCoh
mol#1; \mathop{\rm FlatCoh}(#1)
O2 0 1
OSub_of_Fin
mol#1; \mathop{\rm SubFin}(#1)
O3 0 1
Ograph
mol#1; \mathop{\rm graph}(#1)
O4 0 1
OTrace
mol#1; \mathop{\rm Trace}(#1)
O5 0 2
OStabCoh
mol#1#2; \mathop{\rm StabCoh}(#1,#2)
O6 0 1
OLinTrace
mol#1; \mathop{\rm LinTrace}(#1)
O7 0 2
OLinCoh
mol#1#2; \mathop{\rm LinCoh}(#1,#2)
O8 1 1
OU+
moi#1#2; #1\uplus #2
R1 1 1
Rincludes_lattice_of
h #1 includes lattice of #2
#1 does not include lattice of #2
R1 1 2
Rincludes_lattice_of
h #1 includes lattice of #2,#3
#1 does not include lattice of #2,#3
V1 1
Vc=directed
a $\cup$-directed
V2 1
Vc=filtered
a $\cap$-directed
V3 1
Vd.union-closed
a closed under directed unions
V4 1
Vunion-distributive
a preserving arbitrary unions
V5 1
Vd.union-distributive
a preserving directed unions
V6 1
Vc=-monotone
a $\subseteq$-monotone
V7 1
Vcap-distributive
a preserving binary intersections
V8 1
VU-continuous
a continuous
V9 1
VU-stable
a stable
V10 1
VU-linear
a linear
#COH_SP
M1 0
MCoherence_Space
ha coherent space #0
coherent spaces #0
O1 0 1
OWeb
mol@s#1; {\rm Web}(#1)
O2 0 1
OCohSp
mol@s#1; {\rm CohSp}(#1)
O3 0 1
OCSp
mol@s#1; {\rm CSp}(#1)
O4 0 1
OFuncsC
mol@s; {\rm Funcs}_{\rm C} #1
O5 0 1
OMapsC
mol@s; {\rm Maps}_{\rm C} #1
O6 0 1
OCDom
mol@s; \mathop{\rm Dom}_{\rm CSp} #1
O7 0 1
OCCod
mol@s; \mathop{\rm Cod}_{\rm CSp} #1
O8 0 1
OCComp
mol@s; \mathop{\cdot}_{\rm CSp} #1
O9 0 1
OCId
mol@s; \mathop{\rm Id}_{\rm CSp} #1
O10 0 1
OCohCat
ho#1; #1-coherent space category
O11 0 1
OToler
hopl; tolerances on #1
O11 1 0
OToler
mor; #1 \mathop{\rm Toler}
O12 0 1
OToler_on_subsets
hopl; tolerances on subsets of #1
O13 0 1
OTOL
mol@s#1; {\rm TOL}(#1)
O14 0 1
OFuncsT
mol@s; {\rm Funcs}_{\rm T} #1
O15 0 1
OMapsT
mol@s; {\rm Maps}_{\rm T} #1
O16 0 1
OTolCat
hosl; #1-tolerance category
V1 1
Vbinary_complete
a binary complete
#COLLSP
G1 2
GCollStr
mc#1#2; \langle #1, #2\rangle
J1 1
GCollStr
hol#1; collinearity structure of #1
L1 0
GCollStr
ha collinearity structure #0
collinearity structures #0
M1 1
MRelation3
ha 3-ary relation #0 of #1
3-ary relations #0 of #1
M2 0
MCollSp
ha collinearity space #0
collinearity spaces #0
U1 1
UCollinearity
hosl#1; collinearity relation of #1
collinearity relation
#COMBGRAS
G1 2
GIncProjMap
mc#1#2; \langle #1,#2 \rangle
J1 1
GIncProjMap
hol#1; map of #1
L1 2
GIncProjMap
ha map #0 between projective spaces #1 and #2
maps #0 between projective spaces #1 and #2
M1 0
MPartialLinearSpace
ha partial linear space #0
partial linear spaces #0
O1 0 2
OG_
mol#2; \mathop{\rm G}_{#1}(#2)
O2 0 2
Oincprojmap
mol#1#2; \mathop{\rm incprojmap}(#1,#2)
U1 1
Upoint-map
hosl#1; point-map of #1
point-map
U2 1
Uline-map
hosl#1; line-map of #1
line-map
V1 1
Vclique
b a clique
V2 1
Vmaximal_clique
b a maximal-clique
V3 1
VSTAR
b a star
V4 1
VTOP
b a top
V5 1
Vincidence_preserving
p incidence strongly
#COMMACAT
O1 0 2
OcommaObjs
mow#1#2; {\rm Obj}_{(#1,#2)}
O2 0 2
OcommaMorphs
mow#1#2; {\rm Morph}_{(#1,#2)}
O3 0 2
OcommaComp
mow#1#2; \circ_{(#1,#2)}
O4 1 1
Ocomma
mc#1#2; (#1,#2)
#COMPACT1
O1 0 1
OOne-Point_Compactification
hol; one-point compactification of #1
V1 1
Vrelatively-compact
a relatively-compact
V2 1
Vpre-compact
a pre-compact
V3 1
Vliminally-compact
a liminally-compact
V4 1
Vlocally-relatively-compact
a locally-relatively-compact
V5 1
Vlocally-closed/compact
a locally-closed/compact
V6 1
Vcompactification
a compactification
#COMPLEX1
K1 1 L1 vCOMPLEX1
K|.
L.|
mc#1; \vert #1 \vert
O1 0 1
ORe
mcl@s#1; \Re(#1)
O2 0 0
O0c
mow; 0_{\mathbb C}
O2 0 1
O0c
mcr@s/1m#1; 0_{\mathbb C}^{#1}
O3 0 0
O1r
mow; 1_{\mathbb C}
O4 0 1
Oabs
mc#1; \mathopen{\vert} #1 \mathclose{\vert}
#COMPLEX2
O1 0 2
Oangle
mol#1#2; \mathop{\measuredangle}(#1,#2)
O1 0 3
Oangle
mol#1#2#3; \mathop{\measuredangle}(#1,#2,#3)
#COMPLFLD
O1 0 0
OF_Complex
mow; {\mathbb C}_{\rm F}
#COMPLSP1
O1 0 0
Oabscomplex
mow; {\vert\cdot\vert}_{\mathbb C}
O2 0 1
OComplexOpenSets
hop#1; open subsets of ${\mathbb C}^{#1}$
O3 0 1
Othe_Complex_Space
hos; #1\hbox{-}dimensional complex space
#COMPL_SP
O1 0 2
Owell_dist
mol#1#2; \mathop{\rm well\hbox{-}dist}(#1,#2)
O2 0 2
OWellSpace
mol#1#2; \mathop{\rm WellSpace}(#1,#2)
V1 1
Vcountably_compact
a countably-compact
#COMPOS_1
G1 5
GCOM-Struct
mc#1#2#3#4#5; \langle #1,#2,#3,#4,#5 \rangle
J1 1
GCOM-Struct
hol#1; COM structure of #1
L1 1
GCOM-Struct
hn COM #0 over #1
COM's #0 over #1
O1 0 1
OTrivial-COM
mol; \mathop{\rm Trivial-COM} #1
U1 1
UhaltF
hosl#1; halt of #1
halt
V1 1
Vproper-halt
a proper halt
#COMPTRIG
M1 2
MCRoot
ha complex root #0 of #1,#2
complex roots #0 of #1,#2
O1 0 1
OArg
mol; \mathop{\rm Arg} #1
#COMPTS_1
O1 0 1
O1TopSp
mow#1; \lbrace #1 \rbrace_{\rm top}
V1 1
VHausdorff
a Hausdorff
#COMPUT_1
O1 0 1
OHFuncs
mol#1; \mathop{\rm HFuncs} #1
O2 0 3
Oprimrec
mol#1#2#3; \mathop{\rm primrec}(#1,#2,#3)
O2 0 4
Oprimrec
mol#1#2#3#4; \mathop{\rm primrec}(#1,#2,#3,#4)
O3 0 0
OPrimRec
mol; \mathop{\rm PrimRec}
O4 0 0
Oinitial-funcs
hopl; initial functions
O5 0 1
OPR-closure
hosl; primitive recursion closure of #1
O6 0 1
Ocomposition-closure
hosl; composition closure of #1
O7 0 0
OPrimRec-Approximation
moq; \mathop{\rm PrimRec}^\approx
O8 0 1
O(1,2)->(1,?,2)
mok; {}^{\langle 1,?,2\rangle}\! #1
O9 0 0
O[!]
mc; [!]
O10 0 0
O[^]
mc; [^\wedge]
O11 0 0
O[pred]
mc; [{\rm pred}]
R1 1 3
Ris_primitive-recursively_expressed_by
i primitive recursively expressed by #2, #3 and #4
not primitive recursively expressed by #2, #3 and #4
V1 1
Vto-naturals
c into $\mathbb N$
V2 1
Vlen-total
a length total
V3 1
Vwith_the_same_arity
x the same arity
V4 1
Vcomposition_closed
a composition closed
V5 1
Vprimitive-recursion_closed
a primitive recursion closed
V6 1
Vprimitive-recursively_closed
a primitive recursively closed
V7 1
Vprimitive-recursive
a primitive recursive
V8 1
Vnullary
a nullary
V9 1
Vunary
a unary
V10 1
Vternary
a ternary
#COMSEQ_1
M1 0
MComplex_Sequence
ha complex sequence #0
complex sequences #0
#COMSEQ_3
O1 1 1
O#N
mor{qrw}@s#2; #1^{#2}_{\mathbb N}
#CONAFFM
V1 1
Vsatisfying_DES
s Desargues Axiom
V2 1
Vsatisfying_AH
s AH
V3 1
Vsatisfying_3H
s theorem on three perpendiculars
V4 1
Vsatisfying_ODES
s orthogonal version of Desargues Axiom
V5 1
Vsatisfying_LIN
s LIN
V6 1
Vsatisfying_LIN1
s first indirect form of LIN
V7 1
Vsatisfying_LIN2
s second indirect form of LIN
#CONLAT_1
G1 3
GContextStr
mc#1#2#3; \langle #1,#2,#3 \rangle
G2 2
GConceptStr
mc#1#2; \langle #1,#2 \rangle
J1 1
GContextStr
hol#1; ContextStr of #1
J2 1
GConceptStr
hol#1; ConceptStr of #1
L1 0
GContextStr
ha ContextStr #0
ContextStr #0
L2 1
GConceptStr
ha ConceptStr #0 over #1
ConceptStr #0 over #1
M1 0
MFormalContext
ha FormalContext #0
FormalContexts #0
M2 1
MAttribute
hn Attribute #0 of #1
Attributes #0 of #1
M3 1
MFormalConcept
ha FormalConcept #0 of #1
FormalConcepts #0 of #1
M4 1
MSet-of-FormalConcepts
ha Set of FormalConcepts #0 of #1
Sets of FormalConcepts #0 of #1
O1 0 1
OObjectDerivation
mol#1; \mathop{\rm ObjectDerivation} #1
O2 0 1
OAttributeDerivation
mol#1; \mathop{\rm AttributeDerivation} #1
O3 0 1
Ophi
mcl@s#1; \phi(#1)
O4 0 1
Opsi
mol#1; \mathop{\rm psi} #1
O5 0 1
OConcept-with-all-Objects
mol#1; \mathop{\rm Concept-with-all-Objects} #1
O6 0 1
OConcept-with-all-Attributes
mol#1; \mathop{\rm Concept-with-all-Attributes} #1
O7 0 1
OB-carrier
mol#1; \mathop{\rm B-carrier} #1
O8 0 1
OB-meet
mol#1; \mathop{\rm B-meet} #1
O9 0 1
OB-join
mol#1; \mathop{\rm B-join} #1
O10 0 1
OConceptLattice
mol#1; \mathop{\rm ConceptLattice} #1
R1 1 1
Ris-connected-with
h #1 is connected with #2
#1 is not connected with #2
R2 1 1
Ris-not-connected-with
h #1 is not connected with #2
#1 is connected with #2
R3 1 1
Ris-SubConcept-of
h #1 is SubConcept of #2
#1 is not SubConcept of #2
R4 1 1
Ris-SuperConcept-of
h #1 is SuperConcept of #2
#1 is not SuperConcept of #2
U1 1
UInformation
honl#1; information of #1
information
U2 1
UExtent
honl#1; extent of #1
extent
U3 1
UIntent
honl#1; intent of #1
intent
V1 1
Vquasi-empty
a quasi-empty
V2 1
Vco-Galois
a co-Galois
V3 1
Vconcept-like
a concept-like
V4 1
Vco-universal
a co-universal
#CONLAT_2
O1 0 1
Ogamma
mol#1; \gamma (#1)
O2 0 1
OContext
mol#1; \mathop{\rm Context} #1
O3 0 1
ODualHomomorphism
mol#1; \mathop{\rm DualHomomorphism} #1
#CONMETR
V1 1
Vsatisfying_OPAP
s Pappos Axiom with orthogonal axes
V2 1
Vsatisfying_PAP
s Pappos Axiom
V3 1
Vsatisfying_MH1
s MH1
V4 1
Vsatisfying_MH2
s MH2
V5 1
Vsatisfying_TDES
s trapezium variant of Desargues Axiom
V6 1
Vsatisfying_SCH
s Scherungssatz
V7 1
Vsatisfying_OSCH
s Scherungssatz with orthogonal axes
V8 1
Vsatisfying_des
s des
#CONMETR1
V1 1
Vsatisfying_minor_Scherungssatz
s minor Scherungssatz
V2 1
Vsatisfying_major_Scherungssatz
s major Scherungssatz
V3 1
Vsatisfying_Scherungssatz
s Scherungssatz
V4 1
Vsatisfying_indirect_Scherungssatz
s indirect Scherungssatz
V5 1
Vsatisfying_minor_indirect_Scherungssatz
s minor indirect Scherungssatz
V6 1
Vsatisfying_major_indirect_Scherungssatz
s major indirect Scherungssatz
#CONNSP_1
O1 0 1
OComponent_of
hol; component of #1
O1 0 2
OComponent_of
hol#1#2; component of (#1,#2)
R1 2 0
Rare_separated
h #1 and #2 are separated
#1 and #2 are not separated
R2 2 0
Rare_joined
h #1 and #2 are joined
not #1 and #2 are not joined
R3 1 1
Ris_a_component_of
i a component of #2
not a component of #2
V1 1
Va_component
n a component
#CONNSP_2
M1 1
Ma_neighborhood
ha neighbourhood #0 of #1
neighbourhoods #0 of #1
O1 0 1
OqComponent_of
hol; q Component of #1
R1 1 1
Ris_locally_connected_in
i locally connected in #2
not locally connected in #2
V1 1
Vlocally_connected
a locally connected
#CONNSP_3
M1 1
Ma_union_of_components
ha union of components #0 of #1
unions of components #0 of #1
O1 0 1
ODown
mol; \mathop{\rm Down} #1
O1 0 2
ODown
mol#1#2; \mathop{\rm Down}(#1,#2)
#CONVEX1
O1 0 1
OConvex-Family
mol; \mathop{\rm Convex\hbox{-}Family} #1
O2 0 1
Oconv
mol#1; \mathop{\rm conv} #1
V1 1
Vconvex
a convex
#CONVEX2
M1 1
MConvex_Combination
ha convex combination #0 of #1
convex combinations #0 of #1
#CONVEX3
O1 0 1
OConvexComb
mol#1; \mathop{\rm ConvexComb}(#1)
V1 1
Vcone
a cone
#CONVEX4
M1 1
MC_Linear_Combination
ha \mbC-linear combination #0 of #1
\mbC-linear combinations #0 of #1
O1 0 1
OZeroCLC
mol; \mathop{\rm ZeroCLC} #1
O2 0 1
OC_LinComb
mol; \mathop{\rm\mbC\hbox{-}LinComb} #1
O3 0 1
OC_LCAdd
mol; \mathop{\rm\mbC\hbox{-}LCAdd} #1
O4 0 1
OC_LCMult
mol; \mathop{\rm\mbC\hbox{-}LCMult} #1
O5 0 1
OLC_CLSpace
mol; \mathop{\rm L\mbC\hbox{-}CLSpace} #1
#CONVFUN1
O1 0 2
OAdd_in_Prod_of_RLS
mol#1#2; \mathop{\rm AddInProdRLS}(#1,#2)
O2 0 2
OMult_in_Prod_of_RLS
mol#1#2; \mathop{\rm MultInProdRLS}(#1,#2)
O3 0 2
OProd_of_RLS
mol#1#2; \mathop{\rm ProdRLS}(#1,#2)
O4 0 0
ORLS_Real
mow; {\mathbb R}_{\rm RLS}
O5 0 1
Oepigraph
mol; \mathop{\rm epigraph}\: #1
#CQC_LANG
M1 0
MSubstitution
ha substitution #0
substitutions #0
M2 1
MCQC-variable_list
ha variables list #0 of #1
variables lists #0 of #1
O1 0 2
OSubst
mor@s#2; #1 \lbrack #2 \rbrack
O2 0 0
OCQC-WFF
mc; \mathop{\rm CQC\hbox{-}WFF}
#CQC_SIM1
O1 0 1
ONEGATIVE
mol@s#1; \mathop{\rm NEG}(#1)
O2 0 3
OCON
mol@s#1#2#3; \mathop{\rm CON}(#1,#2,#3)
O3 0 2
OUNIVERSAL
mol@s#1#2; \mathop{\rm UNIV}(#1,#2)
O4 0 2
OATOMIC
mol@s#1#2; \mathop{\rm ATOM}(#1,#2)
O5 0 1
OQuantNbr
hol; number of quantifiers in #1
O6 0 0
OSepFunc
mc; \mathop{\rm Renum}
O6 0 3
OSepFunc
mol@s#1#2#3; \mathop{\rm Renum}_{#2,#3}(#1)
O7 0 1
ONBI
mol@s#1; \mathop{\rm NBI}(#1)
O8 0 1
Oindex
mow#1; \vert \bullet: #1 \vert_{\mathbb N}
O8 0 2
Oindex
mow#1#2; [#1: #2]_{\mathbb N}
O9 0 1
OSepVar
mor; #1 \mathop{\rm with\ variables\ separated}
O10 0 1
OSepQuadruples
mow#1; \mathop{\bf Quadruples}_{#1}
R1 1 1
Ris_Sep-closed_on
i closed w.r.t. #2
not closed w.r.t. #2
R2 2 0
Rare_similar
h #1 and #2 are similar
#1 and #2 are not similar
#CQC_THE1
O1 0 1
OCn
mol@s; \mathop{\rm Cn} #1
O2 0 0
OProof_Step_Kinds
mc; {\mathbb K}
O3 0 1
OEffect
mol@s; \mathop{\rm Effect} #1
O4 0 0
OTAUT
mc; \mathop{\rm Taut}
R1 2 1
Ris_a_correct_step_wrt
h $#1(#2)$ is a correct proof step w.r.t. #3
$#1(#2)$ is not a correct proof step w.r.t. #3
R2 1 1
Ris_a_proof_wrt
i a proof w.r.t. #2
not a proof w.r.t. #2
R3 0 1
R|-
m \vdash #1
\nvdash #1
R3 1 1
R|-
m #1 \vdash #2
#1 \nvdash #2
V1 1
Vbeing_a_theory
b a theory
V2 1
Vvalid
a valid
#CQC_THE3
R1 1 1
R|-|
m #1 \vdash\!\dashv #2
#1 \nvdash\!\dashv #2
R2 1 1
Ris_an_universal_closure_of
i an universal closure of #2
not an universal closure of #2
#CSSPACE
G1 5
GCUNITSTR
mc#1#2#3#4#5; \langle #1, #2, #3, #4, #5\rangle
J1 1
GCUNITSTR
hol#1; complex unitary space structure of #1
L1 0
GCUNITSTR
ha complex unitary space structure #0
complex unitary space structures #0
M1 0
MComplexUnitarySpace
ha complex unitary space #0
complex unitary spaces #0
O1 0 0
Othe_set_of_ComplexSequences
hol; set of complex sequences
O2 0 1
OC_id
mol#1; \mathop{\rm id_{\mathbb C}}(#1)
O3 0 0
OCZeroseq
mow; \mathop{\rm CZeroseq}
O4 0 0
OLinear_Space_of_ComplexSequences
hol; linear space of complex sequences
O5 0 0
Othe_set_of_l2ComplexSequences
hol; set of l2-complex sequences
O6 0 0
Ocl_scalar
mow; \mathop{\rm scalar_{\rm cl}}
O7 0 0
OComplex_l2_Space
mow; \mathop{\rm Complexl2\hbox{-}Space}
V1 1
VComplexUnitarySpace-like
a complex unitary space-like
#CSSPACE2
M1 0
MComplexHilbertSpace
ha complex Hilbert space #0
complex Hilbert spaces #0
#CSSPACE3
O1 0 0
Othe_set_of_l1ComplexSequences
hol; set of l1-complex sequences
O2 0 0
Ocl_norm
mow; \mathop{\rm cl\_norm}
O3 0 0
OComplex_l1_Space
mow; \mathop{\rm Complex\hbox{-}l1\hbox{-}Space}
#CSSPACE4
O1 0 0
Othe_set_of_BoundedComplexSequences
hol; set of bounded complex sequences
O2 0 0
OComplex_linfty_norm
mow; \mathop{\rm Clinfty\hbox{-}norm}
O3 0 0
OComplex_linfty_Space
mow; \mathop{\rm Clinfty\hbox{-}Space}
O4 0 2
OComplexBoundedFunctions
mow#1#2; \mathop{\rm CBdFuncs}(#1,#2)
O5 0 2
OC_VectorSpace_of_BoundedFunctions
hol; set of bounded complex sequences from #1 into #2
O6 0 2
OComplexBoundedFunctionsNorm
mow#1#2; \mathop{\rm CBdFuncsNorm}(#1,#2)
O7 0 2
OC_NormSpace_of_BoundedFunctions
hol; complex normed space of bounded functions from #1 into #2
#DECOMP_1
M1 1
Malpha-set
hn \alphasym-set #0 of #1
\alphasym-sets #0 of #1
O1 0 1
OsInt
mol#1; \mathop{\rm sInt}(#1)
O2 0 1
OpInt
mol#1; \mathop{\rm pInt}(#1)
O3 0 1
OalphaInt
mol#1; \mathop{\alpha{\rm Int}}(#1)
O4 0 1
OpsInt
mol#1; \mathop{\rm psInt}(#1)
O5 0 1
OspInt
mol#1; \mathop{\rm spInt}(#1)
O6 1 0
O^alpha
mor; #1^\alpha
O7 0 1
OSO
mol#1; \mathop{\rm SO}(#1)
O8 0 1
OPO
mol#1; \mathop{\rm PO}(#1)
O8 0 3
OPO
mol#1#2#3; \mathop{\rm PO}(#1,#2,#3)
O9 0 1
OSPO
mol#1; \mathop{\rm SPO}(#1)
O10 0 1
OPSO
mol#1; \mathop{\rm PSO}(#1)
O11 0 1
OD(c,alpha)
mol#1; D(c,\alpha)(#1)
O12 0 1
OD(c,p)
mol#1; D(c,p)(#1)
O13 0 1
OD(c,s)
mol#1; D(c,s)(#1)
O14 0 1
OD(c,ps)
mol#1; D(c,ps)(#1)
O15 0 1
OD(alpha,p)
mol#1; D(\alpha,p)(#1)
O16 0 1
OD(alpha,s)
mol#1; D(\alpha,s)(#1)
O17 0 1
OD(alpha,ps)
mol#1; D(\alpha,ps)(#1)
O18 0 1
OD(p,sp)
mol#1; D(p,sp)(#1)
O19 0 1
OD(p,ps)
mol#1; D(p,ps)(#1)
O20 0 1
OD(sp,ps)
mol#1; D(sp,ps)(#1)
V1 1
Vsemi-open
a semi-open
V2 1
Vpre-open
a pre-open
V3 1
Vpre-semi-open
a pre-semi-open
V4 1
Vsemi-pre-open
a semi-pre-open
V5 1
Vs-continuous
n $s$-continuous
V6 1
Vp-continuous
a $p$-continuous
V7 1
Valpha-continuous
n $\alpha$-continuous
V8 1
Vps-continuous
a $ps$-continuous
V9 1
Vsp-continuous
n $sp$-continuous
V10 1
V(c,alpha)-continuous
a $(c,\alpha)$-continuous
V11 1
V(c,s)-continuous
a $(c,s)$-continuous
V12 1
V(c,p)-continuous
a $(c,p)$-continuous
V13 1
V(c,ps)-continuous
a $(c,ps)$-continuous
V14 1
V(alpha,p)-continuous
n $(\alpha,p)$-continuous
V15 1
V(alpha,s)-continuous
n $(\alpha,s)$-continuous
V16 1
V(alpha,ps)-continuous
n $(\alpha,ps)$-continuous
V17 1
V(p,ps)-continuous
a $(p,ps)$-continuous
V18 1
V(p,sp)-continuous
a $(p,sp)$-continuous
V19 1
V(sp,ps)-continuous
n $(sp,ps)$-continuous
#DICKSON
O1 0 1
O<=E
mol#1; \;\le_E\!\! #1
O2 1 0
O\~
mor#1; #1 \setminus^\smallsmile
O3 0 1
Omin-classes
mol#1; \mathop{\rm MinClasses} #1
O4 1 1
Omindex
moi#1#2; #1 \mathop{\rm mindex} #2
O4 1 2
Omindex
moi#1#2#3; #1 \mathop{\rm mindex}(#2,#3)
O5 0 2
ODickson-bases
mol#1#2; \mathop{\rm Dickson\hbox{-}Bases}(#1,#2)
O6 0 0
ONATOrd
mol; \mathop{\rm NATOrd}
O7 0 0
OOrderedNAT
mol; \mathop{\rm OrderedNAT}
R1 1 2
Ris_Dickson-basis_of
i Dickson basis of #2,#3
not Dickson basis of #2,#3
V1 1
Vweakly-ascending
a weakly ascending
V2 1
Vquasi_ordered
a quasi ordered
V3 1
VDickson
a Dickson
#DIFF_1
K1 3 L1 vDIFF_1
K[!
L!]
mol#1#2#3; \Delta[#1](#2,#3)
K1 4 L1 vDIFF_1
K[!
L!]
mc#1#2#3#4; \Delta[#1](#2,#3,#4)
K1 5 L1 vDIFF_1
K[!
L!]
mc#1#2#3#4#5; \Delta[#1](#2,#3,#4,#5)
K1 6 L1 vDIFF_1
K[!
L!]
mol#1#2#3#4#5#6; \Delta[#1](#2,#3,#4,#5,#6)
K1 7 L1 vDIFF_1
K[!
L!]
mol#1#2#3#4#5#6#7; \Delta[#1](#2,#3,#4,#5,#6,#7)
M1 0
MSeq_Sequence
ha sequence #0 of real sequences
sequences #0 of real sequences
O1 0 2
OfD
mol#1#2; \Delta_{#2}[#1]
O2 0 2
ObD
mol#1#2; \nabla_{#2}[#1]
O3 0 2
OcD
mol#1#2; \delta_{#2}[#1]
O4 0 2
Oforward_difference
hol#1#2; forward difference of #1 and #2
O5 0 2
Ofdif
mol#1#2; \vec\Delta_{#2}[#1]
O6 0 2
Obackward_difference
hol#1#2; backward difference of #1 and #2
O7 0 2
Obdif
mol#1#2; \vec\nabla_{#2}[#1]
O8 0 2
Ocentral_difference
hol#1#2; central difference of #1 and #2
O9 0 2
Ocdif
mol#1#2; \vec\delta_{#2}[#1]
V1 1
VSequence-yielding
a sequence-yielding
#DILWORTH
M1 1
MClique
ha clique #0 of #1
cliques #0 of #1
M2 1
MStableSet
ha stable set #0 of #1
stable sets #0 of #1
M3 1
MClique-partition
ha clique-partition #0 of #1
clique-partitions #0 of #1
M4 1
MColoring
ha coloring #0 of #1
colorings #0 of #1
O1 0 1
Oclique#
mcl; \mathop{\omega}(#1)
O2 0 1
Ostability#
mcl; \mathop{\alpha}(#1)
O3 0 1
Ominimals
mol; \mathop{\rm minimals}(#1)
O4 0 1
Omaximals
mol; \mathop{\rm maximals}(#1)
V1 1
Vwith_finite_clique#
w finite clique number
V2 1
Vwith_finite_stability#
x finite stability number
V3 1
VClique-wise
a clique-wise
V4 1
VStableSet-wise
a stable-wise
V5 1
Vstrong-chain
a strong-chain
#DIRAF
M1 0
MAffinSpace
hn affine space #0
affine spaces #0
M2 0
MAffinPlane
hn affine plane #0
affine planes #0
O1 0 1
Olambda
mol@s#1; \lambda(#1)
O2 0 1
OLambda
mol@s#1; \Lambda(#1)
R1 0 3
RMid
h #2 is a midpoint of #1, #3
#2 is not a midpoint of #1, #3
R2 0 3
RLIN
m {\bf L}(#1, #2, #3)
{\rm not}\ {\bf L}(#1, #2, #3)
V1 1
VAffinSpace-like
n affine space-like
#DIRORT
M1 0
MOriented_Orthogonality_Space
hn oriented orthogonality space #0
oriented orthogonality spaces #0
R1 2 2
R'//'
m #1,#2 \top^{{>}} #3,#4
\mathop{\rm not} #1,#2 \top^{{>}} #3,#4
V1 1
VOriented_Orthogonality_Space-like
n oriented orthogonality
V2 1
Vbach_transitive
a semi transitive
V3 1
Vright_transitive
a right transitive
V4 1
Vleft_transitive
a left transitive
V5 1
VEuclidean_like
n Euclidean like
V6 1
VMinkowskian_like
a Minkowskian like
#DIST_1
M1 1
MdistProbFinS
ha probability distribution finite sequence #0 on #1
probability distribution finite sequences #0 on #1
O1 0 1
Owhole_event
hol; certain event of #1
O2 0 2
Oevent_pick
mol#1#2; {\cal E}_{i}(#2(i)=#1)
O3 0 2
Ofrequency
mol#1#2; \mathop{\rm frequency}(#1,#2)
O4 0 2
OFDprobability
mol#1#2; \mathop{\rm Prob}_{\rm D}(#1,#2)
O5 0 1
OFDprobSEQ
mol; \mathop{\rm FDprobSEQ} #1
O6 0 1
OFinseq-EQclass
hol; equivalence class of #1
O7 0 1
Odistribution_family
hol; distribution family of #1
O8 0 1
OGenProbSEQ
mol; \mathop{\rm GenProbSEQ} #1
O9 0 2
Odistribution
mol#1#2; \mathop{\rm distribution}(#1,#2)
O10 0 1
OfreqSEQ
mol; \mathop{\rm freqSEQ} #1
O11 0 1
Ouniform_distribution
hol; uniform distribution #1
O12 0 1
OUniform_FDprobSEQ
mol; \mathop{\rm UniformFDprobSEQ} #1
R1 2 0
R-are_prob_equivalent
h #1 and #2 are probability equivalent
#1 and #2 are not probability equivalent
R2 1 0
Ris_uniformly_distributed
i uniformly distributed
not uniformly distributed
#DTCONSTR
M1 1
MTerminal
ha terminal #0 of #1
terminals #0 of #1
M2 1
MNonTerminal
ha nonterminal #0 of #1
nonterminals #0 of #1
M3 1
MSubtreeSeq
ha subtree sequence #0 joinable by #1
subtree sequences #0 joinable by #1
O1 0 1
OTS
mcl#1; \mathop{\rm TS}(#1)
O2 0 0
OPeanoNat
mow; {\mathbb N}_{\rm Peano}
O3 0 1
Oplus-one
mor(1)#1; (#1)(_1+1)
O4 0 0
OPN-to-NAT
moi@a; {\mathbb N}_{\rm Peano}\to{\mathbb N}
O5 0 1
OPNsucc
mc#1; \mathop{\rm succ}(#1)
O6 0 0
ONAT-to-PN
moi@a; {\mathbb N}\to{{\mathbb N}_{\rm Peano}}
O7 0 1
OTerminalString
hopl; terminals of #1
O8 0 1
OPreTraversal
hosl; pretraversal string of #1
O9 0 1
OPostTraversal
hosl; posttraversal string of #1
O10 0 1
OTerminalLanguage
hosl; language derivable from #1
O11 0 1
OPreTraversalLanguage
hosl; language of pretraversals derivable from #1
O12 0 1
OPostTraversalLanguage
hosl; language of posttraversals derivable from #1
V1 1
Vwith_terminals
x terminals
V2 1
Vwith_nonterminals
x nonterminals
V3 1
Vwith_useful_nonterminals
x useful nonterminals
#DYNKIN
M1 1
MDynkin_System
ha Dynkin system #0 of #1
Dynkin systems #0 of #1
O1 0 2
OseqIntersection
mol#1#2; \mathop{\rm seqIntersection}(#1,#2)
O2 0 1
Odisjointify
mol#1; \mathop{\rm disjointify} #1
O2 0 2
Odisjointify
mol#1#2; \mathop{\rm disjointify}(#1,#2)
O3 0 1
Ogenerated_Dynkin_System
mol#1; \mathop{\rm GenDynSys} #1
O4 0 2
ODynSys
mol#1#2; \mathop{\rm DynSys}(#1,#2)
V1 1
Vintersection_stable
n intersection stable
#ENDALG
O1 0 1
OUAEnd
mol#1; \mathop{\rm end}(#1)
O2 0 1
OUAEndComp
mol#1; \mathop{\rm Comp}(#1)
O3 0 1
OUAEndMonoid
mol#1; \mathop{\rm End}(#1)
O4 0 1
OMSAEnd
mol#1; \mathop{\rm end}(#1)
O5 0 1
OMSAEndComp
mol#1; \mathop{\rm Comp}(#1)
O6 0 1
OMSAEndMonoid
mol#1; \mathop{\rm End}(#1)
#ENS_1
O1 0 1
OMaps
mol@s; \mathop{\rm Maps} #1
O1 0 2
OMaps
mol@s#1#2; \mathop{\rm Maps}(#1,#2)
O2 0 1
Oid$
mol@s#1; \mathop{\rm id}(#1)
O3 0 1
OfDom
mow#1; \mathop{\rm Dom}_{#1}
O4 0 1
OfCod
mow#1; \mathop{\rm Cod}_{#1}
O5 0 1
OfComp
mow#1; {\cdot}_{#1}
O6 0 1
OfId
mow#1; \mathop{\rm Id}_{#1}
O7 0 1
OEns
mow#1; \mathop{\bf Ens}_{#1}
O8 0 1
Ohom?-
mol@s#1; \mathop{\rm hom}(#1,{-})
O8 0 2
Ohom?-
mo@s#1#2; \mathop{\rm hom}_{#1}(#2,{-})
O9 0 1
Ohom-?
mol@s#1; \mathop{\rm hom}({-},#1)
O9 0 2
Ohom-?
mo@s#1#2; \mathop{\rm hom}_{#1}({-},#2)
O10 0 1
Ohom??
mo@s#1; \mathop{\rm hom}_{#1}({-},{-})
O10 0 2
Ohom??
mo@s#1#2; \mathop{\rm hom}_{#1}^{#2}({-},{-})
V1 1
Vsurjective
a surjective
#ENTROPY1
O1 0 1
OVec2DiagMx
mol; \mathop{\rm Vec2DiagMx} #1
O2 0 1
OMx2FinS
mol; \mathop{\rm Mx2FinS} #1
O3 0 2
OFinSeq_log
mol(2)@s/1k#1; {\mathop{\overrightarrow{\rm log}}_{#1}#2}
O4 0 1
OInfor_FinSeq_of
mol@s/1k#1; {\mathop{\overrightarrow{\rm id\ log}}#1}
O5 0 1
OEntropy
mol; \mathop{\rm Entropy} #1
O6 0 1
OEntropy_of_Joint_Prob
hol; entropy of joint probability of #1
O7 0 1
OEntropy_of_Cond_Prob
hol; entropy of conditional probability of #1
R1 1 1
Rhas_onlyone_value_in
j only one value in #2
not only one value in #2
#EQREL_1
M1 1
MTolerance
ha tolerance #0 of #1
tolerances #0 of #1
M2 1
MEquivalence_Relation
hn equivalence relation #0 of #1
equivalence relations #0 of #1
M3 1
Ma_partition
ha partition #0 of #1
partitions #0 of #1
M4 1
MFamily-Class
ha family class #0 of #1
family classes #0 of #1
M5 1
MPart-Family
ha partition family #0 of #1
partition families #0 of #1
O1 0 1
Onabla
mow/1k#1; \nabla_{#1}
O2 0 1
O"\/"
mol@s; \bigsqcup #1
O2 0 2
O"\/"
mol(1)@s; \bigsqcup_{#2} #1
O2 1 1
O"\/"
moi@a; #1 \sqcup #2
O3 0 1
OClass
mol@s; \mathop{\rm Classes} #1
O3 0 2
OClass
mow/1k#1#2; {\lbrack #2 \rbrack}_{#1}
O4 0 2
OEqClass
mol#1#2; \mathop{\rm EqClass}(#1,#2)
O5 0 1
OSmallestPartition
mol#1; \mathop{\rm SmallestPartition}(#1)
O6 0 1
OIntersection
mol@s; \mathop{\rm Intersection} #1
O6 0 3
OIntersection
mol#1#2#3; \mathop{\rm Intersection}(#1,#2,#3)
V1 1
Vpartition-membered
a partition-membered
#EQUATION
M1 1
MEqualSet
ha set #0 of equations of #1
sets #0 of equations of #1
O1 0 1
OSuperAlgebraSet
mol#1; \mathop{\rm SuperAlgebraSet}(#1)
O2 0 1
OTermAlg
mol#1; {\rm T}_{#1}(\mathbb N)
O3 0 1
OEquations
hopl#1; equations of #1
#EUCLID
K1 1 L1 vEUCLID
K|[
L]|
mc#1; \mathopen{\vert[} #1 \mathclose{]\vert}
K1 2 L1 vEUCLID
K|[
L]|
mc#1#2; [#1,\allowbreak #2]
K1 3 L1 vEUCLID
K|[
L]|
mc#1#2#3; [#1,\allowbreak #2, \allowbreak #3]
O1 0 0
Oabsreal
mow; |\square|_{\mathbb R}
O2 0 1
O0*
mc#1; \langle\underbrace{0,\dots,0}_{#1}\rangle
O2 0 2
O0*
mol#1#2; 0^{#2}_{#1}
O3 0 1
OPitag_dist
moq#1; \rho^{#1}
O4 0 1
OEuclid
moq#1; {\cal E}^{#1}
O5 0 1
OTOP-REAL
mo{qw}@s#1; {\cal E}^{#1}_{\rm T}
O6 0 1
O0.REAL
mow#1; 0_{{\cal E}^{#1}_{\rm T}}
#EUCLIDLP
O1 0 1
Oline_of_REAL
mol#1; \mathop{\rm Lines}({\cal R}^{#1})
O2 0 2
Odist_v
hol#1#2; dist_v(#1,#2)
O3 0 1
Oplane_of_REAL
mol#1; \mathop{\rm Planes}({\cal R}^{#1})
R1 2 0
Rare_coplane
hy #1 and #2 are coplanar
#1 and #2 are not coplanar
#EUCLID_3
O1 0 1
Ocpx2euc
mol#1; \mathop{\rm cpx2euc}(#1)
O2 0 1
Oeuc2cpx
mol#1; \mathop{\rm euc2cpx}(#1)
O3 0 3
OTriangle
mol#1#2#3; \mathop{\rm Triangle}(#1,#2,#3)
O4 0 3
Oclosed_inside_of_triangle
mol#1#2#3; \mathop{\rm ClInsideOfTriangle}(#1,#2,#3)
O5 0 3
Oinside_of_triangle
mol#1#2#3; \mathop{\rm InsideOfTriangle}(#1,#2,#3)
O6 0 3
Ooutside_of_triangle
mol#1#2#3; \mathop{\rm OutsideOfTriangle}(#1,#2,#3)
O7 0 3
Oplane
mol#1#2#3; \mathop{\rm Plane}(#1,#2,#3)
O8 0 4
Otricord1
mol#1#2#3#4; \mathop{\rm tricord1}(#1,#2,#3,#4)
O9 0 4
Otricord2
mol#1#2#3#4; \mathop{\rm tricord2}(#1,#2,#3,#4)
O10 0 4
Otricord3
mol#1#2#3#4; \mathop{\rm tricord2}(#1,#2,#3,#4)
O11 0 3
Otrcmap1
mol#1#2#3; \mathop{\rm trcmap1}(#1,#2,#3)
O12 0 3
Otrcmap2
mol#1#2#3; \mathop{\rm trcmap2}(#1,#2,#3)
O13 0 3
Otrcmap3
mol#1#2#3; \mathop{\rm trcmap3}(#1,#2,#3)
R1 2 0
Rare_lindependent2
h #1 and #2 are linearly independent
#1 and #2 are linearly dependent
R2 2 0
Rare_ldependent2
h #1 and #2 are linearly dependent
#1 and #2 are linearly independent
#EUCLID_4
O1 0 1
OTPn2Rn
mol#1; \mathop{\rm TPn2Rn}(#1)
#EUCLID_5
K1 3 L1 vEUCLID_5
K|{
L}|
mc#1#2#3; \langle| #1,#2,#3 |\rangle
O1 1 1
O<X>
moi@m; #1\times #2
#EUCLID_6
O1 0 3
Othe_area_of_polygon3
hol#1#2#3; area of $\mathop{\vartriangle}(#1,#2,#3)$
O2 0 3
Othe_perimeter_of_polygon3
hol#1#2#3; perimeter of $\mathop{\vartriangle}(#1,#2,#3)$
#EUCLID_7
M1 1
MOrthogonal_Basis
hn orthogonal basis #0 of #1
orthogonal bases #0 of #1
O1 0 1
OL_Span
hol; linear span of #1
O2 0 1
Oaccum
mol; \mathop{\rm accum} #1
O3 0 1
OProjFinSeq
mol; \mathop{\rm ProjFinSeq} #1
O4 0 1
ORN_Base
mol; \mathop{\rm{\mathbb R}N\hbox{-}Base} #1
V1 1
VR-orthogonal
n \mbR-orthogonal
V2 1
VR-normal
n \mbR-normal
V3 1
VR-orthonormal
n \mbR-orthonormal
V4 1
Vorthogonal_basis
n orthogonal basis
V5 1
Vlinear_manifold
b linear manifold
#EUCLID_8
O1 0 0
O<e1>
mow; e_1
O2 0 0
O<e2>
mow; e_2
O3 0 0
O<e3>
mow; e_3
O4 0 3
OVFunc
mol#1#2#3; \mathop{\rm VFunc}(#1,#2,#3)
O5 0 4
OVFuncdiff
mol#1#2#3#4; \mathop{\rm VFuncdiff}(#1,#2,#3,#4)
#EUCLID_9
O1 0 2
Omax_diff_index
mol#1#2; \mathop{\rm max\hbox{-}diff\hbox{-}index}(#1,#2)
O2 0 2
OIntervals
mol#1#2; \mathop{\rm Intervals}(#1,#2)
O3 0 2
OOpenHypercube
mol#1#2; \mathop{\rm OpenHypercube}(#1,#2)
O4 0 1
OOpenHypercubes
mol; \mathop{\rm OpenHypercubes} #1
#EUCLMETR
V1 1
VEuclidean
n Euclidean
V2 1
VHomogeneous
a homogeneous
#EULER_1
O1 0 1
OEuler
mol#1; \mathop{\rm Euler} #1
#E_SIEC
G1 3
GG_Net
mc#1#2#3; \langle #1, #2, #3\rangle
J1 1
GG_Net
hol#1; G-net of #1
L1 0
GG_Net
ha G-net structure #0
G-net structures #0
M1 0
Mgg_net
ha G-net #0
G-nets #0
M2 0
Me_net
hn E-net #0
E-nets #0
O1 0 0
Oempty_e_net
mow; \mathop{\rm empty}_e
O2 0 1
OTempty_e_net
mol#1; \mathop{\rm Tempty}_e(#1)
O3 0 1
OPempty_e_net
mol#1; \mathop{\rm Pempty}_e(#1)
O4 0 1
OPsingle_e_net
mol#1; \mathop{\rm Psingle}_e(#1)
O5 0 1
OTsingle_e_net
mol#1; \mathop{\rm Tsingle}_e(#1)
O6 0 2
OPTempty_e_net
mol#1#2; \mathop{\rm PTempty}_e(#1,#2)
O7 0 1
Oe_Places
mol#1; \mathop{\rm Places}_e(#1)
O8 0 1
Oe_Transitions
mol#1; \mathop{\rm Transitions}_e(#1)
O9 0 1
Oe_Flow
mol#1; \mathop{\rm Flow}_e(#1)
O12 0 1
Oe_pre
mol#1; \mathop{\rm pre}_e(#1)
O13 0 1
Oe_post
mol#1; \mathop{\rm post}_e(#1)
O14 0 1
Oe_shore
mol#1; \mathop{\rm shore}_e(#1)
O15 0 1
Oe_prox
mol#1; \mathop{\rm prox}_e(#1)
O16 0 1
Oe_flow
mol#1; \mathop{\rm flow}_e(#1)
O18 0 1
Oe_entrance
mol#1; \mathop{\rm entrance}_e(#1)
O19 0 1
Oe_escape
mol#1; \mathop{\rm escape}_e(#1)
O22 0 1
Oe_adjac
mol#1; \mathop{\rm adjac}_e(#1)
O29 0 1
Os_pre
mol#1; \mathop{\rm pre}_s(#1)
O30 0 1
Os_post
mol#1; \mathop{\rm post}_s(#1)
U1 1
Uentrance
honl#1; entrance of #1
entrance
U2 1
Uescape
honl#1; escape of #1
escape
V1 1
VGG
a GG
V2 1
VEE
n EE
#FACIRC_1
O1 0 0
Oor3
mow; \mathop{\rm or}_3
O2 0 4
O2GatesCircStr
mol#1#2#3#4; \mathop{\rm 2GatesCircStr}(#1,#2,#3,#4)
O3 0 4
O2GatesCircOutput
mol#1#2#3#4; \mathop{\rm 2GatesCircOutput}(#1,#2,#3,#4)
O4 0 4
O2GatesCircuit
mol#1#2#3#4; \mathop{\rm 2GatesCircuit}(#1,#2,#3,#4)
O5 0 3
OBitAdderOutput
mol#1#2#3; \mathop{\rm BitAdderOutput}(#1,#2,#3)
O6 0 3
OBitAdderCirc
mol#1#2#3; \mathop{\rm BitAdderCirc}(#1,#2,#3)
O7 0 3
OMajorityIStr
mol#1#2#3; \mathop{\rm MajorityIStr}(#1,#2,#3)
O8 0 3
OMajorityStr
mol#1#2#3; \mathop{\rm MajorityStr}(#1,#2,#3)
O9 0 3
OMajorityICirc
mol#1#2#3; \mathop{\rm MajorityICirc}(#1,#2,#3)
O10 0 3
OMajorityOutput
mol#1#2#3; \mathop{\rm MajorityOutput}(#1,#2,#3)
O11 0 3
OMajorityCirc
mol#1#2#3; \mathop{\rm MajorityCirc}(#1,#2,#3)
O12 0 3
OBitAdderWithOverflowStr
mol#1#2#3; \mathop{\rm BitAdderWithOverflowStr}(#1,#2,#3)
O13 0 3
OBitAdderWithOverflowCirc
mol#1#2#3; \mathop{\rm BitAdderWithOverflowCirc}(#1,#2,#3)
R1 1 1
Ris_stable_at
i stable at #2
not stable at #2
V1 1
Vpair
a pair
V2 1
Vwith_pair
x a pair
V3 1
Vwithout_pairs
xn no pairs
V4 1
Vnonpair-yielding
a nonpair yielding
#FACIRC_2
O1 0 1
OSingleMSS
mol; \mathop{\rm SingleMSS} #1
O2 0 1
OSingleMSA
mol; \mathop{\rm SingleMSA} #1
O3 1 2
O-BitAdderStr
moi#2#3; #1{\rm\hbox{-}BitAdderStr}(#2,#3)
O4 1 2
O-BitAdderCirc
moi#2#3; #1{\rm\hbox{-}BitAdderCirc}(#2,#3)
O5 1 2
O-BitMajorityOutput
moi#2#3; #1{\rm\hbox{-}BitMajorityOutput}(#2,#3)
O6 2 2
O-BitAdderOutput
moi#1#2#3#4; (#1,#2){\rm\hbox{-}BitAdderOutput}(#3,#4)
#FCONT_1
R1 1 1
Ris_continuous_in
i continuous in #2
not continuous in #2
V1 1
VLipschitzian
a Lipschitzian
#FCONT_2
V1 1
Vuniformly_continuous
n uniformly continuous
#FDIFF_1
M1 0
MREST
ha rest #0
rests #0
M1 2
MREST
ha rest #0 of #1,#2
rests #0 of #1,#2
M2 0
MLINEAR
ha linear function #0
linear functions #0
O1 0 1
Odiff
moi@a/1k#1; \square\setminus_{#1}\square
O1 0 2
Odiff
mor@s/1q#2; #1'(#2)
O1 0 3
Odiff
mcl@s/3k#1#2#3; \mathop{\rm diff}_{#3}(#1,#2)
O2 1 1
O`|
mow/2l@m#2; #1'_{\restriction #2}
R1 1 1
Ris_differentiable_in
i differentiable in #2
not differentiable in #2
R2 1 1
Ris_differentiable_on
i differentiable on #2
not differentiable on #2
R2 1 2
Ris_differentiable_on
i differentiable #2 times on #3
not differentiable #2 times on #3
V1 1
Vconvergent_to_0
a convergent to 0
V2 1
VREST-like
a rest-like
V3 1
Vlinear
a linear
V4 1
Vdifferentiable
a differentiable
#FDIFF_3
O1 0 2
OLdiff
mor(1)@9#2; #1'_-(#2)
O2 0 2
ORdiff
mor(1)@9#2; #1'_+(#2)
R1 1 1
Ris_Lcontinuous_in
i left continuous in #2
not left continuous in #2
R2 1 1
Ris_Rcontinuous_in
i right continuous in #2
not right continuous in #2
R3 1 1
Ris_right_differentiable_in
i right differentiable in #2
not right differentiable in #2
R4 1 1
Ris_left_differentiable_in
i left differentiable in #2
not left differentiable in #2
#FF_SIEC
O1 0 2
OPTempty_f_net
mol#1#2; \mathop{\rm PTempty}_f(#1,#2)
O2 0 1
OTempty_f_net
mol#1; \mathop{\rm Tempty}_f(#1)
O3 0 1
OPempty_f_net
mol#1; \mathop{\rm Pempty}_f(#1)
O4 0 1
OTsingle_f_net
mol#1; \mathop{\rm Tsingle}_f(#1)
O5 0 1
OPsingle_f_net
mol#1; \mathop{\rm Psingle}_f(#1)
O6 0 0
Oempty_f_net
mow; \mathop{\rm empty}_f
O7 0 1
Of_enter
mol#1; \mathop{\rm enter}_f(#1)
O8 0 1
Of_exit
mol#1; \mathop{\rm exit}_f(#1)
O9 0 1
Of_prox
mol#1; \mathop{\rm prox}_f(#1)
O10 0 1
Of_flow
mol#1; \mathop{\rm flow}_f(#1)
O11 0 1
Of_places
mol#1; \mathop{\rm places}_f(#1)
O12 0 1
Of_transitions
mol#1; \mathop{\rm transitions}_f(#1)
O13 0 1
Of_pre
mol#1; \mathop{\rm pre}_f(#1)
O14 0 1
Of_post
mol#1; \mathop{\rm post}_f(#1)
O15 0 1
Of_entrance
mol#1; \mathop{\rm entrance}_f(#1)
O16 0 1
Of_escape
mol#1; \mathop{\rm escape}_f(#1)
O17 0 1
Of_circulation
mol#1; \mathop{\rm circulation}_f(#1)
O18 0 1
Of_adjac
mol#1; \mathop{\rm adjac}_f(#1)
#FIB_FUSC
O1 0 0
OFib_Program
hos@a; program computing Fib
O2 0 1
OFusc'
mol#1; \mathop{\rm Fusc'}(#1)
O3 0 0
OFusc_Program
hos@a; program computing Fusc
#FIB_NUM
O1 0 0
Otau
mc; \tau
O2 0 0
Otau_bar
mc; \overline{\tau}
#FIB_NUM2
O1 0 0
OFIB
mcl; \mathop{\rm FIB}
O2 0 0
OEvenNAT
mcl; {{\mathbb N}_{\rm even}}
O3 0 0
OOddNAT
mcl; {{\mathbb N}_{\rm odd}}
O4 0 1
OEvenFibs
mcl#1; \mathop{\rm EvenFibs}(#1)
O5 0 1
OOddFibs
mcl#1; \mathop{\rm OddFibs}(#1)
#FIB_NUM3
O1 0 1
OLucas
mcl#1; \mathop{\rm Luc}(#1)
O2 0 3
OGenFib
mcl#1#2#3; \mathop{\rm GFib}(#1,#2,#3)
#FILEREC1
M1 1
MFile
ha file #0 of #1
files #0 of #1
R1 1 2
Ris_a_record_of
iy a record of #2 and #3
not a record of #2 and #3
#FILTER_0
K1 1 L1 vFILTER_0
K<.
L.)
mc#1; [#1)
M1 0
MI_Lattice
hn implicative lattice #0
implicative lattices #0
O1 0 1
Olatt
mow/1k#1; {\mathbb L}_{#1}
O1 0 2
Olatt
mol{qrw}#1#2; {\mathbb L}^{#1}_{#2}
O2 0 1
Oequivalence_wrt
mow/1k#1; {\equiv}_{#1}
R1 2 1
Rare_equivalence_wrt
m #1 \mathrel{{\equiv}_{#3}} #2
#1 \mathrel{{\not\equiv}_{#3}} #2
V1 1
Vimplicative
n implicative
#FILTER_1
O1 1 1
O/\/
mow/2l@s#2; #1_{/#2}
O2 0 1
OLattRel
mcl@s#1; \mathop{\rm LattRel}(#1)
#FILTER_2
K1 1 L1 vFILTER_2
K(.
L.>
mc#1; (#1]
R1 1 0
Ris_max-ideal
i maximal
not maximal 
#FINSEQOP
O1 0 1
Othe_inverseOp_wrt
hol; \inverseop #1
R1 1 1
Ris_an_inverseOp_wrt
i an inverse operation w.r.t. #2
not an inverse operation w.r.t. #2
V1 1
Vhaving_an_inverseOp
h inverse operation
#FINSEQ_1
K1 1 L1 vFINSEQ_1
K<*
L*>
mc#1; \langle #1\rangle
K1 2 L1 vFINSEQ_1
K<*
L*>
mc#1#2; \langle #1,\allowbreak #2\rangle
K1 3 L1 vFINSEQ_1
K<*
L*>
mc#1#2#3; \langle #1,\allowbreak #2,\allowbreak #3\rangle
K1 4 L1 vFINSEQ_1
K<*
L*>
mc#1#2#3#4; \langle #1,\allowbreak #2,\allowbreak #3,\allowbreak #4\rangle
K1 5 L1 vFINSEQ_1
K<*
L*>
mc#1#2#3#4#5; \langle #1,\allowbreak #2,\allowbreak #3,\allowbreak #4,\allowbreak #5\rangle
M1 0
MFinSequence
ha finite sequence #0
finite sequences #0
M1 1
MFinSequence
ha finite sequence #0 of elements of #1
finite sequences #0 of elements of #1
M2 0
MFinSubsequence
ha finite subsequence #0
finite subsequences #0
O1 0 1
OSeg
mol@s; \mathop{\rm Seg} #1
O1 0 2
OSeg
mol#1#2; \mathop{\rm Seg}(#1,#2)
O2 0 1
Olen
mol@s; \mathop{\rm len} #1
O2 0 2
Olen
mol#1#2; \mathop{\rm len}(#1,#2)
O3 0 0
O<*>
mc; \varepsilon
O3 0 1
O<*>
mow/1k; \varepsilon_{#1}
O4 0 1
OSgm
mol@s; \mathop{\rm Sgm} #1
O5 0 1
OSeq
mol@s; \mathop{\rm Seq} #1
O6 0 0
O[*]
mc; [*]
O6 1 0
O[*]
moq; #1^\ast
O6 1 1
O[*]
moi@m; #1\otimes #2
V1 1
VFinSequence-like
a finite sequence-like
V2 1
VFinSubsequence-like
a finite subsequence-like
V3 2
V-long
a #1-long
V4 1
VFinSequence-membered
a finite sequence-membered
#FINSEQ_2
M1 1
MFinSequenceSet
ha set #0 of finite sequences of #1
sets #0 of finite sequences of #1
M2 1
MFinSequence-DOMAIN
ha non empty set #0 of finite sequences of #1
non empty sets #0 of finite sequences of #1
M3 2
MTuple
ha #1-tuple #0 of #2
#1-tuples #0 of #2
O1 0 1
Oidseq
mol#1; \mathop{\rm idseq}(#1)
O2 1 1
O|->
mo@m; #1 \mapsto #2
O3 1 1
O-tuples_on
moq(2)/1m#1; #2^{#1}
#FINSEQ_3
O1 0 2
ODel
mow(1)/2l@w#2; #1_{\restriction #2}
O1 0 3
ODel
mol#1#2#3; \mathop{\rm Del}(#1,#2,#3)
#FINSEQ_4
O1 1 1
O<-
moi@s#2; #1 \mathclose{^{-1}}(#2)
O1 2 1
O<-
mow#2#3; #1_{#2\leftarrow #3}
O2 1 1
O..
moi@s; #1 \looparrowleft #2
O2 1 2
O..
mor@s#2#3; #1(#2)(#3)
O2 1 3
O..
mor(1)@9#2#3#4; #1(#2,#3)(#4)
O3 1 1
O-|
mox@w; #1 \leftarrow #2
O4 1 1
O|--
mox@w; #1 \rightarrow #2
O4 1 2
O|--
mow#2#3; #1_{\llangle #2,#3\rrangle}
R1 1 1
Ris_one-to-one_at
i one-to-one at #2
not one-to-one at #2
R2 1 1
Rjust_once_values
h #1 yields #2 just once
#1 yields #2 not once
#FINSEQ_5
O1 1 1
O-:
moi; #1\mathbin{{-}{:}}#2
O2 1 1
O:-
moi; #1\mathbin{{:}{-}}#2
O3 0 1
ORev
mol#1; \mathop{\rm Rev}(#1)
O4 0 3
OIns
mol#1#2#3; \mathop{\rm Ins}(#1,#2,#3)
#FINSEQ_6
O1 0 1
ORotate
mol; \mathop{\rm Rotate} #1
O1 0 2
ORotate
mox@w; #1 \circlearrowleft #2
V1 1
Vcircular
a circular
#FINSEQ_8
O1 0 3
Osmid
mol#1#2#3; \mathop{\rm smid}(#1,#2,#3)
O2 0 2
Oovlpart
mol#1#2; \mathop{\rm ovlpart}(#1,#2)
O3 0 2
Oovlcon
mol#1#2; \mathop{\rm ovlcon}(#1,#2)
O4 0 2
Oovlldiff
mol#1#2; \mathop{\rm ovlldiff}(#1,#2)
O5 0 2
Oovlrdiff
mol#1#2; \mathop{\rm ovlrdiff}(#1,#2)
O6 0 3
Oinstr
mol#1#2; \mathop{\rm instr}(#1,#2)
O7 0 2
Oaddcr
mol#1#2; \mathop{\rm addcr}(#1,#2)
R1 1 0
Rseparates_uniquely
h #1 separates uniquely
#1 does not separate uniquely
R2 1 2
Ris_substring_of
i a substring of #2
not a substring of #2
R3 1 1
Ris_preposition_of
i a preposition of #2
not a preposition of #2
R4 1 1
Ris_postposition_of
i a postposition of #2
not a postposition of #2
R5 1 1
Ris_terminated_by
i terminated by #2
not terminated by #2
#FINSET_1
V1 1
Vfinite
a finite
V2 1
Vinfinite
n infinite
V3 1
Vfinite-yielding
a finite-yielding
V4 1
Vcentered
a centered
#FINSOP_1
O1 1 1
O"**"
moi#1; #1 \odot #2
O2 0 1
Ofindom
mol@s; \mathop{\rm dom}_f #1
#FINSUB_1
M1 1
MFinite_Subset
ha finite subset #0 of #1
finite subsets #0 of #1
O1 0 1
OFin
mol@s; \mathop{\rm Fin} #1
O1 0 2
OFin
mol#1#2; \mathop{\rm Fin}(#1,#2)
V1 1
Vcup-closed
a $\cup$-closed
V2 1
Vcap-closed
a $\cap$-closed
V3 1
Vdiff-closed
a diff-closed
V4 1
VpreBoolean
a preboolean
#FINTOPO2
G1 2
GFMT_Space_Str
mc#1#2; \langle #1,#2 \rangle
J1 1
GFMT_Space_Str
hol#1; formal topological space of #1
L1 0
GFMT_Space_Str
ha formal topological space #0
formal topological spaces #0
O1 0 3
OP_1
mol#1#2#3; \mathop{\rm P_1}(#1,#2,#3)
O2 0 3
OP_2
mol#1#2#3; \mathop{\rm P_2}(#1,#2,#3)
O3 0 2
OP_0
mol#1#2; \mathop{\rm P_0}(#1,#2)
O4 0 2
OP_A
mol#1#2; \mathop{\rm P_A}(#1,#2)
O5 0 2
OP_e
mol#1#2; \mathop{\rm P_e}(#1,#2)
O6 0 1
OU_FMT
mol@s#1; U_{F}(#1)
O7 0 1
ONeighSp
mol#1; \mathop{\rm NeighSp} #1
O8 1 0
O^Fodelta
moq#1; #1^{F\delta}
O9 1 0
O^Fob
moq#1; #1^{F_b}
O10 1 0
O^Foi
moq#1; #1^{F_i}
O11 1 0
O^Fos
moq#1; #1^{F_s}
O12 1 0
O^Fon
moq#1; #1^{F_{on}}
O13 1 0
O^Fodel_i
moq#1; #1^{F\delta_{i}}
O14 1 0
O^Fodel_o
moq#1; #1^{F\delta_{o}}
U1 1
UBNbd
hosl#1; Neighbour-map of #1
Neighbour-map
V1 1
VFo_filled
a filled
V2 1
VFo_open
n open
V3 1
VFo_closed
a closed
#FINTOPO3
O1 1 0
O^d
moq#1; #1^{d}
O2 0 1
OFcl
mol#1; \mathop{\rm Fcl}(#1)
O2 0 2
OFcl
mol#1#2; \mathop{\rm Fcl}(#1,#2)
O3 0 1
OFint
mol#1; \mathop{\rm Fint}(#1)
O3 0 2
OFint
mol#1#2; \mathop{\rm Fint}(#1,#2)
O4 0 1
OFinf
mol#1; \mathop{\rm Finf}(#1)
O4 0 2
OFinf
mol#1#2; \mathop{\rm Finf}(#1,#2)
O5 0 1
OFdfl
mol#1; \mathop{\rm Fdfl}(#1)
O5 0 2
OFdfl
mol#1#2; \mathop{\rm Fdfl}(#1,#2)
R1 2 0
Rare_mutually_symmetric
h #1, #2 are mutually symmetric
#1, #2 are not mutually symmetric
#FINTOPO4
O1 0 1
ONbdl1
mol#1; \mathop{\rm Nbdl1}(#1)
O2 0 1
OFTSL1
mol#1; \mathop{\rm FTSL1}(#1)
O3 0 1
ONbdc1
mol#1; \mathop{\rm Nbdc1}(#1)
O4 0 1
OFTSC1
mol#1; \mathop{\rm FTSC1}(#1)
R1 1 1
Ris_continuous
h #1 is continuous #2
#1 is not continuous #2
#FINTOPO5
O1 0 2
ONbdl2
mol#1#2; \mathop{\rm Nbdl2}(#1,#2)
O2 0 2
OFTSL2
mol#1#2; \mathop{\rm FTSL2}(#1,#2)
O3 0 2
ONbds2
mol#1#2; \mathop{\rm Nbds2}(#1,#2)
O4 0 2
OFTSS2
mol#1#2; \mathop{\rm FTSS2}(#1,#2)
#FINTOPO6
R1 1 3
Ris_minimum_path_in
i minimum path in #2 between #3 and #4
not minimum path in #2 between #3 and #4
V1 1
Vinv_continuous
n inversely continuous
#FIN_TOPO
O1 0 1
OU_FT
mol@s#1; U(#1)
O1 0 2
OU_FT
mol@s#1#2; U(#1,#2)
O2 0 1
OSinglRel
mol; \mathop{\rm SinglRel} #1
O3 0 0
OFT{0}
mow; \mathop{\rm FT}_{\{0\}}
O4 1 0
O^delta
moq; #1^\delta
O5 1 0
O^deltai
moq; #1^{\delta_i}
O6 1 0
O^deltao
moq; #1^{\delta_o}
O7 1 0
O^i
moq; #1^{i}
O8 1 0
O^b
moq; #1^{b}
O9 1 0
O^s
moq; #1^{s}
O10 1 0
O^n
moq; #1^{n}
O11 1 0
O^f
moq; #1^{f}
O12 1 0
O^fb
moq; #1^{f_b}
O13 1 0
O^fi
moq; #1^{f_i}
V1 1
Vfilled
a filled
#FLANG_1
O1 0 1
OLex
mol; \mathop{\rm Lex} #1
#FLANG_3
O1 1 1
O|^..
moi; {#1}^{#2,..}
#FRECHET
O1 0 1
OBalls
mol; \mathop{\rm Balls} #1
O2 0 0
OREAL?
mol; {\mathbb R}^1_{\hbox{$/\mathbb N$}}
R1 1 1
Ris_convergent_to
i convergent to #2
not convergent to #2
V1 1
Vfirst-countable
a first-countable
V2 1
VFrechet
a Frechet
V3 1
Vsequential
a sequential
#FRECHET2
O1 0 1
OCl_Seq
mol; \mathop{\rm Cl}_{\rm Seq} #1
#FREEALG
O1 0 2
Ooper
mol#1#2; \mathop{\rm oper}(#1,#2)
O2 0 2
ODTConUA
mol#1#2; \mathop{\rm DTConUA}(#1,#2)
O3 0 3
OFreeOpNSG
mol#1#2#3; \mathop{\rm FreeOpNSG}(#1,#2,#3)
O4 0 2
OFreeOpSeqNSG
mol#1#2; \mathop{\rm FreeOpSeqNSG}(#1,#2)
O5 0 2
OFreeUnivAlgNSG
mol#1#2; \mathop{\rm FreeUnivAlgNSG}(#1,#2)
O6 0 2
OFreeGenSetNSG
mol#1#2; \mathop{\rm FreeGenSetNSG}(#1,#2)
O7 0 3
OFreeOpZAO
mol#1#2#3; \mathop{\rm FreeOpZAO}(#1,#2,#3)
O8 0 2
OFreeOpSeqZAO
mol#1#2; \mathop{\rm FreeOpSeqZAO}(#1,#2)
O9 0 2
OFreeUnivAlgZAO
mol#1#2; \mathop{\rm FreeUnivAlgZAO}(#1,#2)
O10 0 2
OFreeGenSetZAO
mol#1#2; \mathop{\rm FreeGenSetZAO}(#1,#2)
V1 1
Vdisjoint_with_NAT
a disjoint with $\mathbb{N}$
V2 1
Vwithout_zero
a without zero
#FSCIRC_1
O1 0 3
OBitSubtracterOutput
mol#1#2#3; \mathop{\rm BitSubtracterOutput}(#1,#2,#3)
O2 0 3
OBitSubtracterCirc
mol#1#2#3; \mathop{\rm BitSubtracterCirc}(#1,#2,#3)
O3 0 3
OBorrowIStr
mol#1#2#3; \mathop{\rm BorrowIStr}(#1,#2,#3)
O4 0 3
OBorrowStr
mol#1#2#3; \mathop{\rm BorrowStr}(#1,#2,#3)
O5 0 3
OBorrowICirc
mol#1#2#3; \mathop{\rm BorrowICirc}(#1,#2,#3)
O6 0 3
OBorrowOutput
mol#1#2#3; \mathop{\rm BorrowOutput}(#1,#2,#3)
O7 0 3
OBorrowCirc
mol#1#2#3; \mathop{\rm BorrowCirc}(#1,#2,#3)
O8 0 3
OBitSubtracterWithBorrowStr
mol#1#2#3; \mathop{\rm BitSubtracterWithBorrowStr}(#1,#2,#3)
O9 0 3
OBitSubtracterWithBorrowCirc
mol#1#2#3; \mathop{\rm BitSubtracterWithBorrowCirc}(#1,#2,#3)
#FSCIRC_2
O1 1 2
O-BitSubtracterStr
moi#2#3; #1{\rm\hbox{-}BitSubtracterStr}(#2,#3)
O2 1 2
O-BitSubtracterCirc
moi#2#3; #1{\rm\hbox{-}BitSubtracterCirc}(#2,#3)
O3 1 2
O-BitBorrowOutput
moi#2#3; #1{\rm\hbox{-}BitBorrowOutput}(#2,#3)
O4 2 2
O-BitSubtracterOutput
moi#1#2#3#4; (#1,#2){\rm\hbox{-}BitSubtracterOutput}(#3,#4)
#FSM_1
G1 3
GFSM
mc#1#2#3; \langle #1,#2,#3 \rangle
G2 4
GMealy-FSM
mol#1#2#3#4; \mathop{\rm Mealy\hbox{-}FSM}\langle #1,#2,#3,#4 \rangle
G3 4
GMoore-FSM
mc#1#2#3#4; \langle #1,#2,#3,#4 \rangle
J1 1
GFSM
hol#1; FSM of #1
J2 1
GMealy-FSM
hol#1; Mealy-FSM of #1
J3 1
GMoore-FSM
hol#1; Moore-FSM of #1
L1 1
GFSM
ha FSM #0 over #1
FSM #0 over #1
L2 2
GMealy-FSM
ha Mealy-FSM #0 over #1,#2
Mealy-FSM #0 over #1,#2
L3 2
GMoore-FSM
ha Moore-FSM #0 over #1,#2
Moore-FSM #0 over #1,#2
M1 1
MState
ha state #0 of #1
states #0 of #1
O1 1 1
O-succ_of
moi#2; #1{\rm\hbox{-}succ}(#2)
O1 1 2
O-succ_of
moi#2#3; #1{\rm\hbox{-}succ}_{#3}(#2)
O2 2 0
O-admissible
mor#1#2; (#1,#2){\rm\hbox{-}admissible}
O3 1 1
Oleads_to_under
moi#1; #2{\rm\hbox{-}succ}(#1)
O4 2 0
O-response
mor#1#2; (#1,#2){\rm\hbox{-}response}
O5 1 1
O-eq_states_EqR
moi#2; #1{\rm\hbox{-}EqS\hbox{-}Rel}(#2)
O6 1 1
O-eq_states_partition
moi#2; #1{\rm\hbox{-}EqS\hbox{-}Part}(#2)
O7 0 1
Ofinal_states_partition
moi#1; \mathop{\rm final\hbox{-}Partition}(#1)
O8 2 0
O-succ_class
mol#1#2; (#1,#2){\rm\hbox{-}C\hbox{-}succ}
O9 2 0
O-class_response
mol#1#2; (#1,#2){\rm\hbox{-}C\hbox{-}response}
O10 0 1
Othe_reduction_of
hol#1; reduction of #1
O11 0 1
OaccessibleStates
mol#1; \mathop{\rm accessible\hbox{-}States}(#1)
O12 1 1
O-Mealy_union
mol#1#2; \mathop{\rm Mealy\hbox{-}U}(#1,#2)
R1 2 1
R-leads_to
m #1 \stackrel{#2}{\longrightarrow} #3
#1 \stackrel{#2}{\not\longrightarrow} #3
R2 1 1
Ris_admissible_for
i admissible for #2
not admissible for #2
R3 1 1
Ris_similar_to
i similar to #2
not similar to #2
R4 2 0
R-are_equivalent
h #1 and #2 are equivalent
#1 and #2 are not equivalent
R5 1 2
R-equivalent
h #2 and #3 are #1-equivalent
#2 and #3 are not #1-equivalent
R6 2 0
R-are_isomorphic
h #1 and #2 are isomorphic
#1 and #2 are not isomorphic
U1 1
UTran
hosl#1; transition of #1
transition
U2 1
UInitS
honl#1; initial state of #1
initial state
U3 1
UOFun
honl#1; output function of #1
output function
V1 1
Vreduced
a reduced
V2 1
Vaccessible
n accessible
#FSM_2
G1 4
GSM_Final
mc#1#2#3#4; \langle #1,#2,#3,#4 \rangle
G2 5
GMoore-SM_Final
mc#1#2#3#4#5; \langle #1,#2,#3,#4,#5 \rangle
J1 1
GSM_Final
hol#1; state machine of #1 with final states
J2 1
GMoore-SM_Final
Hol#1; Moore state machine of #1 with final states
L1 1
GSM_Final
ha state machine #0 over #1 with final states
state machines #0 over #1 with final states
L2 2
GMoore-SM_Final
ha Moore state machine #0 over #1 and #2 with final states
Moore state machines #0 over #1 and #2 with final states
O1 0 2
OGEN
mol#1#2; \mathop{\rm GEN}(#1,#2)
O2 1 3
O-TwoStatesMooreSM
moi#2#3#4; #1 \mathop{\rm\hbox{-}TwoStatesMooreSM}(#2,#3,#4)
R1 1 1
Ris_accessible_via
i accessible via #2
not accessible via #2
R2 1 1
Rleads_to_final_state_of
h #1 leads to final state of #2
#1 does not lead to final state of #2
R3 1 2
Ris_result_of
i a result of #2 in #3
not a result of #2 in #3
U1 1
UFinalS
hopl#1; final states of #1
final states
V1 1
Vcalculating_type
a calculating type
#FSM_3
G1 3
Gsemiautomaton
mc#1#2#3; \langle #1,#2,#3 \rangle
G2 4
Gautomaton
mc#1#2#3#4; \langle #1,#2,#3,#4 \rangle
J1 1
Gsemiautomaton
hol#1; semiautomaton of #1
J2 1
Gautomaton
hol#1; automaton of #1
L1 1
Gsemiautomaton
ha semiautomaton #0 over #1
semiautomata #0 over #1
L2 1
Gautomaton
hn automaton #0 over #1
automata #0 over #1
O1 0 1
O_bool
mol; \mathop{\rm bool} #1
O2 0 1
Oleft-Lang
mol; \mathop{\rm left\hbox{-}Lang} #1
O3 0 1
Oright-Lang
mol; \mathop{\rm right\hbox{-}Lang} #1
O4 0 2
Ochop
mol#1#2; \mathop{\rm chop}(#1,#2)
#FTACELL1
O1 0 5
OBitFTA0Str
mol#1#2#3#4#5; \mathop{\rm BitFTA0Str}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O2 0 5
OBitFTA0Circ
mol#1#2#3#4#5; \mathop{\rm BitFTA0Circ}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O3 0 5
OBitFTA0CarryOutput
mol#1#2#3#4#5; \mathop{\rm BitFTA0CarryOutput}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O4 0 5
OBitFTA0AdderOutputI
mol#1#2#3#4#5; \mathop{\rm BitFTA0AdderOutputI}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O5 0 5
OBitFTA0AdderOutputP
mol#1#2#3#4#5; \mathop{\rm BitFTA0AdderOutputP}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O6 0 5
OBitFTA0AdderOutputQ
mol#1#2#3#4#5; \mathop{\rm BitFTA0AdderOutputQ}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O7 0 5
OBitFTA1Str
mol#1#2#3#4#5; \mathop{\rm BitFTA1Str}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O8 0 5
OBitFTA1Circ
mol#1#2#3#4#5; \mathop{\rm BitFTA1Circ}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O9 0 5
OBitFTA1CarryOutput
mol#1#2#3#4#5; \mathop{\rm BitFTA1CarryOutput}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O10 0 5
OBitFTA1AdderOutputI
mol#1#2#3#4#5; \mathop{\rm BitFTA1AdderOutputI}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O11 0 5
OBitFTA1AdderOutputP
mol#1#2#3#4#5; \mathop{\rm BitFTA1AdderOutputP}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O12 0 5
OBitFTA1AdderOutputQ
mol#1#2#3#4#5; \mathop{\rm BitFTA1AdderOutputQ}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O13 0 5
OBitFTA2Str
mol#1#2#3#4#5; \mathop{\rm BitFTA2Str}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O14 0 5
OBitFTA2Circ
mol#1#2#3#4#5; \mathop{\rm BitFTA2Circ}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O15 0 5
OBitFTA2CarryOutput
mol#1#2#3#4#5; \mathop{\rm BitFTA2CarryOutput}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O16 0 5
OBitFTA2AdderOutputI
mol#1#2#3#4#5; \mathop{\rm BitFTA2AdderOutputI}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O17 0 5
OBitFTA2AdderOutputP
mol#1#2#3#4#5; \mathop{\rm BitFTA2AdderOutputP}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O18 0 5
OBitFTA2AdderOutputQ
mol#1#2#3#4#5; \mathop{\rm BitFTA2AdderOutputQ}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O19 0 5
OBitFTA3Str
mol#1#2#3#4#5; \mathop{\rm BitFTA3Str}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O20 0 5
OBitFTA3Circ
mol#1#2#3#4#5; \mathop{\rm BitFTA3Circ}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O21 0 5
OBitFTA3CarryOutput
mol#1#2#3#4#5; \mathop{\rm BitFTA3\-\allowbreak{}Carry\-\allowbreak{}Output}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O22 0 5
OBitFTA3AdderOutputI
mol#1#2#3#4#5; \mathop{\rm BitFTA3\-Adder\-OutputI}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O23 0 5
OBitFTA3AdderOutputP
mol#1#2#3#4#5; \mathop{\rm BitFTA3\-Adder\-OutputP}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
O24 0 5
OBitFTA3AdderOutputQ
mol#1#2#3#4#5; \mathop{\rm BitFTA3\-Adder\-OutputQ}(#1,\,\allowbreak #2,\,\allowbreak #3,\,\allowbreak #4,\,\allowbreak #5)
#FUNCOP_1
O1 1 1
O-->
moi@2; #1 \longmapsto #2
O1 2 1
O-->
moq/1r@m/2l@m#3; (#3)^{#1\times #2}
O1 2 2
O-->
mc/1r@w/2r@w/3l@w/4l@w; [#1\longmapsto #3, #2\longmapsto #4]
O1 4 4
O-->
mc#1#2#3#4#5#6#7#8; [#1\mapsto #5,#2\mapsto #6,#3\mapsto #7,#4\mapsto #8]
O2 1 2
O[:]
mo@s/1q#2#3; #1^\circ (#2,#3)
O3 1 2
O[;]
mo@s/1q#2#3; #1^\circ (#2,#3)
O4 1 1
O.-->
mox@a; #1 \dotlongmapsto #2
O4 2 1
O.-->
mo@w/3l@w#1#2; \langle #1,#2\rangle \longmapsto #3
O5 0 4
OIFEQ
mc#1#2#3#4; (#1 = #2 \rightarrow #3, #4)
O6 1 1
O:->
mc#1#2; [\llangle #1\rrangle\mapsto #3]
O6 2 1
O:->
mc#1#2#3; [\llangle #1,#2\rrangle\mapsto #3]
V1 1
VFunction-yielding
a function yielding
#FUNCSDOM
G1 6
GAlgebraStr
mc#1#2#3#4#5#6; \langle #1, #2, #3, #4, #5, #6\rangle
J1 1
GAlgebraStr
hol#1; algebra structure of #1
L1 0
GAlgebraStr
hn algebra structure #0
algebra structures #0
L1 1
GAlgebraStr
hn algebra structure #0 over #1
algebra structures #0 over #1
M1 0
MRing
ha ring #0
rings #0
M2 0
MAlgebra
hn algebra #0
algebras #0
M2 1
MAlgebra
hn algebra #0 of #1
algebra #0 of #1
O1 0 1
ORealFuncAdd
mow/1m#1; +_{{\mathbb R}^{#1}}
O2 0 1
ORealFuncMult
mow/1m#1; \cdot_{{\mathbb R}^{#1}}
O3 0 1
ORealFuncExtMult
mcr@s/1m#1; \cdot^{\mathbb R}_{{\mathbb R}^{#1}}
O4 0 1
ORealFuncZero
mow/1m#1; {\bf 0}_{{\mathbb R}^{#1}}
O5 0 1
ORealFuncUnit
mow/1m#1; {\bf 1}_{{\mathbb R}^{#1}}
O6 0 1
ORealVectSpace
mor@s/1m#1; {\mathbb R}^{#1}_{\mathbb R}
O6 0 2
ORealVectSpace
mol@s#1#2; \mathop{\rm RealVectSpace}(#1,#2)
O7 0 1
ORRing
mol@s; \mathop{\rm RRing} #1
O8 0 1
ORAlgebra
mol@s; \mathop{\rm RAlgebra} #1
V2 1
Vvector-associative
a vector associative
#FUNCTOR0
G1 1
GBimapStr
mc#1; \langle #1 \rangle
G2 2
GFunctorStr
mc#1#2; \langle #1,#2 \rangle
J1 1
GBimapStr
hol#1; bimap structure of #1
J2 1
GFunctorStr
hol#1; functor structure of #1
L1 2
GBimapStr
ha bimap structure from #1 into #2
bimap structures from #1 into #2
L2 2
GFunctorStr
ha functor structure #0 from #1 to #2
functor structures #0 from #1 to #2
M1 2
Mbifunction
ha bifunction #0 from #1 into #2
bifunctions #0 from #1 into #2
M2 3
MMSUnTrans
h1 #1-transformation #0 from #2 to #3
#1-transformations #0 from #2 to #3
O1 0 3
OMorph-Map
mol#1#2#3; \mathop{\rm Morph\hbox{-}Map}_{#1}(#2,#3)
R1 2 0
Rare_anti-isomorphic
h #1,#2 are anti-isomorphic
#1,#2 are not anti-isomorphic
U1 1
UObjectMap
honl#1; object map of #1
object map
U2 1
UMorphMap
hosl#1; morphism map of #1
morphism map
V1 1
VCovariant
a precovariant
V2 1
VContravariant
a precontravariant
V3 1
Vcoreflexive
a coreflexive
V4 1
Vid-preserving
n id-preserving
V5 1
Vcomp-preserving
a comp-preserving
V6 1
Vcomp-reversing
a comp-reversing
V7 1
Vcovariant
a covariant
V8 1
Vcontravariant
a contravariant
V9 1
Vinjective
n injective
#FUNCTOR2
O1 0 1
Oidt
mow#1; \mathop{\rm id}_{#1}
#FUNCT_1
M1 0
MFunction
ha function #0
functions #0
M1 2
MFunction
ha function #0 from #1 into #2
functions #0 from #1 into #2
M1 3
MFunction
ha binary function #0 from #1, #2 into #3
binary functions #0 from #1, #2 into #3
O1 0 1
O.
mol; \dot{#1}
O1 0 2
O.
mow#2; #1_{#2}
O1 0 3
O.
mow#2#3; #1_{#2,#3}
O1 1 1
O.
mor(1)@9#2; #1(#2)
O1 1 2
O.
mcr(1)@9#2#3; #1(#2,\allowbreak\,#3)
O1 1 3
O.
mcr(1)@9#2#3#4; #1(#2,\allowbreak\,#3,\allowbreak\,#4)
O1 1 4
O.
mcr(1)@9#2#3#4#5; #1(#2,\allowbreak\,#3,\allowbreak\,#4,\allowbreak\,#5)
O1 2 1
O.
mo#1#2; (#1,#2).#3
O2 0 1
Othe_value_of
hol#1; value of #1
V1 1
VFunction-like
a function-like
V2 1
Vone-to-one
a one-to-one
V3 1
Vconstant
a constant
V4 1
Vfunctional
a functional
V5 2
V-compatible
a #1 -compatible
#FUNCT_2
M1 1
MPermutation
ha permutation #0 of #1
permutations #0 of #1
M2 2
MFUNCTION_DOMAIN
ha non empty set #0 of functions from #1 to #2
non empty sets #0 of functions from #1 to #2
O1 0 0
OFuncs
mol; \mathop{\rm Funcs}
O1 0 1
OFuncs
mol@s; \mathop{\rm Funcs} #1
O1 0 2
OFuncs
moq(2)/1m/2q#1; #2^{#1}
O2 0 1
O/*
mom@s; {}_\ast #1
O2 1 1
O/*
moi; #1 {}_\ast #2
V1 1
Vquasi_total
a quasi total
V2 1
Vonto
n onto
V3 1
Vbijective
a bijective
#FUNCT_3
O1 0 1
Ochi
mol@s; \specchi #1
O1 0 2
Ochi
mow/1k#1#2; {\raise.4ex\hbox{$\chi$}}_{#1,#2}
O2 0 1
Oincl
mo{kqmw}/1b#1; {{#1} \atop \hookrightarrow}
O2 0 2
Oincl
mol#1#2; \mathop{\rm incl}(#1,#2)
O2 1 1
Oincl
moi@a; #1\hookrightarrow #2
O3 0 1
Odelta
mow/1k#1; \delta_{#1}
O3 0 3
Odelta
mol#1#2#3; \Delta(#1,#2,#3)
O3 1 1
Odelta
moi#1#2; #1 \mathop{\rm delta} #2
#FUNCT_4
K1 1 L1 vFUNCT_4
K|:
L:|
mc#1; \mathopen{{\vert}\!\!:} #1 \mathclose{:\!\!{\vert}}
K1 2 L1 vFUNCT_4
K|:
L:|
mc#1#2; \mathopen{{\vert}\!\!:} #1,\, #2 \mathclose{:\!\!{\vert}}
O1 1 1
O+*
moi@a; #1 {{+}\cdot} #2
O1 1 2
O+*
moi#2#3; #1\mathbin{{+}\cdot}(#2,#3)
O1 2 1
O+*
moi(1,3)#2; #1 {{{+}\cdot}^{#2}} #3
O2 1 2
O+~
moi#2#3; #1\widetilde{+}(#2,#3)
#FUNCT_5
O1 0 1
Ocurry
mol@s; \mathop{\rm curry} #1
O1 0 2
Ocurry
mol@s#1#2; {\rm curry}(#1,#2)
O2 0 1
Ouncurry
mol@s; \mathop{\rm uncurry} #1
O3 0 1
Ocurry'
mol@s; \mathop{\rm curry'} #1
O4 0 1
Ouncurry'
mol@s; \mathop{\rm uncurry'} #1
O5 0 0
Oop0
mcw; \mathop{\rm op}_0
O6 0 0
Oop1
mcw; \mathop{\rm op}_1
O7 0 0
Oop2
mcw; \mathop{\rm op}_2
#FUNCT_6
O1 0 1
OSubFuncs
mol@s; \mathop{\rm Sub}_{\rm f} #1
O2 0 1
Odoms
mo@a/1r; \mathop{\rm dom}_\kappa #1(\kappa)
O3 0 1
Orngs
mo@a/1r; \mathop{\rm rng}_\kappa #1(\kappa)
O4 0 1
OFrege
mol#1; \mathop{\rm Frege}(#1)
O5 0 1
Ocommute
mol#1; \mathop{\rm commute}(#1)
O5 0 3
Ocommute
mol#1#2#3; \mathop{\rm commute}(#1,#2,#3)
#FUNCT_7
M1 0
MFuncSequence
ha composable sequence #0
composable sequences #0
M1 1
MFuncSequence
ha composable sequence #0 along #1
composable sequences #0 along #1
M1 2
MFuncSequence
ha composable sequence #0 from #1 into #2
composable sequences #0 from #1 into #2
O1 0 2
OIn
mor(1)#2; #1(\in #2)
O2 0 2
Ocompose
mol#2; \mathop{\rm compose}_{#2}#1
O3 0 2
Oapply
mol#1#2; \mathop{\rm apply}(#1,#2)
O4 0 1
Ofirstdom
mol#1; \mathop{\rm firstdom}(#1)
O5 0 1
Olastrng
mol#1; \mathop{\rm lastrng}(#1)
O6 0 2
Oiter
moq/2m#2; #1^{#2}
O6 1 1
Oiter
moq{}#2; #2^{#1}
O6 2 1
Oiter
mor(3)#1#2; {#3}^\ast_{#1\to #2}
O7 0 3
OSwap
mol#1#2#3; \mathop{\rm Swap}(#1,#2,#3)
O8 1 1
Ofollowed_by
Hoi#1#2; #1 followed by #2
O8 2 1
Ofollowed_by
moi#1#2#3; #1,#2 {\rm\;followed\;by\;} #3
R1 2 1
Requal_outside
h #1 and #2 are equal outside #3
#1 and #2 are not equal outside #3
V1 1
VFuncSeq-like
a composable
#FUNCT_8
O1 0 0
Osignum
mc; \mathop{\rm signum}
R1 1 1
Ris_even_on
i even on #2
not even on #2
R2 1 1
Ris_odd_on
i odd on #2
not odd on #2
V1 1
Vsymmetrical
a symmetrical
V2 1
Vwith_symmetrical_domain
x symmetrical domain
V3 1
Vquasi_even
a quasi even
V4 1
Vquasi_odd
a quasi odd
#FUNCT_9
V1 2
V-periodic
a #1 -periodic
V2 1
Vperiodic
a periodic
#FUZZY_1
M1 1
MMembership_Func
ha membership function #0 of #1
membership functions #0 of #1
O1 0 1
O1_minus
mol#1; \mathop{\rm 1\hbox{-}minus} #1
O2 0 1
OEMF
mol#1; \mathop{\rm EMF} #1
O3 0 1
OUMF
mol#1; \mathop{\rm UMF} #1
O4 0 2
Oab_difMF
mc#1#2; \vert #1 - #2 \vert
#FUZZY_2
M1 2
MRMembership_Func
ha membership function #0 of #1,#2
membership functions #0 of #1,#2
O1 0 2
OZmf
mol#1#2; \mathop{\rm Zmf}(#1,#2)
O2 0 2
OUmf
mol#1#2; \mathop{\rm Umf}(#1,#2)
#FUZZY_4
O1 0 1
Oconverse
mol#1; \mathop{\rm converse} #1
O2 0 2
OImf
mol#1#2; \mathop{\rm Imf}(#1,#2)
#FVSUM_1
O1 1 0
Omultfield
mcq#1; \mathop{{\cdot}^{#1}}
O2 0 1
Odiffield
mow#1; -_{#1}
O3 1 1
O"*"
moi@m; #1 \cdot #2
#GATE_1
O1 0 1
ONOT1
mol#1; \mathop{\rm NOT1} #1
O2 0 2
OAND2
mol#1#2; \mathop{\rm AND2}(#1,#2)
O3 0 2
OOR2
mol#1#2; \mathop{\rm OR2}(#1,#2)
O4 0 2
OXOR2
mol#1#2; \mathop{\rm XOR2}(#1,#2)
O5 0 2
OEQV2
mol#1#2; \mathop{\rm EQV2}(#1,#2)
O6 0 2
ONAND2
mol#1#2; \mathop{\rm NAND2}(#1,#2)
O7 0 2
ONOR2
mol#1#2; \mathop{\rm NOR2}(#1,#2)
O8 0 3
OAND3
mol#1#2#3; \mathop{\rm AND3}(#1,#2,#3)
O9 0 3
OOR3
mol#1#2#3; \mathop{\rm OR3}(#1,#2,#3)
O10 0 3
OXOR3
mol#1#2#3; \mathop{\rm XOR3}(#1,#2,#3)
O11 0 3
OMAJ3
mol#1#2#3; \mathop{\rm MAJ3}(#1,#2,#3)
O12 0 3
ONAND3
mol#1#2#3; \mathop{\rm NAND3}(#1,#2,#3)
O13 0 3
ONOR3
mol#1#2#3; \mathop{\rm NOR3}(#1,#2,#3)
O14 0 4
OAND4
mol#1#2#3#4; \mathop{\rm AND4}(#1,#2,#3,#4)
O15 0 4
OOR4
mol#1#2#3#4; \mathop{\rm OR4}(#1,#2,#3,#4)
O16 0 4
ONAND4
mol#1#2#3#4; \mathop{\rm NAND4}(#1,#2,#3,#4)
O17 0 4
ONOR4
mol#1#2#3#4; \mathop{\rm NOR4}(#1,#2,#3,#4)
O18 0 5
OAND5
mol#1#2#3#4#5; \mathop{\rm AND5}(#1,#2,#3,#4,#5)
O19 0 5
OOR5
mol#1#2#3#4#5; \mathop{\rm OR5}(#1,#2,#3,#4,#5)
O20 0 5
ONAND5
mol#1#2#3#4#5; \mathop{\rm NAND5}(#1,#2,#3,#4,#5)
O21 0 5
ONOR5
mol#1#2#3#4#5; \mathop{\rm NOR5}(#1,#2,#3,#4,#5)
O22 0 6
OAND6
mol#1#2#3#4#5#6; \mathop{\rm AND6}(#1,#2,#3,#4,#5,#6)
O23 0 6
OOR6
mol#1#2#3#4#5#6; \mathop{\rm OR6}(#1,#2,#3,#4,#5,#6)
O24 0 6
ONAND6
mol#1#2#3#4#5#6; \mathop{\rm NAND6}(#1,#2,#3,#4,#5,#6)
O25 0 6
ONOR6
mol#1#2#3#4#5#6; \mathop{\rm NOR6}(#1,#2,#3,#4,#5,#6)
O26 0 7
OAND7
mol#1#2#3#4#5#6#7; \mathop{\rm AND7}(#1,#2,#3,#4,#5,#6,#7)
O27 0 7
OOR7
mol#1#2#3#4#5#6#7; \mathop{\rm OR7}(#1,#2,#3,#4,#5,#6,#7)
O28 0 7
ONAND7
mol#1#2#3#4#5#6#7; \mathop{\rm NAND7}(#1,#2,#3,#4,#5,#6,#7)
O29 0 7
ONOR7
mol#1#2#3#4#5#6#7; \mathop{\rm NOR7}(#1,#2,#3,#4,#5,#6,#7)
O30 0 8
OAND8
mol#1#2#3#4#5#6#7#8; \mathop{\rm AND8}(#1,#2,#3,#4,#5,#6,#7,#8)
O31 0 8
OOR8
mol#1#2#3#4#5#6#7#8; \mathop{\rm OR8}(#1,#2,#3,#4,#5,#6,#7,#8)
O32 0 8
ONAND8
mol#1#2#3#4#5#6#7#8; \mathop{\rm NAND8}(#1,#2,#3,#4,#5,#6,#7,#8)
O33 0 8
ONOR8
mol#1#2#3#4#5#6#7#8; \mathop{\rm NOR8}(#1,#2,#3,#4,#5,#6,#7,#8)
O34 0 2
OMODADD2
mol#1#2; \mathop{\rm MODADD2}(#1,#2)
O35 0 3
OADD1
mol#1#2#3; \mathop{\rm ADD1}(#1,#2,#3)
O36 0 3
OCARR1
mol#1#2#3; \mathop{\rm CARR1}(#1,#2,#3)
O37 0 5
OADD2
mol#1#2#3#4#5; \mathop{\rm ADD2}(#1,#2,#3,#4,#5)
O38 0 5
OCARR2
mol#1#2#3#4#5; \mathop{\rm CARR2}(#1,#2,#3,#4,#5)
O39 0 7
OADD3
mol#1#2#3#4#5#6#7; \mathop{\rm ADD3}(#1,#2,#3,#4,#5,#6,#7)
O40 0 7
OCARR3
mol#1#2#3#4#5#6#7; \mathop{\rm CARR3}(#1,#2,#3,#4,#5,#6,#7)
O41 0 9
OADD4
mol#1#2#3#4#5#6#7#8#9; \mathop{\rm ADD4}(#1,#2,#3,#4,#5,#6,#7,#8,#9)
O42 0 9
OCARR4
mol#1#2#3#4#5#6#7#8#9; \mathop{\rm CARR4}(#1,#2,#3,#4,#5,#6,#7,#8,#9)
#GATE_5
O1 0 4
OMULT210
mol#1#2#3#4; \mathop{\rm MULT_{210}}(#1,#2,#3,#4)
O2 0 4
OMULT211
mol#1#2#3#4; \mathop{\rm MULT_{211}}(#1,#2,#3,#4)
O3 0 4
OMULT212
mol#1#2#3#4; \mathop{\rm MULT_{212}}(#1,#2,#3,#4)
O4 0 4
OMULT213
mol#1#2#3#4; \mathop{\rm MULT_{213}}(#1,#2,#3,#4)
O5 0 5
OMULT310
mol#1#2#3#4#5; \mathop{\rm MULT_{310}}(#1,#2,#3,#4,#5)
O6 0 5
OMULT311
mol#1#2#3#4#5; \mathop{\rm MULT_{311}}(#1,#2,#3,#4,#5)
O7 0 5
OMULT312
mol#1#2#3#4#5; \mathop{\rm MULT_{312}}(#1,#2,#3,#4,#5)
O8 0 5
OMULT313
mol#1#2#3#4#5; \mathop{\rm MULT_{313}}(#1,#2,#3,#4,#5)
O9 0 5
OMULT314
mol#1#2#3#4#5; \mathop{\rm MULT_{314}}(#1,#2,#3,#4,#5)
O10 0 6
OMULT321
mol#1#2#3#4#5#6; \mathop{\rm MULT_{321}}(#1,#2,#3,#4,#5,#6)
O11 0 6
OMULT322
mol#1#2#3#4#5#6; \mathop{\rm MULT_{322}}(#1,#2,#3,#4,#5,#6)
O12 0 6
OMULT323
mol#1#2#3#4#5#6; \mathop{\rm MULT_{323}}(#1,#2,#3,#4,#5,#6)
O13 0 6
OMULT324
mol#1#2#3#4#5#6; \mathop{\rm MULT_{324}}(#1,#2,#3,#4,#5,#6)
O14 0 3
OCLAADD1
mol#1#2#3; \mathop{\rm CLAADD1}(#1,#2,#3)
O15 0 3
OCLACARR1
mol#1#2#3; \mathop{\rm CLACARR1}(#1,#2,#3)
O16 0 5
OCLAADD2
mol#1#2#3#4#5; \mathop{\rm CLAADD2}(#1,#2,#3,#4,#5)
O17 0 5
OCLACARR2
mol#1#2#3#4#5; \mathop{\rm CLACARR2}(#1,#2,#3,#4,#5)
O18 0 7
OCLAADD3
mol#1#2#3#4#5#6#7; \mathop{\rm CLAADD3}(#1,#2,#3,#4,#5,#6,#7)
O19 0 7
OCLACARR3
mol#1#2#3#4#5#6#7; \mathop{\rm CLACARR3}(#1,#2,#3,#4,#5,#6,#7)
O20 0 9
OCLAADD4
mol#1#2#3#4#5#6#7#8#9; \mathop{\rm CLAADD4}(#1,#2,#3,#4,#5,#6,#7,#8,#9)
O21 0 9
OCLACARR4
mol#1#2#3#4#5#6#7#8#9; \mathop{\rm CLACARR4}(#1,#2,#3,#4,#5,#6,#7,#8,#9)
#GCD_1
M1 1
MAm
hn amp set #0 of #1
amp sets #0 of #1
M2 1
MAmpleSet
hn AmpleSet #0 of #1
AmpleSets #0 of #1
M3 0
MgcdDomain
ha gcdDomain #0
gcdDomains #0
O1 0 1
OClasses
mol#1; \mathop{\rm Classes} #1
O2 0 2
ONF
mol#1#2; \mathop{\rm NF}(#1,#2)
O3 0 5
Oadd1
mol#1#2#3#4#5; \mathop{\rm add1}_{#5}(#1,#2,#3,#4)
O4 0 5
Oadd2
mol#1#2#3#4#5; \mathop{\rm add2}_{#5}(#1,#2,#3,#4)
O5 0 5
Omult1
mol#1#2#3#4#5; \mathop{\rm mult1}_{#5}(#1,#2,#3,#4)
O6 0 5
Omult2
mol#1#2#3#4#5; \mathop{\rm mult2}_{#5}(#1,#2,#3,#4)
R1 1 1
Ris_associated_to
i associated to #2
not associated to #2
R2 1 1
Ris_not_associated_to
i not associated to #2
associated to #2
R3 2 1
Rare_canonical_wrt
h #1,#2 are canonical w.r.t. #3
#1,#2 are not canonical w.r.t. #3
R4 2 0
Rare_co-prime
h #1,#2 are co-prime
#1,#2 are not co-prime
R5 2 1
Rare_normalized_wrt
h #1,#2 are normalized w.r.t. #3
#1,#2 are not normalized w.r.t. #3
V1 1
Vgcd-like
a gcd-like
#GENEALG1
M1 0
MGene-Set
ha Gene-Set #0
Gene-Sets #0
M2 1
MIndividual
hn Individual #0 of #1
Individuals #0 of #1
O1 0 1
OGA-Space
mol#1; \mathop{\rm GA-Space} #1
O2 0 3
Ocrossover
mol#1#2#3; \mathop{\rm crossover}(#1,#2,#3)
O2 0 4
Ocrossover
mol#1#2#3#4; \mathop{\rm crossover}(#1,#2,#3,#4)
O2 0 5
Ocrossover
mol#1#2#3#4#5; \mathop{\rm crossover}(#1,#2,#3,#4,#5)
O2 0 6
Ocrossover
mol#1#2#3#4#5#6; \mathop{\rm crossover}(#1,#2,#3,#4,#5,#6)
O2 0 7
Ocrossover
mol#1#2#3#4#5#6#7; \mathop{\rm crossover}(#1,#2,#3,#4,#5,#6,#7)
O2 0 8
Ocrossover
mol#1#2#3#4#5#6#7#8; \mathop{\rm crossover}(#1,#2,#3,#4,#5,#6,#7,#8)
#GEOMTRAP
G1 3
GAfMidStruct
mc#1#2#3; \langle #1, #2, #3\rangle
J1 1
GAfMidStruct
hol#1; affine midpoint structure of #1
L1 0
GAfMidStruct
hn affine midpoint structure #0
affine midpoint structures #0
M1 0
MMidOrdTrapSpace
hn ordered midpoint trapezium space #0
ordered midpoint trapezium spaces #0
M2 0
MOrdTrapSpace
hn ordered trapezium space #0
ordered trapezium spaces #0
M3 0
MTrapSpace
ha trapezium space #0
trapezium spaces #0
O1 0 3
ODTrapezium
ho#1; directed trapezium relation defined over #1 in the basis #2,#3
O2 0 1
OMidPoint
hol#1; midpoint operation in #1
O3 0 3
ODTrSpace
ho#1; directed trapezium space defined over #1 in the basis #2,#3
R1 4 2
Rare_DTr_wrt
h #1, #2 and #3, #4 form a directed trapezium w.r.t. #5, #6
#1, #2 and #3, #4 do not form a directed trapezium w.r.t. #5, #6
V1 1
VMidOrdTrapSpace-like
n ordered midpoint trapezium space-like
V2 1
VOrdTrapSpace-like
n ordered trapezium space-like
V3 1
VTrapSpace-like
a trapezium space-like
V4 1
VRegular
a regular
#GFACIRC1
O1 0 0
Oinv1
mol; \mathop{\rm inv1}
O2 0 0
Obuf1
mol; \mathop{\rm buf1}
O3 0 0
Oand2c
mol; \mathop{\rm and2c}
O4 0 0
Oxor2c
mol; \mathop{\rm xor2c}
O5 0 3
OGFA0CarryIStr
mol#1#2#3; \mathop{\rm GFA0CarryIStr}(#1,#2,#3)
O6 0 3
OGFA0CarryICirc
mol#1#2#3; \mathop{\rm GFA0CarryICirc}(#1,#2,#3)
O7 0 3
OGFA0CarryStr
mol#1#2#3; \mathop{\rm GFA0CarryStr}(#1,#2,#3)
O8 0 3
OGFA0CarryCirc
mol#1#2#3; \mathop{\rm GFA0CarryCirc}(#1,#2,#3)
O9 0 3
OGFA0CarryOutput
mol#1#2#3; \mathop{\rm GFA0CarryOutput}(#1,#2,#3)
O10 0 3
OGFA0AdderStr
mol#1#2#3; \mathop{\rm GFA0AdderStr}(#1,#2,#3)
O11 0 3
OGFA0AdderCirc
mol#1#2#3; \mathop{\rm GFA0AdderCirc}(#1,#2,#3)
O12 0 3
OGFA0AdderOutput
mol#1#2#3; \mathop{\rm GFA0AdderOutput}(#1,#2,#3)
O13 0 3
OBitGFA0Str
mol#1#2#3; \mathop{\rm BitGFA0Str}(#1,#2,#3)
O14 0 3
OBitGFA0Circ
mol#1#2#3; \mathop{\rm BitGFA0Circ}(#1,#2,#3)
O15 0 3
OBitGFA0CarryOutput
mol#1#2#3; \mathop{\rm BitGFA0CarryOutput}(#1,#2,#3)
O16 0 3
OBitGFA0AdderOutput
mol#1#2#3; \mathop{\rm BitGFA0AdderOutput}(#1,#2,#3)
O17 0 3
OGFA1CarryIStr
mol#1#2#3; \mathop{\rm GFA1CarryIStr}(#1,#2,#3)
O18 0 3
OGFA1CarryICirc
mol#1#2#3; \mathop{\rm GFA1CarryICirc}(#1,#2,#3)
O19 0 3
OGFA1CarryStr
mol#1#2#3; \mathop{\rm GFA1CarryStr}(#1,#2,#3)
O20 0 3
OGFA1CarryCirc
mol#1#2#3; \mathop{\rm GFA1CarryCirc}(#1,#2,#3)
O21 0 3
OGFA1CarryOutput
mol#1#2#3; \mathop{\rm GFA1CarryOutput}(#1,#2,#3)
O22 0 3
OGFA1AdderStr
mol#1#2#3; \mathop{\rm GFA1AdderStr}(#1,#2,#3)
O23 0 3
OGFA1AdderCirc
mol#1#2#3; \mathop{\rm GFA1AdderCirc}(#1,#2,#3)
O24 0 3
OGFA1AdderOutput
mol#1#2#3; \mathop{\rm GFA1AdderOutput}(#1,#2,#3)
O25 0 3
OBitGFA1Str
mol#1#2#3; \mathop{\rm BitGFA1Str}(#1,#2,#3)
O26 0 3
OBitGFA1Circ
mol#1#2#3; \mathop{\rm BitGFA1Circ}(#1,#2,#3)
O27 0 3
OBitGFA1CarryOutput
mol#1#2#3; \mathop{\rm BitGFA1CarryOutput}(#1,#2,#3)
O28 0 3
OBitGFA1AdderOutput
mol#1#2#3; \mathop{\rm BitGFA1AdderOutput}(#1,#2,#3)
O29 0 3
OGFA2CarryIStr
mol#1#2#3; \mathop{\rm GFA2CarryIStr}(#1,#2,#3)
O30 0 3
OGFA2CarryICirc
mol#1#2#3; \mathop{\rm GFA2CarryICirc}(#1,#2,#3)
O31 0 3
OGFA2CarryStr
mol#1#2#3; \mathop{\rm GFA2CarryStr}(#1,#2,#3)
O32 0 3
OGFA2CarryCirc
mol#1#2#3; \mathop{\rm GFA2CarryCirc}(#1,#2,#3)
O33 0 3
OGFA2CarryOutput
mol#1#2#3; \mathop{\rm GFA2CarryOutput}(#1,#2,#3)
O34 0 3
OGFA2AdderStr
mol#1#2#3; \mathop{\rm GFA2AdderStr}(#1,#2,#3)
O35 0 3
OGFA2AdderCirc
mol#1#2#3; \mathop{\rm GFA2AdderCirc}(#1,#2,#3)
O36 0 3
OGFA2AdderOutput
mol#1#2#3; \mathop{\rm GFA2AdderOutput}(#1,#2,#3)
O37 0 3
OBitGFA2Str
mol#1#2#3; \mathop{\rm BitGFA2Str}(#1,#2,#3)
O38 0 3
OBitGFA2Circ
mol#1#2#3; \mathop{\rm BitGFA2Circ}(#1,#2,#3)
O39 0 3
OBitGFA2CarryOutput
mol#1#2#3; \mathop{\rm BitGFA2CarryOutput}(#1,#2,#3)
O40 0 3
OBitGFA2AdderOutput
mol#1#2#3; \mathop{\rm BitGFA2AdderOutput}(#1,#2,#3)
O41 0 3
OGFA3CarryIStr
mol#1#2#3; \mathop{\rm GFA3CarryIStr}(#1,#2,#3)
O42 0 3
OGFA3CarryICirc
mol#1#2#3; \mathop{\rm GFA3CarryICirc}(#1,#2,#3)
O43 0 3
OGFA3CarryStr
mol#1#2#3; \mathop{\rm GFA3CarryStr}(#1,#2,#3)
O44 0 3
OGFA3CarryCirc
mol#1#2#3; \mathop{\rm GFA3CarryCirc}(#1,#2,#3)
O45 0 3
OGFA3CarryOutput
mol#1#2#3; \mathop{\rm GFA3CarryOutput}(#1,#2,#3)
O46 0 3
OGFA3AdderStr
mol#1#2#3; \mathop{\rm GFA3AdderStr}(#1,#2,#3)
O47 0 3
OGFA3AdderCirc
mol#1#2#3; \mathop{\rm GFA3AdderCirc}(#1,#2,#3)
O48 0 3
OGFA3AdderOutput
mol#1#2#3; \mathop{\rm GFA3AdderOutput}(#1,#2,#3)
O49 0 3
OBitGFA3Str
mol#1#2#3; \mathop{\rm BitGFA3Str}(#1,#2,#3)
O50 0 3
OBitGFA3Circ
mol#1#2#3; \mathop{\rm BitGFA3Circ}(#1,#2,#3)
O51 0 3
OBitGFA3CarryOutput
mol#1#2#3; \mathop{\rm BitGFA3CarryOutput}(#1,#2,#3)
O52 0 3
OBitGFA3AdderOutput
mol#1#2#3; \mathop{\rm BitGFA3AdderOutput}(#1,#2,#3)
#GFACIRC2
O1 1 2
O-BitGFA0Str
moi#2#3; #1{\rm\hbox{-}BitGFA0Str}(#2,\,\allowbreak #3)
O2 1 2
O-BitGFA0Circ
moi#2#3; #1{\rm\hbox{-}BitGFA0Circ}(#2,\,\allowbreak #3)
O3 1 2
O-BitGFA0CarryOutput
moi#2#3; #1{\rm\hbox{-}BitGFA0CarryOutput}(#2,\,\allowbreak #3)
O4 2 2
O-BitGFA0AdderOutput
moi#1#2#3#4; (#1,\,\allowbreak #2){\rm\hbox{-}BitGFA0AdderOutput}(#3,\,\allowbreak #4)
O5 1 2
O-BitGFA1Str
moi#2#3; #1{\rm\hbox{-}BitGFA1Str}(#2,\,\allowbreak #3)
O6 1 2
O-BitGFA1Circ
moi#2#3; #1{\rm\hbox{-}BitGFA1Circ}(#2,\,\allowbreak #3)
O7 1 2
O-BitGFA1CarryOutput
moi#2#3; #1{\rm\hbox{-}BitGFA1CarryOutput}(#2,\,\allowbreak #3)
O8 2 2
O-BitGFA1AdderOutput
moi#1#2#3#4; (#1,\,\allowbreak #2){\rm\hbox{-}BitGFA1AdderOutput}(#3,\,\allowbreak #4)
#GLIB_000
M1 0
MGraphStruct
ha graph structure #0
graph structures #0
M2 0
M_Graph
ha graph #0
graphs #0
M3 1
MSubgraph
ha subgraph #0 of #1
subgraphs #0 of #1
M4 2
MinducedSubgraph
ha subgraph #0 of #1 induced by #2
subgraphs #0 of #1 induced by #2
M4 3
MinducedSubgraph
ha subgraph #0 of #1 induced by #2 and #3
subgraphs #0 of #1 induced by #2 and#3
M5 2
MremoveVertex
ha subgraph #0 of #1 with vertex #2 removed
subgraphs #0 of #1 with vertex #2 removed
M6 2
MremoveVertices
ha subgraph #0 of #1 with vertices #2 removed
subgraphs #0 of #1 with vertices #2 removed
M7 2
MremoveEdge
ha subgraph #0 of #1 with edge #2 removed
subgraphs #0 of #1 with edge #2 removed
M8 2
MremoveEdges
ha subgraph #0 of #1 with edges #2 removed
subgraphs #0 of #1 with edges #2 removed
M9 1
MVertex
ha vertex #0 of #1
vertices #0 of #1
M10 0
MGraphSeq
ha graph sequence #0
graph sequences #0
O1 0 0
OVertexSelector
mol; \mathop{\rm VertexSelector}
O2 0 0
OEdgeSelector
mol; \mathop{\rm EdgeSelector}
O3 0 0
OSourceSelector
mol; \mathop{\rm SourceSelector}
O4 0 0
OTargetSelector
mol; \mathop{\rm TargetSelector}
O5 0 0
O_GraphSelectors
hol; graph selectors
O6 0 1
Othe_Vertices_of
hol; vertices of #1
O7 0 1
Othe_Edges_of
hol; edges of #1
O8 0 1
Othe_Source_of
hol; source of #1
O9 0 1
Othe_Target_of
hol; target of #1
O10 0 4
OcreateGraph
mol#1#2#3#4; \mathop{\rm createGraph}(#1,#2,#3,#4)
O11 1 2
O.set
moi@8#2#3; #1{\rm .set}(#2,#3)
O13 1 0
O.order()
mor; #1{\rm.order()}
O14 1 0
O.size()
mor; #1{\rm.size()}
O15 1 1
O.edgesInto
moi@8#2; #1{\rm.edgesInto}(#2)
O16 1 1
O.edgesOutOf
moi@8#2; #1{\rm .edgesOutOf}(#2)
O17 1 1
O.edgesInOut
moi@8#2; #1{\rm .edgesInOut}(#2)
O18 1 1
O.edgesBetween
moi@8#2; #1{\rm.edgesBetween}(#2)
O18 1 2
O.edgesBetween
moi@8#2#3; #1{\rm.edgesBetween}(#2,#3)
O19 1 2
O.edgesDBetween
moi@8#2#3; #1{\rm.edgesDBetween}(#2,#3)
O20 1 0
O.edgesIn()
mor; #1{\rm.edgesIn()}
O21 1 0
O.edgesOut()
mor; #1{\rm.edgesOut()}
O22 1 0
O.edgesInOut()
mor; #1{\rm.edgesInOut()}
O23 1 1
O.adj
moi@8#2; #1{\rm.adj}(#2)
O24 1 0
O.inDegree()
mor; #1{\rm.inDegree()}
O25 1 0
O.outDegree()
mor; #1{\rm.outDegree()}
O26 1 0
O.degree()
mor; #1{\rm.degree()}
O27 1 0
O.inNeighbors()
mor; #1{\rm.inNeighbors()}
O28 1 0
O.outNeighbors()
mor; #1{\rm.outNeighbors()}
O29 1 0
O.allNeighbors()
mor; #1{\rm.allNeighbors()}
O30 1 0
O.Lifespan()
mor; #1{\rm.Lifespan()}
O31 1 0
O.Result()
mor; #1{\rm.Result()}
R1 1 3
RJoins
hy #1 joins #2 and #3 in #4
#1 does not join #2 and #3 in #4
R2 1 3
RDJoins
hy #1 joins #2 to #3 in #4
#1 does not join #2 to #3 in #4
R3 1 3
RSJoins
hy #1 joins a vertex from #2 and a vertex from #3 in #4
#1 does not join a vertex from #2 and a vertex from #3 in #4
R4 1 3
RDSJoins
hy #1 joins a vertex from #2 to a vertex from #3 in #4
#1 does not join a vertex from #2 to a vertex from #3 in #4
R5 1 1
R==
my #1 \mathrel{=_G} #2
#1 \mathrel{\neq_G} #2
R6 1 1
R!=
mn #1 \mathrel{\neq_G} #2
#1 \mathrel{=_G} #2
V1 1
V[Graph-like]
a graph-like
V2 1
Vloopless
a loopless
V3 1
Vnon-multi
a non-multi
V4 1
Vnon-Dmulti
a non-directed-multi
V5 1
Vsimple
a simple
V6 1
VDsimple
a directed-simple
V7 1
Vspanning
a spanning
V8 1
Visolated
n isolated
V9 1
Vendvertex
n endvertex
V10 1
VGraph-yielding
a graph-yielding
V11 1
Vhalting
a halting
V12 1
Vnon-trivial
a non-trivial
#GLIB_001
M1 1
MVertexSeq
ha vertex sequence #0 of #1
vertex sequences #0 of #1
M2 1
MEdgeSeq
ha edge sequence #0 of #1
edge sequences #0 of #1
M3 1
MWalk
ha walk #0 of #1
walks #0 of #1
M4 1
MTrail
ha trail #0 of #1
trails #0 of #1
M5 1
MDWalk
ha dwalk #0 of #1
dwalks #0 of #1
M6 1
MDTrail
ha dtrail #0 of #1
dtrails #0 of #1
M7 1
MDPath
ha dpath #0 of #1
dpaths #0 of #1
M8 1
MSubwalk
ha subwalk #0 of #1
subwalks #0 of #1
O1 1 1
O.walkOf
moi; #1{\rm .walkOf}(#2)
O1 1 3
O.walkOf
moi#2#3#4; #1{\rm .walkOf}(#2,#3,#4)
O2 1 0
O.first()
mor; #1{\rm .first()}
O3 1 0
O.last()
mor; #1{\rm .last()}
O4 1 1
O.vertexAt
moi; #1{\rm .vertexAt}(#2)
O5 1 0
O.reverse()
mor; #1{\rm .reverse()}
O6 1 1
O.append
moi; #1{\rm .append}(#2)
O7 1 2
O.cut
moi#2#3; #1{\rm .cut}(#2,#3)
O8 1 2
O.remove
moi#2#3; #1{\rm .remove}(#2,#3)
O9 1 1
O.addEdge
moi; #1{\rm .addEdge}(#2)
O10 1 0
O.vertexSeq()
mor; #1{\rm .vertexSeq()}
O11 1 0
O.edgeSeq()
mor; #1{\rm .edgeSeq()}
O12 1 0
O.vertices()
mor; #1{\rm .vertices()}
O13 1 0
O.edges()
mor; #1{\rm .edges()}
O14 1 0
O.length()
mor; #1{\rm.length()}
O15 1 1
O.find
moi; #1{\rm .find}(#2)
O16 1 1
O.rfind
moi; #1{\rm .rfind}(#2)
O17 1 0
O.allWalks()
mor; #1{\rm .allWalks()}
O18 1 0
O.allTrails()
mor; #1{\rm .allTrails()}
O19 1 0
O.allPaths()
mor; #1{\rm .allPaths()}
O20 1 0
O.allDWalks()
mor; #1{\rm .allDWalks()}
O21 1 0
O.allDTrails()
mor; #1{\rm .allDTrails()}
O22 1 0
O.allDPaths()
mor; #1{\rm .allDPaths()}
R1 1 2
Ris_Walk_from
i walk from #2 to #3
!not a walk from #2 to #3
V1 1
VTrail-like
a trail-like
V2 1
VPath-like
a path-like
V3 1
Vvertex-distinct
a vertex-distinct
V4 1
VCycle-like
a cycle-like
#GLIB_002
O1 1 1
O.reachableFrom
moi; #1{\rm .reachableFrom}(#2)
O2 1 1
O.reachableDFrom
moi; #1{\rm .reachableDFrom}(#2)
O3 1 0
O.componentSet()
mor; #1{\rm .componentSet()}
O4 1 0
O.numComponents()
mor; #1{\rm .numComponents()}
R1 1 1
Ris_DTree_rooted_at
iy dtree rooted at #2
!not dtree rooted at #2
V1 1
Vacyclic
n acyclic
V2 1
VComponent-like
a component-like
V3 1
Vcut-vertex
a cut-vertex
#GLIB_003
M1 0
MWGraph
ha w-graph #0
w-graphs #0
M2 0
MEGraph
ha e-graph #0
e-graphs #0
M3 0
MVGraph
ha v-graph #0
v-graphs #0
M4 0
MWEGraph
ha we-graph #0
we-graphs #0
M5 0
MWVGraph
ha wv-graph #0
wv-graphs #0
M6 0
MEVGraph
ha ev-graph #0
ev-graphs #0
M7 0
MWEVGraph
ha wev-graph #0
wev-graphs #0
M8 1
MWSubgraph
ha w-subgraph #0 of #1
w-subgraphs #0 of #1
M9 1
MESubgraph
ha e-subgraph #0 of #1
e-subgraphs #0 of #1
M10 1
MVSubgraph
ha v-subgraph #0 of #1
v-subgraphs #0 of #1
M11 1
MWESubgraph
ha we-subgraph #0 of #1
we-subgraphs #0 of #1
M12 1
MWVSubgraph
ha wv-subgraph #0 of #1
wv-subgraphs #0 of #1
M13 1
MEVSubgraph
ha ev-subgraph #0 of #1
ev-subgraphs #0 of #1
M14 1
MWEVSubgraph
ha wev-subgraph #0 of #1
wev-subgraphs #0 of #1
M15 2
MinducedWSubgraph
ha induced w-subgraph #0 of #1,#2
induced w-subgraphs #0 of #1,#2
M15 3
MinducedWSubgraph
ha induced w-subgraph #0 of #1,#2,#3
induced w-subgraphs #0 of #1,#2,#3
M16 2
MinducedESubgraph
ha induced e-subgraph #0 of #1,#2
induced e-subgraphs #0 of #1,#2
M16 3
MinducedESubgraph
ha induced e-subgraph #0 of #1,#2,#3
induced e-subgraphs #0 of #1,#2,#3
M17 2
MinducedVSubgraph
ha induced v-subgraph #0 of #1,#2
induced v-subgraphs #0 of #1,#2
M17 3
MinducedVSubgraph
ha induced v-subgraph #0 of #1,#2,#3
induced v-subgraphs #0 of #1,#2,#3
M18 2
MinducedWESubgraph
ha induced we-subgraph #0 of #1,#2
induced we-subgraphs #0 of #1,#2
M18 3
MinducedWESubgraph
ha induced we-subgraph #0 of #1,#2,#3
induced we-subgraphs #0 of #1,#2,#3
M19 2
MinducedWVSubgraph
ha induced wv-subgraph #0 of #1,#2
induced wv-subgraphs #0 of #1,#2
M19 3
MinducedWVSubgraph
ha induced wv-subgraph #0 of #1,#2,#3
induced wv-subgraphs #0 of #1,#2,#3
M20 2
MinducedEVSubgraph
ha induced ev-subgraph #0 of #1,#2
induced ev-subgraphs #0 of #1,#2
M20 3
MinducedEVSubgraph
ha induced ev-subgraph #0 of #1,#2,#3
induced ev-subgraphs #0 of #1,#2,#3
M21 2
MinducedWEVSubgraph
ha induced wev-subgraph #0 of #1,#2
induced wev-subgraphs #0 of #1,#2
M21 3
MinducedWEVSubgraph
ha induced wev-subgraph #0 of #1,#2,#3
induced wev-subgraphs #0 of #1,#2,#3
M22 0
MWGraphSeq
ha w-graph sequence #0
w-graph sequences #0
M23 0
MEGraphSeq
ha e-graph sequence #0
e-graph sequences #0
M24 0
MVGraphSeq
ha v-graph sequence #0
v-graph sequences #0
M25 0
MWEGraphSeq
ha we-graph sequence #0
we-graph sequences #0
M26 0
MWVGraphSeq
ha wv-graph sequence #0
wv-graph sequences #0
M27 0
MEVGraphSeq
ha ev-graph sequence #0
ev-graph sequences #0
M28 0
MWEVGraphSeq
ha wev-graph sequence #0
wev-graph sequences #0
O1 0 0
OWeightSelector
mol; {\rm WeightSelector}
O2 0 0
OELabelSelector
mol; {\rm ELabelSelector}
O3 0 0
OVLabelSelector
mol; {\rm VLabelSelector}
O4 0 1
Othe_Weight_of
hol; weight of #1
O5 0 1
Othe_ELabel_of
hol; elabel of #1
O6 0 1
Othe_VLabel_of
hol; vlabel of #1
O7 1 0
O.weightSeq()
mor; #1{\rm .weightSeq()}
O8 1 0
O.cost()
mor; #1{\rm .cost()}
O9 1 0
O.labeledE()
mor; #1{\rm .labeledE()}
O10 1 2
O.labelEdge
moi#2#3; #1{\rm .labelEdge}(#2,#3)
O11 1 2
O.labelVertex
moi#2#3; #1{\rm .labelVertex}(#2,#3)
O12 1 0
O.labeledV()
mor; #1{\rm .labeledV()}
V1 1
V[Weighted]
a weighted
V2 1
V[ELabeled]
a elabeled
V3 1
V[VLabeled]
a vlabeled
V4 1
Vweight-inheriting
i weight
V5 1
Velabel-inheriting
i elabel
V6 1
Vvlabel-inheriting
i vlabel
V7 1
Vreal-weighted
a real-weighted
V8 1
Vnonnegative-weighted
a nonnegative-weighted
V9 1
Vreal-elabeled
a real-elabeled
V10 1
Vreal-vlabeled
a real-vlabeled
V11 1
Vreal-WEV
a real-wev
#GLIB_004
M1 1
MDIJK:Labeling
ha DIJK:labeling #0 of #1
DIJK:labeling #0 of #1
M2 1
MDIJK:LabelingSeq
ha DIJK:labeling sequence #0 of #1
DIJK:labeling sequences #0 of #1
M3 1
MPRIM:Labeling
ha PRIM:labeling #0 of #1
PRIM:labeling #0 of #1
M4 1
MPRIM:LabelingSeq
ha PRIM:labeling sequence #0 of #1
PRIM:labeling sequences #0 of #1
M5 1
MminimumSpanningTree
ha minimum spanning tree #0 of #1
minimum spanning trees #0 of #1
O1 1 2
O.min_DPath_cost
hoi#2#3; #1{\rm .mincost-d-path}(#2,#3)
O2 0 0
OWGraphSelectors
mol; {\rm WGraphSelectors}
O3 1 0
O.allWSubgraphs()
mor; #1{\rm .allWSubgraphs()}
O4 0 1
ODIJK:NextBestEdges
mol; {\rm  DIJK:NextBestEdges}(#1)
O5 0 1
ODIJK:Step
mol; {\rm DIJK:Step}(#1)
O6 0 1
ODIJK:Init
mol#1;{\rm DIJK:Init} #1
O7 0 1
ODIJK:CompSeq
mol#1; {\rm DIJK:CompSeq} #1
O8 0 2
ODIJK:SSSP
mol#1#2; {\rm DIJK:SSSP}(#1,#2)
O9 0 1
OPRIM:NextBestEdges
mol; {\rm PRIM:NextBestEdges}(#1)
O10 0 1
OPRIM:Init
mol; {\rm PRIM:Init}(#1)
O11 0 1
OPRIM:Step
mol; {\rm PRIM:Step}(#1)
O12 0 1
OPRIM:CompSeq
mol; {\rm PRIM:CompSeq}(#1)
O13 0 1
OPRIM:MST
mol; {\rm PRIM:MST}(#1)
R1 1 1
Ris_mincost_DTree_rooted_at
iy mincost d-tree rooted at #2
!not mincost d-tree rooted at #2
R2 1 2
Ris_mincost_DPath_from
iy mincost d-path from #2 to #3
!not mincost d-path from #2 to #3
V1 1
Vmin-cost
a min-cost
#GLIB_005
M1 1
MFF:ELabeling
ha FF_{E}:labeling #0 of #1
FF_{E}-labeling #0 of #1
M2 1
MAP:VLabeling
ha AP_{V}:labeling #0 of #1
AP_{V}:labeling #0 of #1
M3 1
MAP:VLabelingSeq
ha AP_{V}:labeling sequence #0 of #1
AP_{V}:labeling sequences #0 of #1
M4 1
MFF:ELabelingSeq
ha FF_{E}:labeling sequence #0 of #1
FF_{E}:labeling sequences #0 of #1
O1 1 2
O.flow
moi#2#3; #1{\rm .flow}(#2,#3)
O2 0 1
OAP:NextBestEdges
mol; {\rm AP:NextBestEdges}(#1)
O3 0 1
OAP:Step
mol; {\rm AP:Step}(#1)
O4 0 2
OAP:CompSeq
mol#1#2; {\rm AP:CompSeq}(#1,#2)
O5 0 2
OAP:FindAugPath
mol#1#2; {\rm AP:FindAugPath}(#1,#2)
O6 0 3
OAP:GetAugPath
mol#1#2#3; {\rm AP:GetAugPath}(#1,#2,#3)
O7 1 1
O.flowSeq
moi; #1 \mathop{\rm .flowSeq} #2
O8 1 1
O.tolerance
moi; #1 \mathop{\rm .tolerance} #2
O9 0 2
OFF:PushFlow
mol#1#2; {\rm FF:PushFlow}(#1,#2)
O10 0 3
OFF:Step
mol#1#2#3; {\rm FF:Step}(#1,#2,#3)
O11 0 3
OFF:CompSeq
mol#1#2#3; {\rm FF:CompSeq}(#1,#2,#3)
O12 0 3
OFF:MaxFlow
mol#1#2#3; {\rm FF:MaxFlow}(#1,#2,#3)
R1 1 2
Rhas_valid_flow_from
jy valid flow from #2 to #3
!not valid flow from #2 to #3
R2 1 2
Rhas_maximum_flow_from
jy maximum flow from #2 to #3
!not maximum flow from #2 to #3
R3 1 1
Ris_forward_edge_wrt
h is forward edge w.r.t. #2
is not forward edge w.r.t. #2
R4 1 1
Ris_backward_edge_wrt
h is backward edge w.r.t. #2
is not backward edge w.r.t. #2
R5 1 1
Ris_augmenting_wrt
h is augmenting w.r.t. #2
is not augmenting w.r.t. #2
V1 1
Vnatural-weighted
a natural-weighted
#GOBOARD1
M1 0
MGo-board
ha Go-board #0
Go-boards #0
O1 0 1
OX_axis
mol@s#1; \mathop{\bf X\rm\hbox{-}coordinate}(#1)
O2 0 1
OY_axis
mol@s#1; \mathop{\bf Y\rm\hbox{-}coordinate}(#1)
R1 1 1
Ris_sequence_on
i a sequence which elements belong to #2
not a sequence which elements belong to #2
V1 1
VX_equal-in-line
a line {\bf X}-constant
V2 1
VY_equal-in-column
a column {\bf Y}-constant
V3 1
VY_increasing-in-line
a line {\bf Y}-increasing
V4 1
VX_increasing-in-column
a column {\bf X}-increasing
#GOBOARD2
O1 0 1
OGoB
hol@s#1; Go-board of #1
O1 0 2
OGoB
hol@s#1#2; Go-board of #1, #2
O2 0 1
OIncr
mol@s#1; \mathop{\rm Inc}(#1)
#GOBOARD4
R1 1 2
Rlies_between
h #1 lies between #2 and #3
#1 does not lie between #2 and #3
#GOBOARD5
M1 0
Mspecial_circular_sequence
ha special circular sequence #0
special circular sequences #0
O1 0 2
Ov_strip
mol#1#2; \mathop{\rm vstrip}(#1,#2)
O2 0 2
Oh_strip
mol#1#2; \mathop{\rm hstrip}(#1,#2)
O3 0 2
Ocell
mol#1#2; \mathop{\rm cell}(#1,#2)
O3 0 3
Ocell
mol#1#2#3; \mathop{\rm cell}(#1,#2,#3)
O4 0 2
Oright_cell
mol#1#2; \mathop{\rm rightcell}(#1,#2)
O4 0 3
Oright_cell
mol#1#2#3; \mathop{\rm right\_cell}(#1,#2,#3)
O5 0 2
Oleft_cell
mol#1#2; \mathop{\rm leftcell}(#1,#2)
O5 0 3
Oleft_cell
mol#1#2#3; \mathop{\rm left\_cell}(#1,#2,#3)
V1 1
Vs.c.c.
a s.c.c.
V2 1
Vstandard
a standard
#GOBOARD9
O1 0 1
OLeftComp
mol#1; \mathop{\rm LeftComp}(#1)
O2 0 1
ORightComp
mol#1; \mathop{\rm RightComp}(#1)
#GOBRD10
R1 2 0
Rare_adjacent1
h #1 and #2 are adjacent
#1 and #2 are not adjacent
R2 4 0
Rare_adjacent2
h #1, #2, #3, and #4 are adjacent
#1, #2, #3, and #4 are not adjacent
#GOBRD13
O1 0 1
OValues
mol#1; \mathop{\rm Values} #1
O2 0 3
Ofront_right_cell
mol#1#2#3; \mathop{\rm front\_right\_cell}(#1,#2,#3)
O3 0 3
Ofront_left_cell
mol#1#2#3; \mathop{\rm front\_left\_cell}(#1,#2,#3)
R1 1 2
Rturns_right
h #1 turns right #2,#3
#1 does not turn right #2,#3
R2 1 2
Rturns_left
h #1 turns left #2,#3
#1 does not turn left #2,#3
R3 1 2
Rgoes_straight
h #1 goes straight #2,#3
#1 does not go straight #2,#3
#GOEDELCP
O1 0 0
OExCl
mol; \mathop{\rm ExCl}
O2 0 1
OEx-bound_in
mol#1; \mathop{\rm ExBound}(#1)
O3 0 1
OEx-the_scope_of
mol#1; \mathop{\rm ExScope}(#1)
V1 1
Vnegation_faithful
a negation faithful
V2 1
Vwith_examples
x examples
#GRAPHSP
O1 1 1
O:=
moi@s; #1{\verb|:=|\,} #2
O1 1 2
O:=
moi@s/2w@9#3; #1{:=} #2_{#3}
O1 2 1
O:=
moi(1,3)@0/1w@9#2; #1_{#2}{:=} #3
O1 2 2
O:=
moi#1#2#3#4; (#1,#2):=(#3,#4)
O2 0 1
Orepeat
mol; \mathop{\rm repeat} #1
O3 0 2
OOuterVx
mol#1#2; \mathop{\rm OuterVx} (#1,#2)
O4 0 2
OLifeSpan
mol#1#2; \mathop{\rm LifeSpan}(#1,#2)
O4 0 3
OLifeSpan
mol#1#2#3; \mathop{\rm LifeSpan}(#1,#2,#3)
O5 0 2
Owhile_do
mol#1#2; \mathop{\rm WhileDo} (#1,#2)
O6 0 2
OXEdge
mol#1#2; \mathop{\rm XEdge}(#1,#2)
O7 0 3
OWeight
mol#1#2#3; \mathop{\rm Weight} (#1,#2,#3)
O8 0 2
OUnusedVx
mol#1#2; \mathop{\rm UnusedVx} (#1,#2)
O9 0 2
OUsedVx
mol#1#2; \mathop{\rm UsedVx} (#1,#2)
O10 0 3
OArgmin
mol#1#2#3; \mathop{\rm Argmin} (#1,#2,#3)
O11 0 1
Ofindmin
mol; \mathop{\rm findmin} #1
O12 0 3
Onewpathcost
mol#1#2#3; \mathop{\rm newpathcost} (#1,#2,#3)
O13 0 1
ORelax
mol; \mathop{\rm Relax} #1
O13 0 2
ORelax
mol#1#2; \mathop{\rm Relax} (#1,#2)
O14 0 1
ODijkstraAlgorithm
mol; \mathop{\rm DijkstraAlgorithm} #1
R1 1 2
RhasBetterPathAt
j better path at #2,#3
no better path at #2,#3
R2 2 2
Requal_at
h #1,#2 are equal at #3,#4
#1,#2 are different at #3,#4
R3 1 3
Ris_vertex_seq_at
i vertex sequence at #2,#3,#4
not vertex sequence at #2,#3,#4
R4 1 3
Ris_simple_vertex_seq_at
i simple vertex sequence at #2,#3,#4
not simple vertex sequence at #2,#3,#4
R5 1 1
Ris_oriented_edge_seq_of
i oriented edge sequence at #2
not oriented edge sequence at #2
R6 1 3
Ris_Input_of_Dijkstra_Alg
i input of Dijkstra algorithm #2 to #3 in #4
not input of Dijkstra algorithm #2 to #3 in #4
#GRAPH_1
G1 4
GMultiGraphStruct
mc#1#2#3#4; \langle #1, #2, #3, #4\rangle
J1 1
GMultiGraphStruct
hol#1; multi graph structure of #1
L1 0
GMultiGraphStruct
ha multi graph structure #0
multi graph structures #0
M1 1
MEdge
ha edge #0 of #1
edges #0 of #1
M2 0
MGraph
ha graph #0
graphs #0
M3 1
MPath
ha path #0 of #1
paths #0 of #1
M3 2
MPath
ha path #0 from #1 to #2
paths #0 from #1 to #2
M4 1
MOrientedPath
hn oriented path #0 of #1
oriented paths #0 of #1
M5 1
MCycle
ha cycle #0 of #1
cycles #0 of #1
M5 2
MCycle
ha #1-cycle #0 of #2
#1-cycles #0 of #2
M6 1
MOrientedCycle
hn oriented cycle #0 of #1
oriented cycles #0 of #1
O1 0 1
Ocod
mol@s; \mathop{\rm cod} #1
O2 0 1
OVerticesCount
hol; number of vertices of #1
O3 0 1
OEdgesCount
hol; number of edges of #1
O4 0 1
OEdgesIn
mcl@s#1; \mathop{\rm EdgIn}(#1)
O5 0 1
OEdgesOut
mcl@s#1; \mathop{\rm EdgOut}(#1)
O6 0 1
ODegree
hol; degree of #1
O6 0 2
ODegree
mol#1#2; \mathop{\rm Degree}(#1,#2)
R1 1 2
Ris_sum_of
i a sum of #2 and #3
not a sum of #2 and #3
R2 1 2
Rjoins
h #1 joins #2 with #3
#1 does not join #2 with #3
R3 2 0
Rare_incident
h #1 and #2 are incident
#1 and #2 are not incident
U1 1
USource
hosl#1; source of #1
source
U2 1
UTarget
hosl#1; target of #1
target
V1 1
Voriented
n oriented
V2 1
Vcyclic
a cyclic
#GRAPH_2
O1 2 1
O-cut
mc/3r#1#2; \langle #3(#1),\dots,#3(#2)\rangle
O2 1 1
O^'
moi; #1\smallfrown\!\!\smallfrown #2
O3 1 1
O-VSet
moi#2; #1{\rm\hbox{-}VSet}(#2)
O4 0 1
Overtex-seq
mol#1; \mathop{\rm vertex\hbox{-}seq}(#1)
O5 0 3
Omin_at
mol(1)@a/2r/3q; \mathop{{\rm min}_{#2}^{#3}}#1
R1 1 1
Ris_vertex_seq_of
i vertex sequence of #2
not vertex sequence of #2
R2 1 1
Ralternates_vertices_in
h #1 alternates vertices in #2
#1 does not alternate vertices in #2
R3 1 2
Ris_non_decreasing_on
h #1 is non decreasing on #2,#3
#1 is decreasing on #2,#3
R4 1 1
Ris_split_at
i split at #2
not split at #2
V1 1
VTwoValued
a two-valued
V2 1
VAlternating
n alternating
#GRAPH_3
O1 0 1
OEdges_In
mol; \mathop{\rm EdgesIn} #1
O1 0 2
OEdges_In
mol#1#2; \mathop{\rm EdgesIn}(#1,#2)
O2 0 1
OEdges_Out
mol; \mathop{\rm EdgesOut} #1
O2 0 2
OEdges_Out
mol#1#2; \mathop{\rm EdgesOut}(#1,#2)
O3 0 2
OEdges_At
mol#1#2; \mathop{\rm EdgesAt}(#1,#2)
O4 0 2
OAddNewEdge
mol#1#2; \mathop{\rm AddNewEdge}(#1,#2)
O5 1 0
O-CycleSet
mor; #1{\hbox{-}\rm CycleSet}
O5 1 1
O-CycleSet
moi; #1{\hbox{-}\rm CycleSet} #2
O6 0 2
OCatCycles
mol#1#2; \mathop{\rm CatCycles}(#1,#2)
O7 1 1
O-PathSet
moi#2; #1{\rm\hbox{-}PathSet}(#2)
O8 0 1
OExtendCycle
mol; \mathop{\rm ExtendCycle} #1
V1 1
VEulerian
n Eulerian
#GRAPH_4
O1 1 1
O-SVSet
moi; #1 \mathop{\rm\hbox{-}SVSet} #2
O2 1 1
O-TVSet
moi; #1 \mathop{\rm\hbox{-}TVSet} #2
O3 0 1
Ooriented-vertex-seq
mol; \mathop{\rm oriented\hbox{-}vertex\hbox{-}seq} #1
R1 1 2
Rorientedly_joins
h #1 orientedly joins #2,#3
#1 does not orientedly join #2,#3
R2 2 0
Rare_orientedly_incident
h #1,#2 are orientedly incident
#1,#2 are not orientedly incident
R3 1 1
Ris_oriented_vertex_seq_of
h #1 is oriented vertex seq of #2
#1 is not oriented vertex seq of #2
V1 1
VSimple
a Simple
#GRAPH_5
O1 0 1
Overtices
mol; \mathop{\rm vertices} #1
O2 0 2
OOrientedPaths
mol#1#2; \mathop{\rm OrientedPaths}(#1,#2)
O3 0 1
OAcyclicPaths
mol#1; \mathop{\rm AcyclicPaths}(#1)
O3 0 2
OAcyclicPaths
mol#1#2; \mathop{\rm AcyclicPaths}(#1,#2)
O3 0 3
OAcyclicPaths
mol#1#2#3; \mathop{\rm AcyclicPaths}(#1,#2,#3)
O4 0 0
OReal>=0
mol; {\mathbb R}_{\geq 0}
O5 0 2
ORealSequence
mol#1#2; \mathop{\rm RealSequence}(#1,#2)
O6 0 2
Ocost
mol#1#2; \mathop{\rm cost}(#1,#2)
R1 1 2
Ris_orientedpath_of
i oriented path from #2 to #3
not oriented path from #2 to #3
R1 1 3
Ris_orientedpath_of
i oriented path from #2 to #3 in #4
not oriented path from #2 to #3 in #4
R2 1 2
Ris_acyclicpath_of
i acyclic path from #2 to #3
not acyclic path from #2 to #3
R2 1 3
Ris_acyclicpath_of
i acyclic path from #2 to #3 in #4
not acyclic path from #2 to #3 in #4
R3 1 1
Ris_weight>=0of
i nonnegative weight of #2
not nonnegative weight of #2
R4 1 1
Ris_weight_of
i weight of #2
not weight of #2
R5 1 3
Ris_shortestpath_of
i shortest path from #2 to #3 in #4
not shortest path from #2 to #3 in #4
R5 1 4
Ris_shortestpath_of
i shortest path from #2 to #3 in #4 w.r.t. #5
not shortest path from #2 to #3 in #4 w.r.t. #5
R6 1 3
RislongestInShortestpath
i longest in shortest path from #3 in #2 w.r.t. #4
not longest in shortest path from #3 in #2 w.r.t. #4
#GRCAT_1
G1 3
GGroupMorphismStr
mc#1#2#3; \langle #1, #2, #3\rangle
J1 1
GGroupMorphismStr
hol#1; group morphism structure of #1
L1 0
GGroupMorphismStr
ha group morphism structure #0
group morphism structures #0
M1 0
MGroupMorphism
ha morphism #0 of groups
morphisms #0 of groups
M2 0
MGroup_DOMAIN
ha non empty set #0 of groups
non empty sets #0 of groups
M3 0
MGroupMorphism_DOMAIN
ha non empty set #0 of morphisms of groups
non empty sets #0 of morphisms of groups
M3 2
MGroupMorphism_DOMAIN
ha non empty set #0 of morphisms from #1 into #2
non empty sets #0 of morphisms from #1 into #2
M4 2
MMapsSet
ha set of maps #0 from #1 into #2
sets of maps #0 from #1 into #2
O1 0 1
OMorphs
mol@s; \mathop{\rm Morphs} #1
O1 0 2
OMorphs
mol@s#1#2; \mathop{\rm Morphs}(#1,#2)
O2 0 1
Ocat
mol@s; \mathop{\rm cat} #1
O3 0 2
OZeroMap
mol@s#1#2; \mathop{\rm ZeroMap}(#1,#2)
O4 0 1
Ofun
mol@s; \mathop{\rm fun} #1
O5 0 1
OZERO
mol#1; \mathop{\rm ZERO} #1
O5 0 2
OZERO
mol@s; \mathop{\rm ZERO} (#1,#2)
O6 0 1
OGroupObjects
mol@s#1; \mathop{\rm GroupObj}(#1)
O7 0 1
OGroupCat
mol@s#1; \mathop{\rm GroupCat}(#1)
O8 0 1
OAbGroupObjects
mol@s#1; \mathop{\rm AbGroupObj}(#1)
O9 0 1
OAbGroupCat
mol@s#1; \mathop{\rm AbGroupCat}(#1)
O10 0 1
OMidOpGroupObjects
mol@s#1; {1\over 2}\mathop{\rm GroupObj}(#1)
O11 0 1
OMidOpGroupCat
mol@s#1; {1\over 2}\mathop{\rm GroupCat}(#1)
R1 0 2
RGO
m \mathop{\rm P_{ob}} #1,#2
\mathop{\rm not\ P_{ob}} #1,#2
R1 0 3
RGO
m \mathop{\rm P_{ob}} #1,#2,#3
\mathop{\rm not\ P_{ob}} #1,#2,#3
U1 1
UFun
hosl#1; {\tt Fun} of #1
{\tt Fun}
V1 1
VGroupMorphism-like
a morphism of groups-like
V2 1
VGroup_DOMAIN-like
a non empty set of groups-like
V3 1
VGroupMorphism_DOMAIN-like
a non empty set of morphisms of groups-like
#GRNILP_1
O1 0 1
Othe_normal_subgroups_of
hol; normal subgroups of #1
#GROEB_1
O1 0 1
Omultiples
mcl@s#1; \mathop{\rm multiples}(#1)
O2 0 1
ODivOrder
mcl@s#1; \mathop{\rm DivOrder}(#1)
R1 1 1
Ris_Groebner_basis_wrt
i a Groebner basis w.r.t. #2
not Groebner basis w.r.t. #2
R2 1 2
Ris_Groebner_basis_of
i a Groebner basis of #2,#3
not Groebner basis of #2,#3
R3 1 1
Ris_monic_wrt
i monic w.r.t. #2
not monic w.r.t. #2
R4 1 1
Ris_reduced_wrt
i reduced w.r.t. #2
not reduced w.r.t. #2
R5 1 1
Ris_autoreduced_wrt
i autoreduced w.r.t. #2
not autoreduced w.r.t. #2
#GROEB_2
O1 0 2
OS-Poly
mcl@s#1; \mathop{\rm S\hbox{-}Poly}(#1,#2)
O1 0 3
OS-Poly
mcl@s#1; \mathop{\rm S\hbox{-}Poly}(#1,#2,#3)
R1 2 0
Rare_disjoint
h #1,#2 are disjoint
#1,#2 are not disjoint
R2 2 0
Rare_non_disjoint
h #1,#2 are non disjoint
#1,#2 are disjoint
R3 1 1
Ris_MonomialRepresentation_of
i a monomial representation of #2
not monomial representation of #2
R4 1 3
Ris_Standard_Representation_of
i a standard representation of #2,#3,#4
not standard representation of #2,#3,#4
R4 1 4
Ris_Standard_Representation_of
i a standard representation of #2,#3,#4,#5
not standard representation of #2,#3,#4,#5
R5 1 2
Rhas_a_Standard_Representation_of
j a standard representation of #2,#3
no standard representation of #2,#3
R5 1 3
Rhas_a_Standard_Representation_of
j a standard representation of #2,#3,#4
no standard representation of #2,#3,#4
#GROEB_3
O1 0 3
OUpper_Support
mol#1#2#3; \mathop{\rm UpperSupport}(#1,#2,#3)
O2 0 3
OLower_Support
mol#1#2#3; \mathop{\rm LowerSupport}(#1,#2,#3)
O3 0 3
OLow
mol#1#2#3; \mathop{\rm Low}(#1,#2,#3)
#GROUP_1
M1 0
MGroup
ha group #0
groups #0
O1 0 1
O1_
mow#1; {\bf 1}_{#1}
O1 0 2
O1_
mol#1#2; \mathop{\rm 1\_}(#1,#2)
O2 0 1
Oinverse_op
mcr@s/1k#1; {\cdot^{-1}_{#1}}
O3 0 1
Opower
mow/1k#1; {\rm power}_{#1}
O4 0 1
Oord
mcl@s#1; \mathop{\rm ord}(#1)
V1 1
Vunital
a unital
V2 1
VGroup-like
a group-like
V3 1
Vbeing_of_order_0
b of order 0
V4 1
Vunity-preserving
a unity-preserving
#GROUP_10
M1 2
MLeftOperation
ha left operation #0 of #1 on #2
left operations #0 of #1 on #2
O1 0 1
Othe_left_translation_of
mcl@2; \mathbin{\bm\gamma}_{#1}
O1 0 2
Othe_left_translation_of
mcl@2#1#2; \mathbin{\bm\gamma}_{#1,#2}
O2 0 1
Othe_left_operation_of
mcl@2; \mathbin{\bf\Gamma}_{#1}
O2 0 2
Othe_left_operation_of
mcl@2#1#2; \mathbin{\bf\Gamma}_{#1,#2}
O3 0 2
Othe_subsets_of_card
mol@2#1#2; [#2]^{#1}
O4 0 3
Othe_extension_of_left_translation_of
mcl@2#1#2#3; \mathbin{\bm\gamma}^{#1}_{#2,#3}
O5 0 2
Othe_extension_of_left_operation_of
mcl@2#1#2; \mathbin{\bf\Gamma}^{#1}_{#2}
O6 0 2
Othe_strict_stabilizer_of
mol@2#1#2; #2_{#1}
O7 0 1
Othe_fixed_points_of
mcl@2; #1_0
O8 0 2
Othe_orbit_of
mol@2#1#2; #2(#1)
O9 0 1
Othe_orbits_of
hol; orbits of #1
O10 0 2
Othe_sylow_p-subgroups_of_prime
mol@2#1#2; \mathbin{\mathsf{Syl}}_{#1}(#2)
R1 1 1
Ris_fixed_under
iy fixed under #2
not fixed under #2
R2 2 1
Rare_conjugated_under
hy #1 and #2 are conjugated under #3
#1 and #2 are not conjugated under #3
R4 1 1
Ris_Sylow_p-subgroup_of_prime
iy a Sylow #2-subgroup
not a Sylow #2-subgroup 
V1 1
Vbeing_left_operation
a left-operation
V2 2
V-group
a #1-group
#GROUP_2
M1 1
MSubgroup
ha subgroup #0 of #1
subgroups #0 of #1
O1 0 1
O(1).
mow/1k#1; \lbrace {\bf 1} \rbrace_{#1}
O2 0 1
Ocarr
mct#1; \overline{#1}
O3 0 1
OLeft_Cosets
hol; left cosets of #1
O4 0 1
ORight_Cosets
hol; right cosets of #1
O5 0 1
OIndex
mc#1; \vert \bullet: #1 \vert
O5 0 2
OIndex
mol#1#2; \mathop{\rm Index}(#1,#2)
#GROUP_3
O1 0 1
OSubgroups
mol@s; \mathop{\rm SubGr} #1
O2 0 1
Ocon_class
mcr; #1^\bullet
O3 0 1
ONormalizator
mc#1; {\rm N}(#1)
R1 2 0
Rare_conjugated
h #1 and #2 are conjugated
#1 and #2 are not conjugated
R2 2 0
Rare_not_conjugated
hn #1 and #2 are not conjugated
#1 and #2 are conjugated
#GROUP_4
O1 0 1
Ogr
mcl@s#1; \mathop{\rm gr}(#1)
O2 0 1
OPhi
mol@s; \mathop\Phi(#1)
O2 0 2
OPhi
mol@s#1#2; \Phi(#1,#2)
O3 0 1
Olattice
mow/1k; {\mathbb L}_{#1}
V1 1
Vmaximal
a maximal
#GROUP_5
O1 0 1
Ocommutators
ho#1; commutators of #1
O1 0 2
Ocommutators
ho#1#2; commutators of #1 \& #2
O2 0 1
Ocenter
mol#1; {\rm Z}(#1)
#GROUP_6
M1 2
MHomomorphism
ha homomorphism #0 from #1 to #2
homomorphisms #0 from #1 to #2
M1 3
MHomomorphism
ha homomorphism #0 from #2 to #3 by #1
homomorphisms #0 from #2 to #3 by #1
O1 0 1
OCosets
mol@s; \mathop{\rm Cosets} #1
O2 0 1
OCosOp
mol@s; \mathop{\rm CosOp} #1
O3 1 1
O./.
mo{kqmw}@m; {}^{#1}/_{#2}
O4 0 2
O1:
moi{w}@w#2; #1\to\lbrace{\bf 1}\rbrace_{#2}
O5 0 1
Onat_hom
hol#1; canonical homomorphism onto cosets of #1
O6 0 1
OKer
mol@s; \mathop{\rm Ker} #1
O7 0 1
OImage
mol@s; \mathop{\rm Im} #1
#GROUP_7
M1 1
MmultMagma-Family
ha multiplicative magma family #0 of #1
multiplicative magma families #0 of #1
V1 1
VmultMagma-yielding
a multiplicative magma yielding
#GROUP_8
O1 0 2
ODouble_Cosets
mol@s#1#2; \mathop{\rm DoubleCosets}(#1,#2)
#GROUP_9
G1 3
GHGrWOpStr
mc#1#2#3; \langle #1,#2,#3 \rangle
J1 1
GHGrWOpStr
hol#1; group structure with operators of #1
L1 1
GHGrWOpStr
ha group structure #0 with operators in #1
group structures #0 with operators in #1
M1 2
MAction
hn action #0 of #1 on #2
actions #0 of #1 on #2
M2 1
MGroupWithOperators
ha group #0 with operators in #1
groups #0 with operators in #1
M3 1
MStableSubgroup
ha stable subgroup #0 of #1
stable subgroups #0 of #1
M4 1
MCompositionSeries
ha composition series #0 of #1
composition series #0 of #1
O1 0 2
Othe_stable_subset_generated_by
hol#1#2; stable subset generated by #1
O2 0 1
Othe_stable_subgroups_of
hol; stable subgroups of #1
O3 0 1
OCosAc
mol; \mathop{\rm CosAc} #1
O4 0 1
Othe_stable_subgroup_of
hol; stable subgroup of #1
O5 0 1
Othe_series_of_quotients_of
hol; series of quotients of #1
O6 0 2
Othe_schreier_series_of
hol#1#2; Schreier series of #1 and #2
R1 1 1
Ris_stable_under_the_action_of
iy stable under the action of #2
not stable under the action of #2
R2 2 2
Rare_equivalent_under
hy #1 and #2 are equivalent under #3 in #4
#1 and #2 are not equivalent under #3 in #4
U1 1
Uaction
honl#1; action of #1
action
V1 1
Vhomomorphic
a homomorphic
V2 1
Vcomposition_series
a composition series
V3 1
Vstrictly_decreasing
a strictly decreasing
V4 1
Vjordan_holder
a Jordan-H\"older
#GRSOLV_1
V1 1
Vsolvable
a solvable
#GR_CY_1
O1 0 0
OINT.Group
mo; {\mathbb Z}^{+}
O1 0 1
OINT.Group
mo{qrw}#1; {\mathbb Z}_{#1}^{+}
O2 0 1
O@'
mok@w; \mathopen{^@} #1
#GR_CY_3
O1 0 1
OMersenne
mol; \mathop{M}_{#1}
V1 1
VSafe
a safe
V2 1
VSophie_Germain
a Sophie Germain
#HAHNBAN
M1 1
MFunctional
ha functional #0 in #1
functionals #0 in #1
M2 1
MBanach-Functional
ha Banach functional #0 in #1
Banach functionals #0 in #1
M3 1
Mlinear-Functional
ha linear functional #0 in #1
linear functionals #0 in #1
V1 1
Vsubadditive
a subadditive
V2 1
Vpositively_homogeneous
a positively homogeneous
V3 1
Vsemi-homogeneous
a semi-homogeneous
V4 1
Vabsolutely_homogeneous
n absolutely homogeneous
V5 1
V0-preserving
a 0-preserving
#HAHNBAN1
K1 2 L1 vHAHNBAN1
K[**
L**]
moi@a/2r@m; #1 + #2 i_{{\mathbb C}_{\rm F}}
M1 1
MRFunctional
ha RFunctional #0 of #1
RFunctionals #0 of #1
M2 1
MSemi-Norm
ha Semi-Norm #0 of #1
Semi-Norms #0 of #1
O1 0 0
Oi_FC
mol; i_{{\mathbb C}_{\rm F}}
O2 0 1
O0Functional
mol#1; \mathop{\rm 0Functional} #1
O3 0 1
O0RFunctional
mol#1; \mathop{\rm 0RFunctional} #1
O4 0 1
ORealVS
mol#1; \mathop{\rm RealVS} #1
O5 0 1
OprojRe
mol#1; \mathop{\rm projRe} #1
O6 0 1
OprojIm
mol#1; \mathop{\rm projIm} #1
O7 0 1
ORtoC
mol#1; #1_{\mathbb R\rightarrow\mathbb C}
O8 0 1
OCtoR
mol#1; #1_{\mathbb C\rightarrow\mathbb R}
O9 0 1
Oi-shift
mol#1; \mathop{\rm i\hbox{-}shift} #1
O10 0 1
OprodReIm
mol#1; \mathop{\rm prodReIm} #1
V1 1
VReal_homogeneous
a Real-homogeneous
#HALLMAR1
M1 1
MReduction
ha reduction #0 of #1
reductions #0 of #1
M1 2
MReduction
ha reduction #0 of #1 at #2-th position
reductions #0 of #1 at #2-th position
M2 1
MSinglification
ha singlification #0 of #1
singlifications #0 of #1
M2 2
MSinglification
ha singlification #0 of #1 at #2-th position
singlifications #0 of #1 at #2-th position
O1 0 3
OCut
mol#1#2#3; \mathop{\rm Cut}(#1,#2,#3)
R1 1 1
Ris_a_system_of_different_representatives_of
i a system of different representatives of #2
not a system of different representatives of #2
V1 1
VHall
s Hall condition
#HAUSDORF
O1 0 2
OHausDist
mol#1#2; \mathop{\rm HausDist}(#1,#2)
#HELLY
M1 0
M_Tree
ha tree #0
trees #0
M2 1
M_Subtree
ha subtree #0 of #1
subtrees #0 of #1
O1 0 2
OmaxPrefix
mol#1#2; \mathop{\rm maxPrefix}(#1,#2)
O2 1 2
O.pathBetween
moi#2#3; #1{\rm .pathBetween}(#2,#3)
O3 0 3
OMiddleVertex
mol#1#2#3; \mathop{\rm middleVertex}(#1,#2,#3)
V1 1
Vwith_Helly_property
x Helly property
#HENMODEL
M1 1
MHenkin_interpretation
ha Henkin interpretation #0 of #1
Henkin interpretations #0 of #1
O1 0 0
OHCar
mcl; \mathop{\rm HCar}
O2 0 0
OvalH
mcl; \mathop{\rm valH}
V1 1
VConsistent
a consistent
V2 1
VInconsistent
n inconsistent
#HERMITAN
M1 1
Mantilinear-Functional
hn antilinear functional #0 of #1
antilinear functionals #0 of #1
M2 2
Msesquilinear-Form
ha sesquilinear form #0 of #1,#2
sesquilinear forms #0 of #1,#2
M3 1
Mhermitan-Form
ha hermitan form #0 of #1
hermitan forms #0 of #1
O1 0 1
OQcFunctional
mol; \mathop{\rm QcFunctional} #1
O2 0 2
Osignnorm
mol#1#2; ||#2||^2_{#1}
O3 0 1
Oquasinorm
mol#1; ||\cdot||_{#1}
O4 0 1
ORQ*Form
mol#1; \mathop{{\rm RQForm}^{\ast}} (#1)
O5 0 1
OQ*Form
mol#1; \mathop{{\rm QForm}^{\ast}} #1
O6 0 1
OScalarForm
mol#1; \langle\cdot |\cdot\rangle_{#1}
V1 1
Vcmplxhomogeneous
a complex-homogeneous
V2 1
VcmplxhomogeneousFAF
a complex-homogeneous w.r.t. second argument
V3 1
Vhermitan
a hermitan
V4 1
VdiagRvalued
a diagonal real valued
V5 1
VdiagReR+0valued
a diagonal plus-real valued
V6 1
Vpositivediagvalued
a positive diagonal valued
#HEYTING1
O1 0 1
OAtom
mow/1k#1; \lbrace\square\rbrace_{#1}
O1 0 2
OAtom
mol#1#2; \mathop{\rm Atom}(#1,#2)
O2 0 1
Opair_diff
mci@a/1k#1; \square\setminus_{#1}\square
O3 1 1
O=>>
mox; #1 \rightarrowtail #2
O4 0 1
Opseudo_compl
mow/1k#1; \square\mathclose{^{\rm c}}_{#1}
O4 0 2
Opseudo_compl
mol#1#2; \mathop{\rm pseudo\_compl}(#1,#2)
O5 0 1
OStrongImpl
moi@w/1k#1; \square\rightarrowtail_{#1}\square
O5 0 2
OStrongImpl
mol#1#2; \mathop{\rm StrongImpl}(#1,#2)
O6 0 1
OSUB
moq/1m#1; 2^{#1}
#HEYTING2
O1 0 1
OInvolved
mol#1; \mathop{\rm Involved} #1
#HEYTING3
O1 0 2
OSubstPoset
mol#1#2; \mathop{\rm SubstPoset}(#1,#2)
O2 0 2
OPFArt
mol#1#2; \mathop{\rm PF_A}(#1,#2)
O3 0 2
OPFCrt
mol#1#2; \mathop{\rm PF_C}(#1,#2)
O4 0 2
OPFBrt
mol#1#2; \mathop{\rm PF_B}(#1,#2)
O5 0 1
OPFDrt
mol#1; \mathop{\rm PF_D}(#1)
#HIDDEN
G1 1
G1-sorted
mc#1; \langle #1\rangle
G2 2
GZeroStr
mc#1#2; \langle #1, #2\rangle
J1 1
G1-sorted
hol#1; 1-sorted structure of #1
J2 1
GZeroStr
hol#1; zero structure of #1
K1 1 L1 vHIDDEN
K[
L]
mc#1; \lbrack #1 \rbrack
K1 2 L1 vHIDDEN
K[
L]
mc#1#2; \llangle #1,\allowbreak\, #2\rrangle
K1 3 L1 vHIDDEN
K[
L]
mc#1#2#3; \llangle #1,\allowbreak\, #2,\allowbreak\, #3\rrangle
K1 4 L1 vHIDDEN
K[
L]
mc#1#2#3#4; \llangle #1, #2, #3, #4\rrangle
K1 5 L1 vHIDDEN
K[
L]
mc#1#2#3#4#5; \llangle #1, #2, #3, #4, #5\rrangle
K1 6 L1 vHIDDEN
K[
L]
mc#1#2#3#4#5#6; \llangle #1, #2, #3, #4, #5, #6\rrangle
K1 7 L1 vHIDDEN
K[
L]
mc#1#2#3#4#5#6#7; \llangle #1, #2, #3, #4, #5, #6, #7\rrangle
K1 8 L1 vHIDDEN
K[
L]
mc#1#2#3#4#5#6#7#8; \llangle #1, #2, #3, #4, #5, #6, #7, #8\rrangle
K1 9 L1 vHIDDEN
K[
L]
mc#1#2#3#4#5#6#7#8#9; \llangle #1, #2, #3, #4, #5, #6, #7, #8, #9\rrangle
K2 1 L2 vHIDDEN
K{
L}
mc#1; \lbrace #1 \rbrace
K2 2 L2 vHIDDEN
K{
L}
mc#1#2; \lbrace #1, #2 \rbrace
K2 3 L2 vHIDDEN
K{
L}
mc#1#2#3; \lbrace #1, #2, #3 \rbrace
K2 4 L2 vHIDDEN
K{
L}
mc#1#2#3#4; \lbrace #1, #2, #3, #4 \rbrace
K2 5 L2 vHIDDEN
K{
L}
mc#1#2#3#4#5; \lbrace #1, #2, #3, #4, #5 \rbrace
K2 6 L2 vHIDDEN
K{
L}
mc#1#2#3#4#5#6; \lbrace #1, #2, #3, #4, #5, #6 \rbrace
K2 7 L2 vHIDDEN
K{
L}
mc#1#2#3#4#5#6#7; \lbrace #1, #2, #3, #4, #5, #6, #7 \rbrace
K2 8 L2 vHIDDEN
K{
L}
mc#1#2#3#4#5#6#7#8; \lbrace #1, #2, #3, #4, #5, #6, #7, #8 \rbrace
K2 9 L2 vHIDDEN
K{
L}
mc#1#2#3#4#5#6#7#8#9; \lbrace #1, #2, #3, #4, #5, #6, #7, #8, #9 \rbrace
K2 10 L2 vHIDDEN
K{
L}
mc#1#2#3#4#5#6#7#8#9#10; \llangle #1,#2,#3,#4,#5,#6,#7,#8,#9,#10\rrangle
L1 0
G1-sorted
ha 1-sorted structure #0
1-sorted structures #0
L2 0
GZeroStr
ha zero structure #0
zero structures #0
M1 0
Mset
ha set #0
sets #0
R1 1 1
R=
m #1 = #2
#1 \neq #2
R2 1 1
R<>
m #1 \neq #2
#1 = #2
R3 1 1
Rin
m #1 \in #2
#1 \notin #2
U1 1
Ucarrier
hosl#1; carrier of #1
carrier
U2 1
UZero
hosl#1; zero of #1
zero
V1 1
Vstrict
a strict
#HILBASIS
O1 1 1
Obag_extend
moi; #1 {\rm\;extended\;by\;}#2
O2 0 1
OUnitBag
mol#1; \mathop{\rm UnitBag} #1
O3 0 2
O1_1
mol#1#2; \mathop{\rm 1\_1}(#1,#2)
O4 0 1
Ominlen
mol#1; \mathop{\rm minlen} #1
O5 0 2
Omonomial
mol#1#2; \mathop{\rm monomial}(#1,#2)
O6 0 2
Oupm
mol#1#2; \mathop{\rm upm}(#1,#2)
O7 0 2
Ompu
mol#1#2; \mathop{\rm mpu}(#1,#2)
#HILBERT1
M1 0
MHP-formula
ha HP-formula #0
HP-formulas #0
O1 0 0
OHP-WFF
mol; \mathop{\rm HP\hbox{-}WFF}
O2 0 1
OCnPos
mol#1; \mathop{\rm CnPos} #1
O3 0 0
OHP_TAUT
mol; \mathop{\rm HP\_TAUT}
V1 1
Vwith_VERUM
x VERUM
V2 1
Vwith_implication
x implication
V3 1
Vwith_conjunction
x conjunction
V4 1
Vwith_propositional_variables
x propositional variables
V5 1
VHP-closed
a HP-closed
V6 1
VHilbert_theory
a Hilbert theory
#HILBERT2
O1 0 1
Oprop
mol#1; \mathop{\rm prop} #1
O2 0 0
OHP-Subformulae
mol; \mathop{\rm HP\hbox{-}Subformulae}
#HILBERT3
M1 0
MSetValuation
ha SetValuation #0
SetValuations #0
O1 0 1
OSetVal
mol#1; \mathop{\rm SetVal} #1
O1 0 2
OSetVal
mol#1#2; \mathop{\rm SetVal}(#1,#2)
O2 0 1
OPerm
mol#1; \mathop{\rm Perm} #1
O2 0 2
OPerm
mol#1#2; \mathop{\rm Perm}(#1,#2)
V1 1
Vcanonical
a canonical
V2 1
Vpseudo-canonical
a pseudo-canonical
#HOMOTHET
R1 1 1
Ris_Sc
i Sc #2
not Sc #2
#HURWITZ
O1 0 2
OCoeff
mol#1#2; \mathop{\rm Coeff}(#1,#2)
O2 0 1
Odeg
mol; \mathop{\rm deg} #1
O3 0 2
Orpoly
mol#1#2; \mathop{\rm rpoly}(#1,#2)
O4 0 2
Oqpoly
mol#1#2; \mathop{\rm qpoly}(#1,#2)
O5 0 2
OF*
mol#1#2; F*(#1,#2)
V1 1
VHurwitz
a Hurwitz
#IDEAL_1
M1 1
MRightIdeal
ha right ideal #0 of #1
right ideals #0 of #1
M2 1
MLeftIdeal
ha left ideal #0 of #1
left ideals #0 of #1
M3 1
MLinearCombination
ha linear combination #0 of #1
linear combinations #0 of #1
M4 1
MLeftLinearCombination
ha left linear combination #0 of #1
left linear combinations #0 of #1
M5 1
MRightLinearCombination
ha right linear combination #0 of #1
right linear combinations #0 of #1
O1 0 2
Oadd|
mol#1#2; \mathop{\rm add}|(#1,#2)
O2 0 2
Omult|
mol#1#2; \mathop{\rm mult}|(#1,#2)
O3 0 2
OGr
mol#1#2; \mathop{\rm Gr}(#1,#2)
O4 1 0
O-Ideal
mor; #1{\rm\hbox{--}ideal}
O5 1 0
O-LeftIdeal
mor; #1{\rm\hbox{--}left\hbox{-}ideal}
O6 1 0
O-RightIdeal
mor; #1{\rm\hbox{--}right\hbox{-}ideal}
V1 1
Vadd-closed
n add closed
V2 1
Vleft-ideal
a left ideal
V3 1
Vright-ideal
a right ideal
V4 1
Vfinitely_generated
a finitely generated
V5 1
VNoetherian
a Noetherian
V6 1
VPID
a PID
#IDEA_1
O1 0 3
OADD_MOD
mol#1#2#3; \mathop{\rm ADD\_MOD}(#1,#2,#3)
O2 0 2
ONEG_N
mol#1#2; \mathop{\rm NEG\_N}(#1,#2)
O3 0 2
ONEG_MOD
mol#1#2; \mathop{\rm NEG\_MOD}(#1,#2)
O4 0 2
OChangeVal_1
mol#1#2; \mathop{\rm ChangeVal\_1}(#1,#2)
O5 0 2
OChangeVal_2
mol#1#2; \mathop{\rm ChangeVal\_2}(#1,#2)
O6 0 3
OMUL_MOD
mol#1#2#3; \mathop{\rm MUL\_MOD}(#1,#2,#3)
O7 0 2
OINV_MOD
mol#1#2; \mathop{\rm INV\_MOD}(#1,#2)
O8 0 3
OIDEAoperationA
mol#1#2#3; \mathop{\rm IDEAoperationA}(#1,#2,#3)
O9 0 3
OIDEAoperationB
mol#1#2#3; \mathop{\rm IDEAoperationB}(#1,#2,#3)
O10 0 1
OIDEAoperationC
mol#1; \mathop{\rm IDEAoperationC} #1
O11 0 0
OMESSAGES
mol; \mathop{\rm MESSAGES}
O12 0 2
OIDEA_P
mol#1#2; \mathop{\rm IDEA\_P}(#1,#2)
O13 0 2
OIDEA_Q
mol#1#2; \mathop{\rm IDEA\_Q}(#1,#2)
O14 0 3
OIDEA_P_F
mol#1#2#3; \mathop{\rm IDEA\_P\_F}(#1,#2,#3)
O15 0 3
OIDEA_Q_F
mol#1#2#3; \mathop{\rm IDEA\_Q\_F}(#1,#2,#3)
O16 0 2
OIDEA_PS
mol#1#2; \mathop{\rm IDEA\_PS}(#1,#2)
O17 0 2
OIDEA_QS
mol#1#2; \mathop{\rm IDEA\_QS}(#1,#2)
O18 0 2
OIDEA_PE
mol#1#2; \mathop{\rm IDEA\_PE}(#1,#2)
O19 0 2
OIDEA_QE
mol#1#2; \mathop{\rm IDEA\_QE}(#1,#2)
R1 1 1
Ris_expressible_by
h #1 is expressible by #2
#1 is not expressible by #2
#INCPROJ
M1 0
MIncProjSp
ha projective space #0 defined in terms of incidence
projective spaces #0 defined in terms of incidence
O1 0 1
OProjectiveLines
mcl@s#1; {\eusm L}(#1)
O2 0 1
OProj_Inc
mow/1k#1; {\bf I}_{#1}
O3 0 1
OIncProjSp_of
mcl@s#1; \mathop{\rm Inc\hbox{-}ProjSp}(#1)
V1 1
Vpartial
a partial
V2 1
Vup-2-dimensional
n at least 2-dimensional
V3 1
Vup-3-rank
n at least 3-rank
V4 1
V3-dimensional
a 3-dimensional
#INCSP_1
G1 3
GIncProjStr
mc#1#2#3; \langle #1,#2,#3 \rangle
G2 6
GIncStruct
mc#1#2#3#4#5#6; \langle #1, #2, #3, #4, #5, #6\rangle
J1 1
GIncProjStr
hol#1; projective incidence structure of #1
J2 1
GIncStruct
hol#1; incidence structure of #1
L1 0
GIncProjStr
ha projective incidence structure #0
projective incidence structures #0
L2 0
GIncStruct
hn incidence structure #0
incidence structures #0
M1 1
MPOINT
ha point #0 of #1
points #0 of #1
M2 1
MLINE
ha line #0 of #1
lines #0 of #1
M3 1
MPLANE
ha plane #0 of #1
planes #0 of #1
M4 0
MIncSpace
hn incidence space #0
incidence spaces #0
O1 0 2
OLine
mcl@s#1#2; \mathop{\rm Line}(#1,#2)
O2 0 2
OPlane
mcl@s#1#2; \mathop{\rm Plane}(#1,#2)
O2 0 3
OPlane
mcl@s#1#2#3; \mathop{\rm Plane}(#1,#2,#3)
R1 1 1
Ron
h #1 lies on #2
#1 does not lie on #2
R1 1 2
Ron
h #1 lies on #2,#3
#1 does not lie on #2,#3
R1 1 3
Ron
h #1 lies on #2,#3,#4
#1 does not lie on #2,#3,#4
U1 1
UPoints
hopl#1; points of #1
points
U2 1
ULines
hopl#1; lines of #1
lines
U3 1
UInc
honl#1; incidence of #1
incidence
U4 1
UPlanes
hopl#1; planes of #1
planes
U5 1
UInc2
honl#1; incidence2 of #1
incidence2
U6 1
UInc3
honl#1; incidence3 of #1
incidence3
V1 1
Vplanar
a planar
V2 1
Vwith_non-trivial_lines
x non-trivial-lines
V3 1
Vup-2-rank
n up-2-rank
V4 1
Vwith_non-empty_planes
x non-empty-planes
V5 1
Vwith_<=1_plane_per_3_pts
x at-least-one-plane-per-3-pts
V6 1
Vwith_lines_inside_planes
x lines-inside-planes
V7 1
Vwith_planes_intersecting_in_2_pts
x planes-intersecting-in-2-pts
V8 1
Vup-3-dimensional
n up 3-dimensional
V9 1
Vinc-compatible
n incidence-compatible
V10 1
VIncSpace-like
n incidence space-like
#INDEX_1
M1 1
MManySortedCategory
ha many sorted category #0 indexed by #1
many sorted categories #0 indexed by #1
M2 2
MManySortedFunctor
ha many sorted functor #0 from #1 to #2
many sorted functors #0 from #1 to #2
M3 1
MIndexing
hn indexing #0 of #1
indexings #0 of #1
M3 2
MIndexing
hn indexing #0 of #1 and #2
indexings #0 of #1 and #2
M3 4
MIndexing
hn indexing #0 of #1, #2, #3 and #4
indexings #0 of #1, #2, #3 and #4
M4 1
MTargetCat
ha target category #0 of #1
target categories #0 of #1
M5 1
McoIndexing
ha coindexing #0 of #1
coindexings #0 of #1
O1 0 1
OObjs
mol#1; \mathop{\rm Objs}(#1)
O2 0 1
OMphs
mol#1; \mathop{\rm Mphs}(#1)
O3 1 2
O-functor
moi#2#3; #1\mathop{\rm \hbox{-}functor}(#2,#3)
O4 1 1
O-indexing_of
moi@s; #1{\rm\hbox{-}indexing\ of\ }#2
V1 1
VCategory-yielding
a category-yielding
V2 1
VCategory-yielding_on_first
a category-yielding on first
V3 1
VFunction-yielding_on_second
a function-yielding on second
#INSTALG1
M1 1
MSubsignature
ha subsignature #0 of #1
subsignatures #0 of #1
#INTEGR10
O1 0 3
Oext_right_integral
mol/1r@s#2#3; \displaystyle{(R^>)\!\int\limits_{#2}^{#3}#1(x)dx}
O2 0 3
Oext_left_integral
mol/1r@s#2#3; \displaystyle{(R^<)\!\int\limits_{#2}^{#3}#1(x)dx}
O3 0 2
Oinfty_ext_right_integral
mol/1r@s#2; \displaystyle{(R^>)\!\int\limits_{#2}^{+\infty}#1(x)dx}
O4 0 2
Oinfty_ext_left_integral
mol/1r@s#2; \displaystyle{(R^<)\!\int\limits_{-\infty}^{#2}#1(x)dx}
O5 0 1
Oinfty_ext_integral
mol/1r@s; \displaystyle{(R)\!\int\limits_{-\infty}^{+\infty}#1(x)dx}
O6 0 1
Oexp*-
moq/1a; e^{-#1\cdot\square}
O7 0 1
OOne-sided_Laplace_transform
hol; one-sided Laplace transform of #1
R1 1 2
Ris_right_ext_Riemann_integrable_on
i right extended Riemann integrable on #2, #3
not right extended Riemann integrable on #2, #3
R2 1 2
Ris_left_ext_Riemann_integrable_on
i left extended Riemann integrable on #2, #3
not left extended Riemann integrable on #2, #3
R3 1 1
Ris_+infty_ext_Riemann_integrable_on
i extended Riemann integrable on #2, $+\infty$
not extended Riemann integrable on #2, $+\infty$
R4 1 1
Ris_-infty_ext_Riemann_integrable_on
i extended Riemann integrable on $-\infty,$ #2
not extended Riemann integrable on $-\infty,$ #2
V1 1
Vinfty_ext_Riemann_integrable
n $\infty$-extended Riemann integrable
#INTEGR15
M1 2
Mmiddle_volume
ha middle volume #0 of #1 and #2
middle volumes #0 of #1 and #2
M2 2
Mmiddle_volume_Sequence
ha middle volume sequence #0 of #1 and #2
middle volume sequences #0 of #1 and #2
O1 0 2
Omiddle_sum
mol#1#2; \mathop{\rm middle~sum}(#1,#2)
#INTEGR1C
M1 0
MC1-curve
ha $C_1$-curve #0
$C_1$-curves #0
O1 0 0
OR2-to-C
mol@w; {\Bbb R}^2\to\Bbb C
V1 1
VC1-curve-like
a $C_1$-curve-like
#INTEGRA1
M1 1
MDivision
ha Division #0 of #1
Divisions #0 of #1
O1 0 1
Odivs
mol#1; \mathop{\rm divs} #1
O2 0 2
Odivset
mol#1#2; \mathop{\rm divset}(#1,#2)
O3 0 2
Oupper_volume
mol#1#2; \mathop{\rm upper\_volume}(#1,#2)
O4 0 2
Olower_volume
mol#1#2; \mathop{\rm lower\_volume}(#1,#2)
O5 0 2
Oupper_sum
mol#1#2; \mathop{\rm upper\_sum}(#1,#2)
O6 0 2
Olower_sum
mol#1#2; \mathop{\rm lower\_sum}(#1,#2)
O7 0 1
Oupper_sum_set
mol#1; \mathop{\rm upper\_sum\_set} #1
O8 0 1
Olower_sum_set
mol#1; \mathop{\rm lower\_sum\_set} #1
O9 0 1
Oupper_integral
mol#1; \mathop{\rm upper\_integral} #1
O10 0 1
Olower_integral
mol#1; \mathop{\rm lower\_integral} #1
O11 0 1
Ointegral
mol#1; \mathop{\rm integral} #1
O11 0 2
Ointegral
mol\1r@s#2; \displaystyle{\int\limits_{#2}#1(x)dx}
O11 0 3
Ointegral
mol#2#3; \displaystyle{\int\limits_{#2}^{#3}#1(x)dx}
O11 0 4
Ointegral
mol#1#2#3#4; \int\limits_{#1}#4\,{\rm d}#3
O11 0 6
Ointegral
mol#1#2#3#4#5#6; \int(#1,#2,#3,#4,#5,#6)
O12 0 1
Oindx
mol#1; \mathop{\rm index}(#1)
O12 0 3
Oindx
mol#1#2#3; \mathop{\rm indx}(#1,#2,#3)
O13 0 1
OPartSums
mol#1; \mathop{\rm PartSums} #1
V1 1
Vclosed-interval
a closed-interval
V2 1
Vupper_integrable
n upper integrable
V3 1
Vlower_integrable
a lower integrable
V4 1
Vintegrable
n integrable
#INTEGRA2
M1 1
MDivSequence
ha division sequence #0 of #1
division sequences #0 of #1
#INTEGRA4
R1 1 1
Rdivide_into_equal
h #1 divides into equal #2
#1 does not divide into equal #2
#INTEGRA5
K1 2 L1 vINTEGRA5
K['
L']
mc#1#2; [ #1,#2 ]
R1 1 1
Ris_integrable_on
h #1 is integrable on #2
#1 is not integrable on #2
#INTEGRA7
O1 0 2
OIntegralFuncs
mol#1#2; \mathop{\rm IntegralFuncs}(#1,#2)
R1 1 2
Ris_integral_of
i an integral of #2 on #3
not an integral of #2 on #3
#INTEGRA8
O1 0 1
OCst
mol; \mathop{\rm Cst} #1
#INTEGRA9
K1 3 L1 vINTEGRA9
K|||(
L)|||
mow#1#2#3; \langle #1,#2 \rangle_{#3}
K2 2 L2 vINTEGRA9
K||..
L..||
mow#1#2; || #1 ||_{#2}
R1 1 2
Ris_orthogonal_with
i orthogonal with #2 in #3
not orthogonal with #2 in #3
#INTERVA1
M1 1
MIntervalSet
hn interval set #0 of #1
interval sets #0 of #1
O1 0 2
OInter
mol#1#2; {[#1,#2]}_{\mathop{\rm I}}
O2 1 1
O_/\_
moi@m; #1 \cap_{\rm I} #2
O3 1 1
O_\/_
moi@a; #1 \cup_{\rm I} #2
O4 1 0
O``2
mow; {#1_{\bf 2}}
O5 1 1
O_\_
moi@5; #1 \setminus_{\rm I} #2
O6 0 1
OIntervalSets
mol#1; {\rm I}(2^{#1})
O7 0 1
OInterLatt
mol; \mathop{\rm InterLatt} #1
O8 0 1
ORS
mol; \mathop{\rm RS} #1
O9 0 1
ORoughSets
mol; \mathop{\rm RoughSets} #1
O10 0 1
ORSLattice
mol; \mathop{\rm RSLattice} #1
O11 0 1
OERS
mol; \mathop{\rm ERS} #1
V1 1
Vordered
n ordered
#INTPRO_1
M1 0
MMC-formula
ha MC-formula #0
MC-formulas #0
O1 0 0
OMC-wff
mol; \mathop{\rm MC\hbox{-}wff}
O2 0 1
ONes
mol#1; \mathop{\rm Nes} (#1)
O3 0 1
OCnIPC
mol#1; \mathop{\rm CnIPC} (#1)
O4 0 0
OIPC-Taut
mol; \mathop{\rm IPC\hbox{-}Taut}
O5 0 1
Oneg
mol#1; \mathop{\rm neg} (#1)
O6 0 0
OIVERUM
mol; \mathop{\rm IVERUM}
O7 0 1
OCnCPC
mol#1; \mathop{\rm CnCPC} (#1)
O8 0 0
OCPC-Taut
mol; \mathop{\rm CPC\hbox{-}Taut}
O9 0 1
OCnS4
mol#1; \mathop{\rm CnS4} (#1)
O10 0 0
OS4-Taut
mol; \mathop{\rm S4\hbox{-}Taut}
V1 1
Vwith_FALSUM
x FALSUM
V2 1
Vwith_int_implication
x intuitionistic implication
V3 1
Vwith_int_conjunction
x intuitionistic conjunction
V4 1
Vwith_int_disjunction
x intuitionistic disjunction
V5 1
Vwith_int_propositional_variables
x intuitionistic propositional variables
V6 1
Vwith_modal_operator
x intuitionistic modal operator
V7 1
VMC-closed
a MC-closed
V8 1
VIPC_theory
n IPC theory
V9 1
VCPC_theory
a CPC theory
V10 1
VS4_theory
n S4 theory
#INT_1
K1 1 L1 vINT_1
K[\
L/]
mc{ktq}@s#1; \mathopen{\lfloor} #1 \mathclose{\rfloor}
K2 1 L2 vINT_1
K[/
L\]
mc{mbw}@s#1; \mathopen{\lceil} #1 \mathclose{\rceil}
M1 0
MInteger
hn integer #0
integers #0
O1 0 1
Ofrac
mol@s; \mathop{\rm frac} #1
O2 1 1
Odiv
moi@a; #1 \div #2
O3 0 2
Omod
mol#1#2; \mathop{\rm mod}(#1,#2)
O3 1 1
Omod
moi@a; #1 \mathbin{\rm\,mod\,} #2
R1 2 1
Rare_congruent_mod
m #1 \equiv #2 \ (\mathop{\rm mod} #3)
#1 \not\equiv #2 \ (\mathop{\rm mod} #3)
V1 1
Vinteger
n integer
#INT_2
O1 0 3
Ogcd
moi#1#2#3; \mathop{\rm gcd}_{#3}(#1,#2)
O1 1 1
Ogcd
moi#1#2; #1 \mathop{\rm gcd} #2
V1 1
Vprime
a prime
#INT_3
M1 0
MEuclidianRing
hn EuclidianRing #0
EuclidianRings #0
M2 1
MDegreeFunction
ha DegreeFunction #0 of #1
DegreeFunctions #0 of #1
O1 0 0
OINT.Ring
mo; {\mathbb Z}^{\rm R}
O1 0 1
OINT.Ring
mo{qrw}#1; {\mathbb Z}_{#1}^{\rm R}
O2 0 0
Oabsint
mol; \mathop{\rm absint}
V1 1
VEuclidian
n Euclidian
#INT_4
O1 0 1
OCong
mol; \mathop{\rm Cong} #1
R1 1 1
Ris_CRS_of
i a complete residue system modulo #2
not a complete residue system modulo #2 #2
#INT_5
O1 0 1
OPoly-INT
mol#1; \mathop{\cal P}_{\mathbb Z}(#1)
O2 0 2
OLege
mc#1#2; \left(\frac{#1}{#2}\right)
R1 1 1
Ris_quadratic_residue_mod
i quadratic residue mod #2
not quadratic residue mod #2
#INT_6
M1 0
MCR_Sequence
ha CR-sequence #0
CR-sequences #0
M2 1
MCR_coefficients
ha CR-coefficient sequence #0 for #1
CR-coefficient sequences #0 for #1
O1 0 2
Oto_int
mol#1#2; {\mathbb Z}(#1,#2)
V1 1
Vmultiplicative-trivial
a multiplicative-trivial
V2 1
VChinese_Remainder
a Chinese remainder
#INT_7
O1 0 1
OSegm0
mow#1; {{\mathbb Z}_{#1}^\ast}
O2 0 1
Omultint0
mow#1; \cdot_{{\mathbb Z}_{#1}^\ast}
O3 0 1
OZ/Z*
mol/1w; {\mathbb Z}/#1{{\mathbb Z}^\ast}
V1 1
Vprime-factorization-like
a prime-factorization-like
#IRRAT_1
O1 0 1
Oaseq
mosw#1; {\bf a}_{#1}
O2 0 1
Obseq
mosw#1; {\bf b}_{#1}
O3 0 1
Ocseq
mosw#1; {\bf c}_{#1}
O4 0 0
Odseq
mc; {\bf d}
O5 0 0
Oeseq
mc; {\bf e}
V1 1
Virrational
n irrational
#ISOCAT_1
M1 2
MEquivalence
hn equivalence #0 of #1 and #2
equivalences #0 of #1 and #2
R1 1 1
Ris_equivalent_with
i equivalent with #2
not equivalent with #2
#ISOCAT_2
O1 0 1
Oexport
mol@s#1; {\rm export}(#1)
O1 0 3
Oexport
mow#1#2#3; {\bf export}_{#1,#2,#3}
O2 0 3
Odistribute
mow#1#2#3; {\bf distribute}_{#1,#2,#3}
#ISOMICHI
O2 0 1
OBorder
mol; \mathop{\rm Border} #1
R1 2 0
Rare_c=-incomparable
hy #1 and #2 are $\subseteq$-incomparable
#1 and #2 are $\subseteq$-comparable
V1 1
Vsupercondensed
a supercondensed
V2 1
Vsubcondensed
a subcondensed
V3 1
Vregular_open
a regular open
V4 1
Vregular_closed
a regular closed
V5 1
V1st_class
n of the $1^{\rm st}$ class
V6 1
V2nd_class
n of the $2^{\rm nd}$ class
V7 1
V3rd_class
n of the $3^{\rm rd}$ class
V8 1
Vwith_1st_class_subsets
x subsets of the $1^{\rm st}$ class
V9 1
Vwith_2nd_class_subsets
x subsets of the $2^{\rm nd}$ class
V10 1
Vwith_3rd_class_subsets
x subsets of the $3^{\rm rd}$ class
#JGRAPH_1
O1 0 1
OPGraph
mol#1; \mathop{\rm PGraph} #1
O2 0 1
OPairF
mol#1; \mathop{\rm PairF} #1
R1 1 1
Ris_Shortcut_of
h #1 is Shortcut of #2
#1 is not Shortcut of #2
V1 1
Vnodic
a nodic
#JGRAPH_2
O1 0 0
OOut_In_Sq
mc; \mathop{\rm OutInSq}
O2 0 2
OAffineMap
moi/1r@m/2l@a; #1{\square}{+}#2
O2 0 4
OAffineMap
mol#1#2#3#4; \mathop{\rm AffineMap}(#1,#2,#3,#4)
#JGRAPH_3
O1 0 0
OSq_Circ
mc; \mathop{\rm SqCirc}
#JGRAPH_4
O1 1 0
ONormF
mor#1; #1 \mathop{\rm NormF}
O2 0 2
OFanW
mol#1; \mathop{\rm FanW}(#1,#2)
O3 1 0
O-FanMorphW
mor#1; #1 \mathop{\rm\hbox{-}FanMorphW}
O4 0 2
OFanN
mol#1; \mathop{\rm FanN}(#1,#2)
O5 1 0
O-FanMorphN
mor#1; #1 \mathop{\rm\hbox{-}FanMorphN}
O6 0 2
OFanE
mol#1; \mathop{\rm FanE}(#1,#2)
O7 1 0
O-FanMorphE
mor#1; #1 \mathop{\rm\hbox{-}FanMorphE}
O8 0 2
OFanS
mol#1; \mathop{\rm FanS}(#1,#2)
O9 1 0
O-FanMorphS
mor#1; #1 \mathop{\rm\hbox{-}FanMorphS}
#JGRAPH_6
O1 0 4
Orectangle
mol#1#2#3#4; \mathop{\rm Rectangle}(#1,#2,#3,#4)
O2 0 4
Oinside_of_rectangle
mol#1#2#3#4; \mathop{\rm InsideOfRectangle}(#1,#2,#3,#4)
O3 0 4
Oclosed_inside_of_rectangle
mol#1#2#3#4; \mathop{\rm ClosedInsideOfRectangle}(#1,#2,#3,#4)
O4 0 4
Ooutside_of_rectangle
mol#1#2#3#4; \mathop{\rm OutsideOfRectangle}(#1,#2,#3,#4)
O5 0 4
Oclosed_outside_of_rectangle
mol#1#2#3#4; \mathop{\rm ClosedOutsideOfRectangle}(#1,#2,#3,#4)
O6 0 3
Ocircle
mol#1#2#3; \mathop{\rm Circle}(#1,#2,#3)
O7 0 3
Oinside_of_circle
mol#1#2#3; \mathop{\rm InsideOfCircle}(#1,#2,#3)
O8 0 3
Oclosed_inside_of_circle
mol#1#2#3; \mathop{\rm ClosedInsideOfCircle}(#1,#2,#3)
O9 0 3
Ooutside_of_circle
mol#1#2#3; \mathop{\rm OutsideOfCircle}(#1,#2,#3)
O10 0 3
Oclosed_outside_of_circle
mol#1#2#3; \mathop{\rm ClosedOutsideOfCircle}(#1,#2,#3)
#JORDAN
O1 0 1
OdiffX2_1
moi; (\square_2)_1-{#1}_1
O2 0 1
OdiffX2_2
moi; (\square_2)_2-{#1}_2
O3 0 0
OdiffX1_X2_1
moi; (\square_1)_1-(\square_2)_1
O4 0 0
OdiffX1_X2_2
moi; (\square_1)_2-(\square_2)_2
O5 0 0
OProj2_1
mow; (\square_2)_1
O6 0 0
OProj2_2
mow; (\square_2)_2
O7 0 3
ODiskProj
mol#1#2#3; \mathop{\rm DiskProj}(#1,#2,#3)
O8 0 3
ORotateCircle
mol#1#2#3; \mathop{\rm RotateCircle}(#1,#2,#3)
#JORDAN1
V1 1
VJordan
a Jordan
#JORDAN10
O1 0 1
OUBD-Family
mol#1; \mathop{\rm UBD\hbox{-}Family} #1
O2 0 1
OBDD-Family
mol#1; \mathop{\rm BDD\hbox{-}Family} #1
#JORDAN11
O1 0 1
OApproxIndex
mol#1; \mathop{\rm ApproxIndex} #1
O2 0 1
OY-InitStart
mol#1; \mathop{\rm Y\hbox{-}InitStart} #1
O3 0 2
OY-SpanStart
mol#1#2; \mathop{\rm Y\hbox{-}SpanStart}(#1,#2)
#JORDAN12
R1 1 1
Ris_in_general_position_wrt
i in general position w.r.t. #2
not in general position w.r.t. #2
R2 2 0
Rare_in_general_position
h #1 and #2 are in general position
#1 and #2 are not in general position
#JORDAN13
O1 0 1
OSpan
mol; \mathop{\rm Span} #1
O1 0 2
OSpan
mol#1#2; \mathop{\rm Span}(#1,#2)
#JORDAN14
O1 0 2
OSpanStart
mol#1#2; \mathop{\rm SpanStart}(#1,#2)
#JORDAN17
R1 4 1
Rare_in_this_order_on
h #1,#2,#3,#4 are in this order on #5
#1,#2,#3,#4 are not in this order on #5
#JORDAN18
O1 0 2
ONorth-Bound
mol#1#2; \mathop{\rm North\hbox{-}Bound}(#1,#2)
O2 0 2
OSouth-Bound
mol#1#2; \mathop{\rm South\hbox{-}Bound}(#1,#2)
R1 3 2
R-separate
h #1,#2 separate #4,#5 on #3
#1,#2 does not separate #4,#5 on #3
R2 2 3
Rare_neighbours_wrt
h #1, #2 are neighbours w.r.t. #3,#4 on #5
#1, #2 are not neighbours w.r.t. #3,#4 on #5
#JORDAN19
O1 0 1
OUpper_Appr
mol#1; \mathop{\rm UpperAppr}(#1)
O2 0 1
OLower_Appr
mol#1; \mathop{\rm LowerAppr}(#1)
O3 0 1
ONorth_Arc
mol#1; \mathop{\rm NorthArc}(#1)
O4 0 1
OSouth_Arc
mol#1; \mathop{\rm SouthArc}(#1)
#JORDAN1A
O1 0 1
OCenter
mol#1; \mathop{\rm Center} #1
#JORDAN1E
O1 0 2
OUpper_Seq
mol#1#2; \mathop{\rm UpperSeq}(#1,#2)
O2 0 2
OLower_Seq
mol#1#2; \mathop{\rm LowerSeq}(#1,#2)
#JORDAN1H
O1 0 0
ORealOrd
mol; \mathop{\rm RealOrd}
O2 0 2
OX-SpanStart
mol#1#2; \mathop{\rm X\hbox{-}SpanStart}(#1,#2)
R1 1 1
Ris_sufficiently_large_for
i sufficiently large for #2
not sufficiently large for #2
#JORDAN20
R1 1 4
Ris_Lin
i LIn of #2,#3,#4,#5
not LIn of #2,#3,#4,#5
R2 1 4
Ris_Rin
i RIn of #2,#3,#4,#5
not RIn of #2,#3,#4,#5
R3 1 4
Ris_Lout
i LOut of #2,#3,#4,#5
not LOut of #2,#3,#4,#5
R4 1 4
Ris_Rout
i ROut of #2,#3,#4,#5
not ROut of #2,#3,#4,#5
R5 1 4
Ris_OSin
i OsIn of #2,#3,#4,#5
not OsIn of #2,#3,#4,#5
R6 1 4
Ris_OSout
i OsOut of #2,#3,#4,#5
not OsOut of #2,#3,#4,#5
#JORDAN21
O1 0 1
OUMP
mol; \mathop{\rm UMP} #1
O2 0 1
OLMP
mol; \mathop{\rm LMP} #1
V1 1
Vwith_the_max_arc
n middle-intersecting
#JORDAN23
V1 1
Valmost-one-to-one
n almost one-to-one
V2 1
Vweakly-one-to-one
a weakly one-to-one
V3 1
Vpoorly-one-to-one
a poorly one-to-one
#JORDAN24
R1 2 1
Rrealize-max-dist-in
hy #1 and #2 realize maximal distance in #3
#1 and #2 do not realize maximal distance in #3
#JORDAN2C
O1 0 1
OBDD
mol#1; \mathop{\rm BDD} #1
O2 0 1
OUBD
mol#1; \mathop{\rm UBD} #1
O3 0 1
O1*
mol#1; 1* #1
O4 0 1
O1.REAL
mol#1; \mathop{\rm 1.REAL} #1
R1 1 1
Ris_inside_component_of
i an inside component of #2
not an inside component of #2
R2 1 1
Ris_outside_component_of
i an outside component of #2
not an outside component of #2
V1 1
VBounded
a Bounded
#JORDAN3
O1 0 3
Omid
mol#1#2#3; \mathop{\rm mid}(#1,#2,#3)
O2 0 2
OL_Cut
mol#1#2; \mathop\downharpoonleft#2, #1
O3 0 2
OR_Cut
mol#1#2; \mathop\downharpoonright#1, #2
O4 0 3
OB_Cut
mol#1#2#3; \mathop{\downharpoonleft\downharpoonright}#2, #1, #3
R1 1 2
Ris_S-Seq_joining
i a special sequence joining #2,#3
not a special sequence joining #2,#3
R2 0 3
RLE
m #1 \leq_{#3} #2
#1 \nleq_{#3} #2
R2 0 4
RLE
m #1 \leq_{#3,#4} #2
#1 \nleq_{#3,#4} #2
R2 0 5
RLE
h LE #1,#2,#3,#4,#5
not LE #1,#2,#3,#4,#5
R3 0 4
RLT
m #1 <_{#3,#4} #2
#1 \not<_{#3,#4} #2
#JORDAN4
O1 0 2
OS_Drop
mol#1#2; \mathop{\rm S\_Drop}(#1,#2)
O2 0 1
OLower
mol; \mathop{\rm Lower} #1
O2 0 3
OLower
mol#1#2#3; \mathop{\rm Lower}(#1,#2,#3)
O3 0 1
OUpper
mol; \mathop{\rm Upper} #1
O3 0 3
OUpper
mol#1#2#3; \mathop{\rm Upper}(#1,#2,#3)
R1 1 3
Ris_a_part>_of
i a right part of #2 from #3 to #4
not a right part of #2 from #3 to #4
R2 1 3
Ris_a_part<_of
i a left part of #2 from #3 to #4
not a left part of #2 from #3 to #4
R3 1 3
Ris_a_part_of
i a part of #2 from #3 to #4
not a part of #2 from #3 to #4
#JORDAN5C
O1 0 4
OFirst_Point
mol#1#2#3#4; \mathop{\rm FPoint}(#1,#2,#3,#4)
O2 0 4
OLast_Point
mol#1#2#3#4; \mathop{\rm LPoint}(#1,#2,#3,#4)
#JORDAN5D
O1 0 1
Oi_s_w
mol; \mathop{\rm i_{SW}} #1
O2 0 1
Oi_n_w
mol; \mathop{\rm i_{NW}} #1
O3 0 1
Oi_s_e
mol; \mathop{\rm i_{SE}} #1
O4 0 1
Oi_n_e
mol; \mathop{\rm i_{NE}} #1
O5 0 1
Oi_w_s
mol; \mathop{\rm i_{WS}} #1
O6 0 1
Oi_e_s
mol; \mathop{\rm i_{ES}} #1
O7 0 1
Oi_w_n
mol; \mathop{\rm i_{WN}} #1
O8 0 1
Oi_e_n
mol; \mathop{\rm i_{EN}} #1
O9 0 1
On_s_w
mol; \mathop{\rm n_{SW}} #1
O10 0 1
On_n_w
mol; \mathop{\rm n_{NW}} #1
O11 0 1
On_s_e
mol; \mathop{\rm n_{SE}} #1
O12 0 1
On_n_e
mol; \mathop{\rm n_{NE}} #1
O13 0 1
On_w_s
mol; \mathop{\rm n_{WS}} #1
O14 0 1
On_e_s
mol; \mathop{\rm n_{ES}} #1
O15 0 1
On_w_n
mol; \mathop{\rm n_{WN}} #1
O16 0 1
On_e_n
mol; \mathop{\rm n_{EN}} #1
#JORDAN6
O1 0 3
Ox_Middle
mol#1#2#3; \mathop{\rm xMiddle}(#1,#2,#3)
O2 0 3
Oy_Middle
mol#1#2#3; \mathop{\rm yMiddle}(#1,#2,#3)
O3 0 4
OL_Segment
mol#1#2#3#4; \mathop{\rm LSegment}(#1,#2,#3,#4)
O4 0 4
OR_Segment
mol#1#2#3#4; \mathop{\rm RSegment}(#1,#2,#3,#4)
O5 0 3
OSegment
mol#1#2#3; \mathop{\rm Segment}(#1,#2,#3)
O5 0 5
OSegment
mol#1#2#3#4#5; \mathop{\rm Segment}(#1,#2,#3,#4,#5)
O6 0 1
OVertical_Line
mol#1; \mathop{\rm VerticalLine}(#1)
O7 0 1
OHorizontal_Line
mol#1; \mathop{\rm HorizontalLine}(#1)
O8 0 1
OUpper_Arc
mol#1; \mathop{\rm UpperArc}(#1)
O9 0 1
OLower_Arc
mol#1; \mathop{\rm LowerArc}(#1)
O10 0 1
OLower_Middle_Point
mol#1; \mathop{\rm LowerMiddlePoint} #1
O11 0 1
OUpper_Middle_Point
mol#1; \mathop{\rm UpperMiddlePoint} #1
#JORDAN8
O1 0 2
OGauge
mol#1#2; \mathop{\rm Gauge}(#1,#2)
#JORDAN9
O1 0 2
OCage
mol#1#2; \mathop{\rm Cage}(#1,#2)
#JORDAN_A
M1 1
MSegmentation
ha segmentation #0 of #1
segmentations #0 of #1
O1 0 1
OEucl_dist
mol#1; \mathop{\rm EuclDist}(#1)
O2 0 1
OS-Gap
mol#1; \mathop{\rm Gap}(#1)
#KNASTER
O1 0 1
Olfp
mol#1; \mathop{\rm lfp}(#1)
O1 0 2
Olfp
mol#1#2; \mathop{\rm lfp}(#1,#2)
O2 0 1
Ogfp
mol#1; \mathop{\rm gfp}(#1)
O2 0 2
Ogfp
mol#1#2; \mathop{\rm gfp}(#1,#2)
O3 2 1
O+.
mol#2#3; #1^{#2}_\sqcup(#3)
O4 2 1
O-.
mol#2#3; #1^{#2}_\sqcap(#3)
O5 0 1
OFixPoints
mol#1; \mathop{\rm FixPoints}(#1)
#KOLMOG01
M1 2
MManySortedSigmaField
ha many sorted $\sigma$-field #0 over #1 and #2
many sorted $\sigma$-fields #0 over #1 and #2
M2 2
MSigmaSection
ha $\sigma$-section #0 over #1 and #2
$\sigma$-sections #0 over #1 and #2
O1 0 2
OIndep
mol#1#2; \mathop{\rm Indep}(#1,#2)
O2 0 2
OsigUn
mol#1#2; \mathop{\rm sigUn}(#1,#2)
O3 0 2
OfutSigmaFields
mol#1#2; \mathop{\rm futSigmaFields}(#1,#2)
O4 0 2
OtailSigmaField
mol#1#2; \mathop{\rm tailSigmaField}(#1,#2)
O5 0 2
OMeetSections
mol#1#2; \mathop{\rm MeetSections}(#1,#2)
O6 0 2
OfinSigmaFields
mol#1#2; \mathop{\rm finSigmaFields}(#1,#2)
R1 1 1
Ris_independent_wrt
i independent w.r.t. #2
not independent w.r.t. #2
#KURATO_1
O1 0 1
OKurat14Part
mol#1; \mathop{\rm Kurat14Part}(#1)
O2 0 1
OKurat14Set
mol#1; \mathop{\rm Kurat14Set}(#1)
O3 0 1
OKurat14ClPart
mol#1; \mathop{\rm Kurat14ClosedPart}(#1)
O4 0 1
OKurat14OpPart
mol#1; \mathop{\rm Kurat14OpenPart}(#1)
O5 0 1
OKurat7Set
mol#1; \mathop{\rm Kurat7Set}(#1)
O6 0 0
OKurExSet
mc; \mathop{\rm KuratExSet}
V1 1
VCl-closed
a closed for closure operator
V2 1
VInt-closed
a closed for interior operator
#KURATO_2
O1 0 1
OLim_K
mol; \mathop{\rm limes}\, #1
O2 0 1
OLim_inf
mol; \mathop{\rm Li}\, #1
O3 0 1
OLim_sup
mol; \mathop{\rm Ls}\, #1
#LANG1
G1 2
GDTConstrStr
mc#1#2; \langle #1,\allowbreak #2\rangle
G2 3
GGrammarStr
mc#1#2#3; \langle #1,\allowbreak #2,\allowbreak #3\rangle
J1 1
GDTConstrStr
hol#1; DTConstrStr of #1
J2 1
GGrammarStr
hol#1; context-free grammar of #1
L1 0
GDTConstrStr
ha tree construction structure #0
tree construction structures #0
L2 0
GGrammarStr
ha context-free grammar #0
context-free grammars #0
M1 1
MSymbol
ha symbol #0 of #1
symbols #0 of #1
M2 1
MString
ha string #0 of #1
strings #0 of #1
O1 0 1
OTerminals
hol; terminals of #1
O2 0 1
ONonTerminals
hol; nonterminals of #1
O3 0 1
OLang
hol; language generated by #1
O3 0 2
OLang
mol#1#2; \mathop{\rm Lang}(#1,#2)
O4 0 1
OEmptyGrammar
mc#1#2; \left\{#1\Rightarrow\varepsilon\right\}
O5 0 2
OSingleGrammar
mc#1#2; \left\{#1\Rightarrow #2\right\}
O6 0 2
OIterGrammar
mc#1#2; \left\{\begin{array}{c} #1\Rightarrow #2#1\\ #1\Rightarrow\varepsilon\end{array}\right\}
O7 0 1
OTotalGrammar
hol@9; total grammar over #1
R1 1 1
Ris_derivable_from
m #2\Rightarrow_\ast #1
#2\nRightarrow_\ast #1
U1 1
URules
hopl#1; rules of #1
rules
U2 1
UInitialSym
honl#1; initial symbol of #1
initial symbol
V1 1
Vefective
n effective
#LAPLACE
O1 0 3
ODelete
mol#1#2#3; \mathop{\rm Delete}(#1,#2,#3)
O2 0 3
OReplaceCol
mol#1#2#3; \mathop{\rm ReplaceCol}(#1,#2,#3)
O3 0 3
ORCol
mol#1#2#3; \mathop{\rm RCol}(#1,#2,#3)
O4 0 2
ORem
mol#1#2; \mathop{\rm Rem}(#1,#2)
O5 0 3
OMinor
mol#1#2#3; \mathop{\rm Minor}(#1,#2,#3)
O6 0 3
OCofactor
mol#1#2#3; \mathop{\rm Cofactor}(#1,#2,#3)
O7 0 1
OMatrix_of_Cofactor
hol; matrix of cofactor #1
O8 0 2
OLaplaceExpL
mol#1#2; \mathop{\rm LaplaceExpL}(#1,#2)
O9 0 2
OLaplaceExpC
mol#1#2; \mathop{\rm LaplaceExpC}(#1,#2)
#LATTICE2
M1 0
MD0_Lattice
ha distributive lower bounded lattice #0
distributive lower bounded lattices #0
M2 0
MH_Lattice
ha Heyting lattice #0
Heyting lattices #0
O1 0 1
OFinJoin
mow#1; \bigsqcup^{\rm f}_{#1}
O1 0 2
OFinJoin
mol(2)@s/1k#1; \bigsqcup^{\rm f}_{#1} #2
O2 0 1
OFinMeet
mow#1; \bigsqcap^{\rm f}_{#1}
O2 0 2
OFinMeet
mol(2)@s/1k#1; \bigsqcap^{\rm f}_{#1} #2
R1 1 1
Rabsorbs
h #1 absorbs #2
#1 does not absorb #2
R2 1 1
Rdoesn't_absorb
h #1 does not absorb #2
#1 absorbs #2
V1 1
VHeyting
a Heyting
#LATTICE3
O1 0 1
OBooleLatt
hol; lattice of subsets of #1
O2 0 1
OLattPOSet
mcl@s#1; {\rm Poset}(#1)
O3 0 1
O%
mok; {}^{\centerdot}#1
O3 1 0
O%
moq; #1^{\centerdot}
O3 1 1
O%
mox@m; #1 \mathbin{\%} #2
R1 1 1
Ris_<=_than
m #1 \leq #2
#1 \not\leq #2
R2 1 1
Ris_>=_than
m #1 \geq #2
#1 \not\geq #2
R3 1 1
Ris_less_than
m #1 \sqsubseteq #2
#1 \not\sqsubseteq #2
R4 1 1
Ris_greater_than
m\sqsupseteq #2
\not\sqsupseteq #2
V1 1
Vwith_suprema
x l.u.b.'s
V2 1
Vwith_infima
x g.l.b.'s
V3 1
V\/-distributive
a $\bigsqcup$-distributive
V4 1
V/\-distributive
a $\bigsqcap$-distributive
#LATTICE4
M1 1
MClosedSubset
ha closed subset #0 of #1
closed subset #0 of #1
O1 0 1
Ofield_by
hol#1; field by #1
O2 0 1
OSetImp
mol#1; \mathop{\rm SetImp}(#1)
R1 1 0
Rpreserves_implication
h #1 preserves implication
#1 does not preserve implication
R2 1 0
Rpreserves_top
h #1 preserves top
#1 does not preserve top
R3 1 0
Rpreserves_bottom
h #1 preserves bottom
#1 does not preserve bottom
R4 1 0
Rpreserves_complement
h #1 preserves complement
#1 does not preserve complement
#LATTICE5
M1 1
MSublattice
ha% sublattice #0 of #1
sublattice #0 of #1
M2 2
MBiFunction
ha bifunction #0 from #1 into #2
bifunctions #0 from #1 into #2
M3 2
Mdistance_function
ha distance function #0 of #1,#2
distance function #0 of #1,#2
M4 1
MQuadrSeq
ha sequence #0 of quadruples of #1
sequences #0 of quadruples of #1
M5 2
MExtensionSeq
hn extension sequence #0 of $(#1, #2)$
extension sequences #0 of $(#1, #2)$
O1 0 1
OEqRelLATT
mol#1; \mathop{\rm EqRelPoset}(#1)
O2 0 1
Otype_of
hosl#1; type of #1
O3 0 1
Oalpha
mol#1; \alpha(#1)
O4 0 1
Onew_set
moq; #1^\ast
O5 0 2
Onew_bi_fun
moq#2; #1^\ast_{#2}
O6 0 1
ODistEsti
mol#1; \mathop{\rm DistEsti}(#1)
O7 0 2
OConsecutiveSet
mol#1#2; \mathop{\rm ConsecutiveSet}(#1,#2)
O8 0 2
OQuadr
mol#1#2; \mathop{\rm Quadr}(#1,#2)
O9 0 3
OBiFun
mol#1#2#3; \mathop{\rm BiFun}(#1,#2,#3)
O10 0 2
OConsecutiveDelta
mol#1#2; \mathop{\rm ConsecutiveDelta}(#1,#2)
O11 0 1
ONextSet
mol#1; \mathop{\rm NextSet}(#1)
O12 0 1
ONextDelta
mol#1; \mathop{\rm NextDelta}(#1)
O13 0 1
OBasicDF
mol#1; \delta_0(#1)
R1 2 3
Rare_joint_by
h #1 and #2 are joint by #3,#4 and #5
#1 and #2 are not joint by #3,#4 and #5
R2 1 1
Ris_extension_of
i an extension of #2
not an extension of #2
R2 2 2
Ris_extension_of
h $(#1, #2)$ is extension of $(#3, #4)$
$(#1, #2)$ is not extension of $(#3, #4)$
V1 1
Vu.t.i.
s triangle inequality
#LATTICE6
O1 0 1
OMIRRS
mol#1; \mathop{\rm MIRRS} #1
O2 0 1
OJIRRS
mol#1; \mathop{\rm JIRRS} #1
R1 1 1
Ris-upper-neighbour-of
h #1 is upper neighbour of #2
#1 is not upper neighbour of #2
R2 1 1
Ris-lower-neighbour-of
h #1 is lower neighbour of #2
#1 is not lower neighbour of #2
V1 1
Vnoetherian
a noetherian
V2 1
Vco-noetherian
a co-noetherian
V3 1
Vcompletely-meet-irreducible
a completely-meet-irreducible
V4 1
Vcompletely-join-irreducible
a completely-join-irreducible
V5 1
Vco-atomic
a co-atomic
V6 1
Vsupremum-dense
a supremum-dense
V7 1
Vinfimum-dense
n infimum-dense
#LATTICE7
M1 0
MRing_of_sets
ha ring of sets #0
rings of sets #0
O1 0 1
OJoin-IRR
mol#1; \mathop{\rm Join\hbox{-}IRR} #1
O2 0 1
OLOWER
mol#1; \mathop{\rm LOWER} #1
R1 1 1
R<(1)
m #1 <_1 #2
#1 \not<_1 #2
#LATTICE8
M1 2
MExtensionSeq2
hn ExtensionSeq2 #0 of #1,#2
ExtensionSeq2s #0 of #1,#2
O1 0 1
Onew_set2
mol#1; \mathop{\rm new\_set2} #1
O2 0 2
Onew_bi_fun2
mol#1#2; \mathop{\rm new\_bi\_fun2}(#1,#2)
O3 0 2
OConsecutiveSet2
mol#1#2; \mathop{\rm ConsecutiveSet2}(#1,#2)
O4 0 2
OQuadr2
mol#1#2; \mathop{\rm Quadr2}(#1,#2)
O5 0 2
OConsecutiveDelta2
mol#1#2; \mathop{\rm ConsecutiveDelta2}(#1,#2)
O6 0 1
ONextSet2
mol#1; \mathop{\rm NextSet2} #1
O7 0 1
ONextDelta2
mol#1; \mathop{\rm NextDelta2} #1
R1 1 1
Rhas_a_representation_of_type<=
h #1 has a representation of type $\le$ #2
#1 has not a representation of type $\le$ #2
R2 2 2
Ris_extension2_of
h #1,#2 is extension2 of #3,#4
#1,#2 is not extension2 of #3,#4
V1 1
Vfinitely_typed
a finitely typed
#LATTICES
G1 2
G/\-SemiLattStr
mc#1#2; \langle #1, #2\rangle
G2 2
G\/-SemiLattStr
mc#1#2; \langle #1, #2\rangle
G3 3
GLattStr
mc#1#2#3; \langle #1,\allowbreak #2,\allowbreak #3\rangle
J1 1
G/\-SemiLattStr
hol#1; lower semilattice structure of #1
J2 1
G\/-SemiLattStr
hol#1; upper semilattice structure of #1
J3 1
GLattStr
hol#1; lattice structure of #1
L1 0
G/\-SemiLattStr
ha $\sqcap$-semi lattice structure #0
$\sqcap$-semi lattice structures #0
L2 0
G\/-SemiLattStr
ha $\sqcup$-semi lattice structure #0
$\sqcup$-semi lattice structures #0
L3 0
GLattStr
ha lattice structure #0
lattice structures #0
M1 0
MLattice
ha lattice #0
lattices #0
M2 0
MD_Lattice
ha distributive lattice #0
distributive lattices #0
M3 0
MM_Lattice
ha modular lattice #0
modular lattices #0
M4 0
M0_Lattice
ha lower bound lattice #0
lower bound lattices #0
M5 0
M1_Lattice
hn upper bound lattice #0
upper bound lattices #0
M6 0
M01_Lattice
ha bound lattice #0
bound lattices #0
M7 0
MC_Lattice
ha complemented lattice #0
complemented lattices #0
M8 0
MB_Lattice
ha Boolean lattice #0
Boolean lattices #0
O1 0 1
O"/\"
mol@s; \bigsqcap #1
O1 0 2
O"/\"
mol(1)@s; \bigsqcap_{#2} #1
O1 1 0
O"/\"
moi; #1\sqcap\square
O1 1 1
O"/\"
moi@a; #1 \sqcap #2
O2 0 1
OBottom
mow#1; \bot_{#1}
O3 0 1
OTop
mow#1; \top_{#1}
R1 1 1
Ris_a_complement_of
i a complement of #2
not a complement of #2
U1 1
UL_meet
hosl#1; meet operation of #1
meet operation
U2 1
UL_join
hosl#1; join operation of #1
join operation
V1 1
Vjoin-commutative
a join-commutative
V2 1
Vjoin-associative
a join-associative
V3 1
Vmeet-commutative
a meet-commutative
V4 1
Vmeet-associative
a meet-associative
V5 1
Vmeet-absorbing
a meet-absorbing
V6 1
Vjoin-absorbing
a join-absorbing
V7 1
VLattice-like
a lattice-like
V8 1
Vdistributive
a distributive
V9 1
Vmodular
a modular
V10 1
Vlower-bounded
a lower-bounded
V11 1
Vupper-bounded
n upper-bounded
V12 1
Vcomplemented
a complemented
V13 1
VBoolean
a Boolean
V14 1
Vfinal
a final
V15 1
Vmeet-closed
a meet-closed
V16 1
Vjoin-closed
a join-closed
#LEXBFS
M1 1
MpreVNumberingSeq
ha pre v numbering sequence #0 of #1
pre v numbering sequences #0 of #1
M2 1
MVNumberingSeq
ha v numbering sequence #0 of #1
v numbering sequences #0 of #1
M3 1
MLexBFS:Labeling
ha BFS:labeling #0 of #1
BFS:labeling #0 of #1
M4 1
MLexBFS:LabelingSeq
ha BFS:labeling sequence #0 of #1
BFS:labeling sequences #0 of #1
M5 1
MMCS:Labeling
ha MCS:labeling #0 of #1
MCS:labeling #0 of #1
M6 1
MMCS:LabelingSeq
ha MCS:labeling sequence #0 of #1
MCS:labeling sequences #0 of #1
O1 1 1
O.\/
moi; #1 [\cup] #2
O2 1 2
O.incSubset
moi#2#3; #1 \mathop{\mbox{.incSubset}}(#2,#3)
O3 1 1
O.PickedAt
moi; #1 \mathop{\mbox{.PickedAt}} #2
O4 0 1
OLexBFS:Init
mol; \mathop{\mbox{LexBFS:Init}} #1
O5 0 1
OLexBFS:PickUnnumbered
mol; \mathop{\mbox{LexBFS:PickUnnumbered}} #1
O6 0 3
OLexBFS:Update
mol#1#2#3; \mathop{\mbox{LexBFS:Update}}(#1,#2,#3)
O7 0 1
OLexBFS:Step
mol; \mathop{\mbox{LexBFS:Step}} #1
O8 1 0
O``1
mow; {#1_{\bf 1}}
O9 0 1
OLexBFS:CSeq
mol; \mathop{\mbox{LexBFS:CSeq}} #1
O10 0 1
OMCS:Init
mol; \mathop{\mbox{MCS:Init}} #1
O11 0 1
OMCS:PickUnnumbered
mol; \mathop{\mbox{MCS:PickUnnumbered}} #1
O12 0 2
OMCS:LabelAdjacent
mol#1#2; \mathop{\mbox{MCS:LabelAdjacent}}(#1,#2)
O13 0 3
OMCS:Update
mol#1#2#3; \mathop{\mbox{MCS:Update}}(#1,#2,#3)
O14 0 1
OMCS:Step
mol; \mathop{\mbox{MCS:Step}} #1
O15 0 1
OMCS:CSeq
mol; \mathop{\mbox{MCS:CSeq}} #1
V1 1
Vwith_finite-elements
x finite elements
V2 1
Vnatsubset-yielding
a natsubset yielding
V3 1
Viterative
n iterative
V4 1
Veventually-constant
n eventually constant
V5 1
Vvertex-numbering
a vertex-numbering
V6 1
Vwith_property_L3
x property {\it L3\/}
V7 1
Vwith_property_T
x property {\it T\/}
#LFUZZY_0
O1 0 1
ORealPoset
mol; \mathop{\rm RealPoset} #1
O2 0 1
OFuzzyLattice
mol; \mathop{\rm FuzzyLattice} #1
R1 1 1
R<<=
my #1 \preceq #2
#1 \not\preceq #2
R2 1 1
R>>=
my #1 \succeq #2
#1 \not\succeq #2
R3 1 1
R~<=
mn #1 \not\preceq #2
#1 \preceq #2
R4 1 1
R~>=
mn #1 \not\succeq #2
#1 \succeq #2
#LFUZZY_1
O1 0 1
OTrCl
mol; \mathop{\rm TrCl} #1
#LIMFUNC1
O1 0 1
Oleft_open_halfline
mc#1; \mathopen{\rbrack} -\infty,#1 \mathclose{\lbrack}
O2 0 1
Oleft_closed_halfline
mc#1; \mathopen{\rbrack} -\infty,#1 \rbrack
O3 0 1
Oright_closed_halfline
mc#1; \lbrack #1,+\infty \mathclose{\lbrack}
O4 0 1
Oright_open_halfline
mc#1; \mathopen{\rbrack} #1,+\infty \mathclose{\lbrack}
O5 0 1
Olim_in+infty
mol@s; \mathop{\rm lim}_{+\infty}#1
O6 0 1
Olim_in-infty
mol@s; \mathop{\rm lim}_{-\infty}#1
V1 1
Vdivergent_to+infty
a divergent to $+\infty$
V2 1
Vdivergent_to-infty
a divergent to $-\infty$
V3 1
Vconvergent_in+infty
a convergent in $+\infty$
V4 1
Vdivergent_in+infty_to+infty
a divergent in $+\infty$ to $+\infty$
V5 1
Vdivergent_in+infty_to-infty
a divergent in $+\infty$ to $-\infty$
V6 1
Vconvergent_in-infty
a convergent in $-\infty$
V7 1
Vdivergent_in-infty_to+infty
a divergent in $-\infty$ to $+\infty$
V8 1
Vdivergent_in-infty_to-infty
a divergent in $-\infty$ to $-\infty$
#LIMFUNC2
O1 0 2
Olim_left
mol@s#2; \mathop{\rm lim}_{{#2}^-}#1
O2 0 2
Olim_right
mol@s#2; \mathop{\rm lim}_{{#2}^+}#1
R1 1 1
Ris_left_convergent_in
i left convergent in #2
not left convergent in #2
R2 1 1
Ris_left_divergent_to+infty_in
i left divergent to $+\infty$ in #2
not left divergent to $+\infty$ in #2
R3 1 1
Ris_left_divergent_to-infty_in
i left divergent to $-\infty$ in #2
not left divergent to $-\infty$ in #2
R4 1 1
Ris_right_convergent_in
i right convergent in #2
not right convergent in #2
R5 1 1
Ris_right_divergent_to+infty_in
i right divergent to $+\infty$ in #2
not right divergent to $+\infty$ in #2
R6 1 1
Ris_right_divergent_to-infty_in
i right divergent to $-\infty$ in #2
not right divergent to $+\infty$ in #2
#LIMFUNC3
R1 1 1
Ris_convergent_in
i convergent in #2
not convergent in #2
R2 1 1
Ris_divergent_to+infty_in
i divergent to $+\infty$ in #2
not divergent to $+\infty$ in #2
R3 1 1
Ris_divergent_to-infty_in
i divergent to $-\infty$ in #2
not divergent to $+\infty$ in #2
#LMOD_7
M1 1
MSUBMODULE_DOMAIN
ha non empty set #0 of submodules of #1
non empty sets #0 of submodules of #1
M2 1
MLINE_DOMAIN
ha non empty set #0 of lines of #1
non empty sets #0 of lines of #1
M3 1
MHIPERPLANE
ha hiperplane #0 of #1
hiperplanes #0 of #1
M4 1
MHIPERPLANE_DOMAIN
ha non empty set #0 of hiperplanes of #1
non empty sets #0 of hiperplanes of #1
O1 0 1
Olines
mol@s#1; \mathop{\rm lines}(#1)
O2 0 1
Ohiperplanes
mol@s#1; \mathop{\rm hiperplanes}(#1)
O3 0 1
OCOMPL
mol@s#1; \mathop{\rm COMPL}(#1)
O4 0 1
OADD
mol@s#1; \mathop{\rm ADD}(#1)
O5 0 1
OLMULT
mol@s#1; \mathop{\rm LMULT}(#1)
#LOPBAN_1
M1 2
MLinearOperator
ha linear operator #0 from #1 into #2
linear operators #0 from #1 into #2
M2 0
MRealBanachSpace
ha real Banach space #0
real Banach spaces #0
O1 0 2
OFuncAdd
mol@s#1#2; \mathop{\rm FuncAdd}(#1,#2)
O2 0 2
OFuncExtMult
mol@s#1#2; \mathop{\rm FuncExtMult}(#1,#2)
O3 0 2
OFuncZero
mol@s#1#2; \mathop{\rm FuncZero}(#1,#2)
O4 0 2
OLinearOperators
mol@s#1#2; \mathop{\rm LinearOperators}(#1,#2)
O5 0 2
OR_VectorSpace_of_LinearOperators
mol@s#1#2; \mathop{\rm RVectorSpaceOfLinearOperators}(#1,#2)
O6 0 2
OBoundedLinearOperators
mol@s#1#2; \mathop{\rm BdLinOps}(#1,#2)
O7 0 2
OR_VectorSpace_of_BoundedLinearOperators
mol@s#1#2; \mathop{\rm RVectorSpaceOfBoundedLinearOperators}(#1,#2)
O8 0 2
Omodetrans
mol#1#2; \mathop{\rm modetrans}(#1,#2)
O8 0 3
Omodetrans
mol@s#1#2; \mathop{\rm modetrans}(#1,#2,#3)
O9 0 1
OPreNorms
mol@s#1; \mathop{\rm PreNorms}(#1)
O10 0 2
OBoundedLinearOperatorsNorm
mol@s#1#2; \mathop{\rm BdLinOpsNorm}(#1,#2)
O11 0 2
OR_NormSpace_of_BoundedLinearOperators
hol#1#2; real norm space of bounded linear operators from #1 into #2
#LOPBAN_2
G1 7
GNormed_AlgebraStr
mc#1#2#3#4#5#6#7; \langle #1, #2, #3, #4, #5,#6,#7\rangle
J1 1
GNormed_AlgebraStr
hol#1; normed algebra structure of #1
L1 0
GNormed_AlgebraStr
ha normed algebra structure #0
normed algebra structures #0
M1 0
MBLAlgebra
ha BL algebra
BL algebras
M2 0
MNormed_Algebra
ha normed algebra
normed algebras
M3 0
MBanach_Algebra
ha Banach algebra
Banach algebras
O1 0 1
OFuncMult
mol#1; \mathop{\rm FuncMult}(#1)
O2 0 1
OFuncUnit
mol#1; \mathop{\rm FuncUnit}(#1)
O3 0 1
ORing_of_BoundedLinearOperators
mol#1; \mathop{\rm RingOfBoundedLinearOperators}(#1)
O4 0 1
OR_Algebra_of_BoundedLinearOperators
mol#1; \mathop{\rm RAlgebraOfBoundedLinearOperators}(#1)
O5 0 1
OR_Normed_Algebra_of_BoundedLinearOperators
mol#1; \mathop{\rm RNormedAlgebraOfBoundedLinearOperators}(#1)
V1 1
VBanach_Algebra-like_1
a Banach Algebra-like1
V2 1
VBanach_Algebra-like_2
a Banach Algebra-like2
V3 1
VBanach_Algebra-like_3
a Banach Algebra-like3
V4 1
VBanach_Algebra-like
a Banach Algebra-like
#LOPBAN_3
V1 1
Vnorm_summable
a norm-summable
#LOPBAN_4
O1 0 1
Oexp_
mol; \mathop{\rm exp} #1
R1 2 0
Rare_commutative
h #1,#2 are commutative
#1,#2 are not commutative
#LOPCLSET
O1 0 1
OOpenClosedSet
mol#1; \mathop{\rm OpenClosedSet}(#1)
O2 0 1
OT_join
mol#1; \mathop{\rm join}(#1)
O3 0 1
OT_meet
mol#1; \mathop{\rm meet}(#1)
O4 0 1
OOpenClosedSetLatt
mol#1; \mathop{\rm OpenClosedSetLatt}(#1)
O5 0 1
Oultraset
mol#1; \mathop{\rm ultraset}(#1)
O6 0 1
OUFilter
mol#1; \mathop{\rm UFilter}(#1)
O7 0 1
OStoneR
mol#1; \mathop{\rm StoneR}(#1)
O8 0 1
OStoneSpace
mol#1; \mathop{\rm StoneSpace}(#1)
O9 0 1
OStoneBLattice
mol#1; \mathop{\rm StoneBLattice}(#1)
#LPSPACE1
O1 0 1
Omultpfunc
mow#1; \cdot_{#1\dot\to{\mathbb R}}
O2 0 1
Omultrealpfunc
mow#1; \cdot^{\mathbb R}_{#1\dot\to{\mathbb R}}
O3 0 1
ORealPFuncZero
mow/1r@m; 0_{#1\dot\to{\mathbb R}}
O4 0 1
ORealPFuncUnit
mow/1r@m; 1_{#1\dot\to{\mathbb R}}
O5 0 1
ORLSp_PFunct
mol; \mathop{\rm PFunct}_{\rm RLS} #1
O6 0 1
OL1_Functions
hol; \Lone{} functions of #1
O7 0 1
ORLSp_L1Funct
mol; L^1{\rm\hbox{-}Funct}_{\rm RLS} #1
O8 0 1
OAlmostZeroFunctions
mol; \mathop{\rm AlmostZeroFunctions} #1
O9 0 1
ORLSp_AlmostZeroFunct
mol; \mathop{\rm AlmostZeroFunct}_{\rm RLS} #1
O10 0 2
Oa.e-eq-class
mor#1#2; [#1]^{#2}_{\rm a.e.}
O11 0 1
OPre-L-Space
mol; \mathop{\rm pre\hbox{-}{\it L}\hbox{-}Space} #1
O12 0 1
OL-1-Norm
mol#1; L^1{\rm\hbox{-}Norm}(#1)
O13 0 1
OL-1-Space
mol#1; L^1{\rm\hbox{-}Space}(#1)
R1 1 2
Ra.e.=
m #1 =_{\rm a.e.}^{#3} #2
#1 \neq_{\rm a.e.}^{#3} #2
V1 1
Vmulti-closed
a multiplicatively-closed
#LPSPACE2
O1 0 2
OLp_Functions
hol#1#2; lp functions(#1,#2)
O2 0 2
ORLSp_LpFunct
hol#1#2; rlsp lp funct(#1,#2)
O3 0 2
OAlmostZeroLpFunctions
mol#1#2; \mathop{\rm AlmostZeroLpFunctions}(#1,#2)
O4 0 2
ORLSp_AlmostZeroLpFunct
hol#1#2; rlsp almost zero lp funct(#1,#2)
O5 0 3
Oa.e-eq-class_Lp
hol#1#2#3; a.e-eq-class lp(#1,#2,#3)
O6 0 2
OPre-Lp-Space
mol#1#2; \mathop{\rm Pre-Lp-Space}(#1,#2)
O7 0 2
OLp-Norm
mol#1#2; \mathop{\rm Lp-Norm}(#1,#2)
O8 0 2
OLp-Space
mol#1#2; \mathop{\rm Lp-Space}(#1,#2)
V1 1
Vgeq_than_1
a geq than 1
#LP_SPACE
O1 1 1
Orto_power
moq{bcmqw}#2; #1^{#2}
O2 0 1
Othe_set_of_RealSequences_l^
moq{}#1; l^{#1}
O3 0 1
Ol_norm^
mor#1; l^{#1}{\rm\hbox{-}norm}
O4 0 1
Ol_Space^
mor@2#1; l^{#1}{\rm\hbox{-}space}
#MARGREL1
M1 0
Mrelation
ha relation #0
relations #0
M1 1
Mrelation
ha relation #0 on #1
relations #0 on #1
M1 2
Mrelation
ha #2-ary relation #0 of #1
#2-ary relations #0 of #1
M2 1
Mrelation_length
ha #1-ary relation #0
#1-ary relations #0
O1 0 1
Othe_arity_of
mcl@s#1; \mathop{\rm Arity}(#1)
O2 0 1
Orelations_on
mcl@s#1; \mathop{\rm Rel}(#1)
O3 0 1
Oempty_rel
mow/1k#1; \varnothing_{#1}
O4 0 0
OBOOLEAN
mc; \mathop{\it Boolean}
O5 0 1
OALL
mc#1; \mathop{\it Boolean}({\it false}\notin #1)
V1 1
Vboolean-valued
a boolean-valued
#MATHMORP
O1 1 1
O(+)
moi@4; #1 \oplus #2
O2 1 1
O(O)
moi@6; #1 \bigcirc #2
O3 1 1
O(o)
moi@6; #1 \circledcirc #2
O4 1 1
O(.)
moi@6; #1 \odot #2
O5 1 2
O(&)
moi@6#2#3; #1 \otimes(#2,#3)
O6 1 2
O(@)
moi@6#2#3; #1 \circledast(#2,#3)
#MATRIX10
R1 1 1
Ris_less_or_equal_with
i less or equal to #2
not less and not equal to #2
V1 1
VPositive
a positive
V2 1
VNegative
a negative
V3 1
VNonpositive
a nonpositive
V4 1
VNonnegative
a nonnegative
#MATRIX11
O1 0 1
O2Set
mol; \mathop{\rm 2Set} #1
O2 0 2
OPart_sgn
mol#1#2; \mathop{\rm Part\hbox{-}sgn}(#1,#2)
O3 0 3
OReplaceLine
mol#1#2#3; \mathop{\rm ReplaceLine}(#1,#2,#3)
O4 0 3
ORLine
mol#1#2#3; \mathop{\rm RLine}(#1,#2,#3)
O5 0 1
OaddFinS
mol; \mathop{\rm addFinS} #1
#MATRIX12
O1 0 3
OInterchangeLine
mol#1#2#3; \mathop{\rm InterchangeLine}(#1,#2,#3)
O2 0 3
OScalarXLine
mol#1#2#3; \mathop{\rm ScalarXLine}(#1,#2,#3)
O3 0 4
ORlineXScalar
mol#1#2#3#4; \mathop{\rm RlineXScalar}(#1,#2,#3,#4)
O4 0 3
OILine
mol#1#2#3; \mathop{\rm ILine}(#1,#2,#3)
O5 0 3
OSXLine
mol#1#2#3; \mathop{\rm SXLine}(#1,#2,#3)
O6 0 4
ORLineXS
mol#1#2#3#4; \mathop{\rm RLineXS}(#1,#2,#3,#4)
O7 0 3
OInterchangeCol
mol#1#2#3; \mathop{\rm InterchangeCol}(#1,#2,#3)
O8 0 3
OScalarXCol
mol#1#2#3; \mathop{\rm ScalarXCol}(#1,#2,#3)
O9 0 4
ORcolXScalar
mol#1#2#3#4; \mathop{\rm RcolXScalar}(#1,#2,#3,#4)
O10 0 3
OICol
mol#1#2#3; \mathop{\rm ICol}(#1,#2,#3)
O11 0 3
OSXCol
mol#1#2#3; \mathop{\rm SXCol}(#1,#2,#3)
O12 0 4
ORColXS
mol#1#2#3#4; \mathop{\rm RColXS}(#1,#2,#3,#4)
#MATRIX13
O1 0 3
OEqSegm
mol#1#2#3; \mathop{\rm EqSegm}(#1,#2,#3)
O2 0 1
OFinS2MX
mol; \mathop{\rm FinS2MX} #1
O3 0 1
OMX2FinS
mol; \mathop{\rm MX2FinS} #1
V1 1
Vwithout_repeated_line
a without repeated line
#MATRIX14
O1 0 3
OSwapDiagonal
mol#1#2#3; \mathop{\rm SwapDiagonal}(#1,#2,#3)
#MATRIX15
O1 0 2
OSolutions_of
hosl#1#2; set of solutions of #1 and #2
O2 0 1
OSpace_of_Solutions_of
hosl; space of solutions of #1
#MATRIX16
O1 0 1
OLCirc
mol; \mathop{\rm LCirc} #1
O2 0 1
OCCirc
mol; \mathop{\rm CCirc} #1
O3 0 1
OACirc
mol; \mathop{\rm ACirc} #1
R1 1 1
Ris_line_circulant_about
i line circulant about #2
not line circulant about #2
R2 1 1
Ris_col_circulant_about
i column circulant about #2
not column circulant about #2
R3 1 1
Ris_anti-circular_about
i anti-circular about #2
not anti-circular about #2
V1 1
Vline_circulant
a line circulant
V2 1
Vfirst-line-of-circulant
a first-line-of-circulant
V3 1
Vcol_circulant
a column circulant
V4 1
Vfirst-col-of-circulant
a first-column-of-circulant
V5 1
Vcirculant
a circulant
V6 1
Vanti-circular
n anti-circular
V7 1
Vfirst-line-of-anti-circular
a first-line-of-anti-circular
#MATRIXC1
O1 1 0
O@"
moq; #1^\ast
O2 0 1
OFinSeq2Matrix
mol; \mathop{\rm FinSeq2Matrix} #1
O3 0 1
OMatrix2FinSeq
mol; \mathop{\rm Matrix2FinSeq} #1
O4 0 1
OFR2FC
mol; \mathop{\rm FR2FC} #1
O5 0 1
OLineSum
mol; \mathop{\rm LineSum} #1
O6 0 1
OColSum
mol; \mathop{\rm ColSum} #1
O7 0 1
OSumAll
mol; \mathop{\rm SumAll} #1
O8 0 3
OQuadraticForm
mol#1#2#3; \mathop{\rm QuadraticForm}(#1,#2,#3)
#MATRIXJ1
M1 1
MFinSequence_of_Matrix
ha finite sequence #0 of matrices over #1
finite sequences #0 of matrices over #1
M2 1
MFinSequence_of_Square-Matrix
ha finite sequence #0 of square-matrices over #1
finite sequences #0 of square-matrices over #1
O1 0 1
OLen
mol; \mathop{\rm Len} #1
O2 0 1
OWidth
mol; \mathop{\rm Width} #1
O3 0 2
Oblock_diagonal
hosl/2r@s#1; #2-block diagonal of #1
V1 1
VMatrix-yielding
a matrix-yielding
V2 1
VSquare-Matrix-yielding
a square-matrix-yielding
#MATRIXJ2
M1 1
MFinSequence_of_Jordan_block
ha finite sequence #0 of Jordan blocks of #1
fininte sequences #0 of Jordan blocks of #1
M1 2
MFinSequence_of_Jordan_block
ha finite sequence #0 of Jordan blocks of #1 and #2
finite sequences #0 of Jordan blocks of #1 and #2
O1 0 2
OJordan_block
hol#1#2; Jordan block of #1 and #2
O2 0 1
Odegree_of_nilpotent
hol; degree of nilpotence of #1
V1 1
VJordan-block-yielding
a Jordan-block-yielding
#MATRIXR1
O1 0 1
OMXR2MXF
mol; ({\mathbb R}\to{\mathbb R}_{\rm F}) #1
O2 0 1
OMXF2MXR
mol; ({\mathbb R}_{\rm F}\to{\mathbb R}) #1
O3 0 1
O0_Rmatrix
mol; 0_{\mathbb R}\mathop{\rm matrix}(#1)
O3 0 2
O0_Rmatrix
moq{w}/2r@m#1; {\left(\begin{array}{ccc}0&\dots&0\\\vdots&\ddots&\vdots\\0&\dots&0\\\end{array}\right)^{#1\times #2}_{\mathbb R}}
O4 0 1
OColVec2Mx
mol; \mathop{\rm ColVec2Mx} #1
O5 0 1
OLineVec2Mx
mol; \mathop{\rm LineVec2Mx} #1
#MATRIXR2
O1 0 1
O1_Rmatrix
mol; 1_{\mathbb R}\mathop{\rm matrix}(#1)
O2 0 2
OBase_FinSeq
hol#1#2; base fin seq(#1,#2)
O2 0 3
OBase_FinSeq
hol/3r@s/1q/2m; #3-versor in ${#1}^{#2}$
#MATRIX_1
M1 1
MMatrix
ha matrix #0 over #1
matrices #0 over #1
M1 2
MMatrix
ha square matrix #0 over #2 of dimension #1
square matrices #0 over #2 of dimension #1
M1 3
MMatrix
ha matrix #0 over #3 of dimension #1$\times$#2
matrices #0 over #3 of dimension #1$\times$#2
M2 2
MDiagonal
ha diagonal #1-dimensional matrix #0 over #2
diagonal #1-dimensional matrices #0 over #2
O1 0 1
OIndices
hol; indices of #1
O2 0 2
OCol
mow(1)#2; #1_{\square,#2}
O3 1 1
O-Matrices_over
moq(2)/1r@m; #2^{#1\times #1}
O4 1 1
O-G_Matrix_over
moq(2)/1r@m; #2^{#1\times #1}_{\rm G}
V1 1
Vtabular
a tabular
V2 1
Vdiagonal
a diagonal
#MATRIX_2
M1 2
MUpper_Triangular_Matrix
hn upper triangular matrix #0 over #2 of dimension #1
upper triangular matrices #0 over #2 of dimension #1
M2 2
MLower_Triangular_Matrix
ha lower triangular matrix #0 over #2 of dimension #1
lower triangular matrices #0 over #2 of dimension #1
O1 2 2
O][
mc#1#2#3#4; \left(\begin{array}{cc}#1&#2\\ #3&#4\end{array}\right)
O2 0 2
ODelCol
ho#1#2; deleting of #2-column in #1
O3 0 2
ODelLine
ho#1#2; deleting of #2-row in #1
O4 0 3
ODeleting
ho#1#2#3; deleting of #2-row and #3-column in #1
O5 0 1
OPermutations
hop/1r@m; permutations of #1
O6 0 1
OGroup_of_Perm
mow#1; A_{#1}
O7 0 1
OFinOmega
mo{qrw}#1; \Omega^{\rm f}_{#1}
V1 1
Vupper_triangular
n upper triangular
V2 1
Vlower_triangular
a lower triangular
V3 1
Vpermutational
a permutational
V4 1
Vbeing_transposition
b transposition
#MATRIX_3
O1 0 2
OPath_matrix
moi; #1\mathop{\rm\hbox{-}Path} #2
O2 0 1
OPath_product
hol; product on paths of #1
O3 0 1
ODet
mol; \mathop{\rm Det} #1
O4 0 1
Odiagonal_of_Matrix
hol; diagonal of #1
#MATRIX_5
O1 0 1
OCOMPLEX2Field
mow{}; {#1}_{{\Bbb C}_{\rm F}}
O2 0 1
OField2COMPLEX
mow{}; {#1}_{{\Bbb C}}
O3 0 2
O0_Cx
moq{q}; {\left(\begin{array}{ccc}0&\dots&0\\\vdots&\ddots&\vdots\\0&\dots&0\\\end{array}\right)^{#1\times #2}_{\Bbb C}}
#MATRIX_6
R1 1 1
Ris_reverse_of
i inverse of #2
not inverse of #2
V1 1
VOrthogonal
n orthogonal
#MATRIX_7
O1 0 4
OIFIN
mol#1#2#3#4; \mathop{\rm IFIN}(#1,#2,#3,#4)
#MATRIX_8
R1 1 1
Ris_congruent_Matrix_of
i congruent to #2
not congruent to #2
V1 1
VIdempotent
n idempotent
V2 1
VNilpotent
a 2-nilpotent
V3 1
VInvolutory
n involutory
V4 1
VSelf_Reversible
a self invertible
#MATRIX_9
O1 0 1
OPPath_product
mol; \mathop{\rm PPath} #1
#MATRLIN
M1 1
MOrdBasis
hn ordered basis #0 of #1
ordered bases #0 of #1
O1 0 2
Olmlt
mol#1#2; \mathop{\rm lmlt}(#1,#2)
O2 0 3
OAutMt
mol#1#2#3; \mathop{\rm AutMt}(#1,#2,#3)
#MATRLIN2
O1 0 3
OAutEqMt
mol#1#2#3; \mathop{\rm AutEqMt}(#1,#2,#3)
O2 0 3
OMx2Tran
mol#1#2#3; \mathop{\rm Mx2Tran}(#1,#2,#3)
#MATROID0
M1 0
MSubsetFamilyStr
ha subset family structure #0
subset family structures #0
M2 0
MMatroid
ha matroid #0
matroids #0
O1 0 1
Othe_family_of
hol; family of #1
O2 0 1
OProdMatroid
mol; \mathop{\rm ProdMatroid} #1
O3 0 1
OLinearlyIndependentSubsets
hosl; matroid of linearly independent subsets of #1
O4 0 1
ORnk
mol; \mathop{\rm Rnk} #1
R1 1 1
Rc/=
mn #1 \not\subseteq #2
#1 \subseteq #2
R2 1 1
Ris_maximal_independent_in
iy maximal independent in #2
not maximal independent in #2
R3 1 1
Ris_dependent_on
iy dependent on #2
not dependent on #2
V1 1
Vdependent
a dependent
V2 1
Vwith_exchange_property
x exchange property
V3 1
Vfinite-membered
a finite-membered
V4 1
Vfinite-degree
a finite-degree
V5 1
Vcycle
b cycle
#MATRPROB
O1 0 1
ORow_Marginal
hol; row marginal #1
O2 0 1
OColumn_Marginal
hol; column marginal #1
V1 1
VProbFinS
b finite probability distribution
V2 1
Vm-nonnegative
a nonnegative
V3 1
Vwith_sum=1
a summable-to-1
V4 1
VJoint_Probability
b joint probability
V5 1
Vwith_line_sum=1
x lines summable-to-1
V6 1
VConditional_Probability
b conditional probability
#MCART_1
O1 1 0
O`1
mow; {#1_{\bf 1}}
O2 1 0
O`2
mow; {#1_{\bf 2}}
O3 1 0
O`3
mow; {#1_{\bf 3}}
O4 1 0
O`4
mow; {#1_{\bf 4}}
O5 0 1
Opr1
mc#1; \mathop{\rm pr1}(#1)
O5 0 2
Opr1
mcl/1r@m/2l@m; {\pi_{1}} ( #1 \times #2 )
O5 0 3
Opr1
mcl(3)@s/1k#1#2#3; \pi^1_{#1,#2}(#3)
O6 0 1
Opr2
mc#1; \mathop{\rm pr2}(#1)
O6 0 2
Opr2
mcl@s/1r@m/2l@m; {\pi_{2}} ( #1 \times #2 )
O6 0 3
Opr2
mcl(3)@s/1k#1#2#3; \pi^2_{#1,#2}(#3)
O7 1 0
O`11
mow; {#1_{{\bf 1},\bf 1}}
O8 1 0
O`12
mow; {#1_{{\bf 1},\bf 2}}
O9 1 0
O`21
mow; {#1_{{\bf 2},\bf 1}}
O10 1 0
O`22
mow; {#1_{{\bf 2},\bf 2}}
#MCART_2
O1 1 0
O`5
mor; {#1_{\bf 5}}
O2 1 0
O`6
mor; {#1_{\bf 6}}
O3 1 0
O`7
mor; {#1_{\bf 7}}
O4 1 0
O`8
mor; {#1_{\bf 8}}
O5 1 0
O`9
mor; {#1_{\bf 9}}
#MEASURE1
M1 1
MMeasure
ha measure #0 on #1
measures #0 on #1
M2 1
Mmeasure_zero
ha set #0 of measure zero w.r.t. #1
sets #0 of measure zero w.r.t. #1
M3 1
MN_Sub_set_fam
ha denumerable family #0 of subsets of #1
denumerable families #0 of subsets of #1
M4 1
MSep_Sequence
ha sequence #0 of separated subsets of #1
sequences #0 of separated subsets of #1
M5 1
Msigma_Measure
ha \FMsig-measure #0 on #1
\FMsig-measures #0 on #1
V1 1
Vsigma-additive
a \FMsig-additive
#MEASURE2
M1 1
MN_Measure_fam
ha family #0 of measurable sets of #1
families #0 of measurable sets of #1
#MEASURE3
M1 1
MN_Sub_fam
ha subfamily #0 of #1
subfamilies #0 of #1
M2 1
Mthin
ha set #0 with measure zero w.r.t. #1
sets #0 with measure zero w.r.t. #1
O1 0 1
OCOM
mol@s#1; {\rm COM}(#1)
O1 0 2
OCOM
mcl#1#2; {\rm COM}(#1,#2)
O2 0 1
OMeasPart
mol; {\rm MeasPart} #1
R1 1 1
Ris_complete
i complete on #2
not complete in #2
#MEASURE4
M1 1
MC_Measure
ha Caratheodor's measure #0 on #1
Caratheodor's measures #0 on #1
O1 0 1
Osigma_Field
mol@s#1; \sigma{\rm\hbox{-}Field}(#1)
O2 0 1
Osigma_Meas
mol@s#1; \sigma{\rm\hbox{-}Meas}(#1)
#MEASURE5
M1 0
MInterval
hn interval #0
intervals #0
O1 0 1
Odiameter
mol@s; \varnothing #1
V1 1
Vopen_interval
n open interval
V2 1
Vclosed_interval
a closed interval
V3 1
Vright_open_interval
a right open interval
V4 1
Vleft_closed_interval
a left closed interval
V5 1
Vleft_open_interval
a left open interval
V6 1
Vright_closed_interval
a right closed interval
V7 1
Vinterval
n interval
#MEASURE6
O1 0 1
OR_EAL
mol#1; \overline{\mathbb R}(#1)
#MEASURE7
M1 1
MInterval_Covering
hn interval covering #0 of #1
interval coverings #0 of #1
O1 0 1
Ovol
mol@s#1; {\rm vol}(#1)
O1 0 2
Ovol
mol#1#2; \mathop{\rm vol}(#1,#2)
O1 1 0
Ovol
mor#1; (#1)\mathop{\rm vol}
O2 0 1
OSvc
mol#1; \mathop{\rm Svc}(#1)
O2 0 2
OSvc
mol#1#2; \mathop{\rm Svc}(#1,#2)
O3 0 0
OOS_Meas
mol; \mathop{\rm OSMeas}
O4 0 0
OLmi_sigmaFIELD
mosl; L_\mu\hbox{-}\sigma{\rm FIELD}
O5 0 0
OL_mi
mow; L_\mu
#MEASURE8
M1 1
MSep_FinSequence
ha disjoint valued finite set sequence #0 of #1
disjoint valued finite set sequences #0 of #1
M2 1
MSet_Sequence
ha set sequence #0 of #1
set sequences #0 of #1
M3 2
MCovering
ha covering #0 of #1 in #2
coverings #0 of #1 in #2
O1 0 2
OVolume
mol#1#2; \mathop{\rm Volume}(#1,#2)
O2 0 1
OC_Meas
hosl; Caratheodory measure determined by #1
O3 0 0
OInvPairFunc
mol; \mathop{\rm InvPairFunc}
V1 1
Vcompletely-additive
a completely-additive
#MEMBERED
V1 1
Vcomplex-membered
a complex-membered
V2 1
Vext-real-membered
n extended real-membered
V3 1
Vreal-membered
a real-membered
V4 1
Vrational-membered
a rational-membered
V5 1
Vinteger-membered
n integer-membered
V6 1
Vnatural-membered
a natural-membered
#MEMBER_1
O1 0 1
O--
mol; \ominus #1
O1 1 1
O--
moi; #1 \ominus #2
O2 1 0
O""
moq; #1^{-1}
O2 1 1
O""
moi@s/1q/2k#2; #1{^{-1}}(#2)
O3 1 1
O++
moi@a; #1 \oplus #2
O4 1 1
O**
moi@m; #1 \circ #2
O4 1 2
O**
moi#3; #1 \circ_{#3}#2
O5 1 1
O///
moi; #1 \oslash #2
#MESFUN10
R1 1 1
Ris_uniformly_convergent_to
i uniformly convergent to #2
not uniformly convergent to #2
V1 1
Vuniformly_bounded
n uniformly bounded
#MESFUNC1
O1 0 0
OINT-
mc; {\mathbb Z_{-}}
O2 0 1
ORAT_with_denominator
mol#1; \mathop{\mathbb Q} (#1)
O3 0 0
O1.
mcl; \mathop{\overline{1}}
O3 0 1
O1.
mow/1k#1; 1_{#1}
O3 0 2
O1.
moq{w}/2r@m#1; {I^{#2\times #2}_{#1}}
O4 0 2
Oeq_dom
mol#1#2; \mathop{\rm EQ\hbox{-}dom}(#1,#2)
O5 0 2
Oless_dom
mol#1#2; \mathop{\rm LE\hbox{-}dom}(#1,#2)
O6 0 2
Oless_eq_dom
mol#1#2; \mathop{\rm LEQ\hbox{-}dom}(#1,#2)
O7 0 2
Ogreat_dom
mol#1#2; \mathop{\rm GT\hbox{-}dom}(#1,#2)
O8 0 2
Ogreat_eq_dom
mol#1#2; \mathop{\rm GTE\hbox{-}dom}(#1,#2)
R1 1 1
Ris_measurable_on
h #1 is measurable on #2
#1 is not measurable on #2
#MESFUNC2
M1 1
MFinite_Sep_Sequence
ha finite sequence #0 of separated subsets of #1
finite sequences #0 of separated subsets of #1
R1 1 1
Ris_simple_func_in
h #1 is simple function in #2
#1 is not simple function in #2
#MESFUNC3
R1 2 1
Rare_Re-presentation_of
h #1 and #2 are representation of #3
#1 and #2 are not representation of #3
#MESFUNC5
M1 0
MExtREAL_sequence
ha sequence #0 of extended reals
sequences #0 of extended reals
O1 0 2
Ointegral'
mol#1#2; \int'#2\,{\rm d}#1
O2 0 2
Ointegral+
mol#1#2; \int^+#2\,{\rm d}#1
O3 0 2
OIntegral
mol#1#2; \int #2\,{\rm d}#1
O4 0 3
OIntegral_on
mol#1#2#3; \int\limits_{#2}#3\,{\rm d}#1
V1 1
Vnonpositive
a non-positive
V2 1
Vwithout-infty
c without $-\infty$
V3 1
Vwithout+infty
c without $+\infty$
V4 1
Vconvergent_to_finite_number
c convergent to finite number
V5 1
Vconvergent_to_+infty
c convergent to $+\infty$
V6 1
Vconvergent_to_-infty
c convergent to $-\infty$
#MESFUNC7
O1 0 0
Omultextreal
mow; {\cdot_{\overline{\mathbb R}}}
V1 1
Vextreal-yielding
n extreal-yielding
#MESFUNC8
V1 1
Vwith_the_same_dom
x the same dom
#MESFUNC9
O1 0 2
OProjMap1
mol#1#2; \mathop{\rm curry}(#1,#2)
O2 0 2
OProjMap2
mol#1#2; \mathop{\rm curry'}(#1,#2)
#METRIC_1
G1 2
GMetrStruct
mc#1#2; \langle #1, #2\rangle
J1 1
GMetrStruct
hol#1; metric structure of #1
L1 0
GMetrStruct
ha metric structure #0
metric structures #0
M1 0
MMetrSpace
ha metric space #0
metric spaces #0
M2 0
MPseudoMetricSpace
ha pseudo metric space #0
pseudo metric spaces #0
M3 0
MSemiMetricSpace
ha semi metric space #0
semi metric spaces #0
M4 0
MNonSymmetricMetricSpace
ha non-symmetric metric space #0
non-symmetric metric spaces #0
M5 0
MUltraMetricSpace
hn ultra metric space #0
ultra metric spaces #0
O1 0 1
Odist
mol#1; \mathop{\rm dist}(#1)
O1 0 2
Odist
mol@s#1#2; \rho(#1, #2)
O2 0 0
OEmpty^2-to-zero
mo@w; \lbrace\lbrack\emptyset,\emptyset\rbrack\rbrace\mapsto 0
O3 0 1
Odiscrete_dist
hol; discrete metric of #1
O4 0 1
ODiscreteSpace
hol; discrete space on #1
O5 0 0
Oreal_dist
mow; \mathinner{\rho_{\mathbb R}}
O6 0 0
ORealSpace
hol; metric space of real numbers
O7 0 2
OBall
mcl@s#1#2; \mathop{\rm Ball} (#1, #2)
O8 0 2
Ocl_Ball
mcl@s#1#2; \mathop{\overline{\rm Ball}} (#1, #2)
O9 0 2
OSphere
mol@s; \mathop{\rm Sphere} (#1, #2)
O10 0 0
OSet_to_zero
mo@w; 2^2\to 0
O11 0 0
OZeroSpace
mc; \circleddash
O12 0 2
Oopen_dist_Segment
mcl@s#1#2; \mathop{\rm IntSeg}(#1,#2)
O13 0 2
Oclose_dist_Segment
mc#1#2; \mathop{\rm ClSeg}(#1,#2)
R1 1 2
Ris_between
i between #2 and #3
not between #2 and #3
U1 1
Udistance
hosl#1; distance of #1
distance
V1 1
VReflexive
a reflexive
V2 1
Vdiscerning
a discernible
V3 1
Vtriangle
a triangle
V4 1
VDiscerning
a Discerning
V5 1
Vultra
n ultra
#METRIC_2
M1 1
Mequivalence_class
ha $\square$-equivalence class #0 of #1
$\square$-equivalence classes #0 of #1
O1 1 0
O-neighbour
mcr; #1^\square
O2 0 2
Oev_eq_1
mc#1#2; \rho^\circ(#1,#2)
O3 0 2
Oev_eq_2
mc#1#2; \rho_{#2}^\square\mathbin{^{-1}}(#1)
O4 0 1
Oreal_in_rel
mc#1; \rho^\circ(#1^\square,#1^\square)
O5 0 1
Oelem_in_rel_1
mc#1; \mathop{\rm dom_1}\rho_{#1}^\square
O6 0 1
Oelem_in_rel_2
mc#1; \mathop{\rm dom_2}\rho_{#1}^\square
O7 0 1
Oelem_in_rel
mc#1; \mathop{\rm dom}\rho_{#1}^\square
O8 0 1
Oset_in_rel
mc#1; \mathop{\rm graph}\rho_{#1}^\square
O9 0 1
Onbourdist
mc#1; \rho_{#1}^\square
O10 0 1
OEq_classMetricSpace
mc; #1_{/\square}
R1 2 1
Ris_dst
h the distance between #1 and #2 is #3
the distance between #1 and #2 is not #3
#METRIC_3
O1 0 2
Odist_cart2
moq/1r@m/2l@m#1#2; \rho^{#1 \times #2}
O2 0 2
Odist2
mcl@s#1#2; \rho(#1, #2)
O3 0 2
OMetrSpaceCart2
mc#1#2; \mizleftcart\,#1,\allowbreak\,#2\,\mizrightcart
O4 0 3
Odist_cart3
moq/1r@m/3l@m/2l@m#1#2#3; \rho^{#1 \times #2 \times #3}
O5 0 3
OMetrSpaceCart3
mc#1#2#3; \mizleftcart\,#1,\allowbreak\,#2,\allowbreak\,#3\,\mizrightcart
O6 0 2
Odist3
mcl@s#1#2; \rho(#1, #2)
O7 0 4
Odist_cart4
moq/1r@m/2l@m/3l@m/4l@m#1#2#3#4; \rho^{#1 \times #2 \times #3 \times #4}
O8 0 4
OMetrSpaceCart4
mc#1#2#3#4; \mizleftcart\,#1,\allowbreak\,#2,\allowbreak\,#3,\allowbreak\,#4\,\mizrightcart
O9 0 2
Odist4
mcl@s#1#2; \rho(#1, #2)
O10 0 2
Odist_cart2S
moq#1#2; \rho^{\mizleftcart #1,#2\mizrightcart}
O11 0 2
Odist2S
mol@s#1#2; \rho^{\bf 2}(#1,#2)
O12 0 2
OMetrSpaceCart2S
mc#1#2; \mizleftcart #1,#2\mizrightcart
O13 0 3
Odist_cart3S
moq#1#2#3; \rho^{\mizleftcart #1,#2,#3\mizrightcart}
O14 0 2
Odist3S
mol@s#1#2; \rho^{\bf 3}(#1,#2)
O15 0 3
OMetrSpaceCart3S
mc#1#2#3; \mizleftcart #1,#2\mizrightcart
O16 0 0
Otaxi_dist2
moq; \rho^{\mizleftcart {\mathbb R},{\mathbb R}\mizrightcart}
O17 0 0
ORealSpaceCart2
mc; \mizleftcart {\mathbb R}_{\rm M},{\mathbb R}_{\rm M}\mizrightcart
O18 0 0
OEukl_dist2
moq; \rho^{{\mathbb R}^2}
O19 0 0
OEuklSpace2
ho; Euclidean plane
O20 0 0
Otaxi_dist3
moq; \rho^{\mizleftcart {\mathbb R},{\mathbb R},{\mathbb R}\mizrightcart}
O21 0 0
ORealSpaceCart3
mc; \mizleftcart {\mathbb R}_{\rm M},{\mathbb R}_{\rm M},{\mathbb R}_{\rm M}\mizrightcart
O22 0 0
OEukl_dist3
moq; \rho^{{\mathbb R}^3}
O23 0 0
OEuklSpace3
ho; Euclidean space
#METRIC_6
O1 0 2
Obounded_metric
mow#1#2; \widetilde{#2}_{#1}
O2 0 2
Odist_to_point
mol@s#1#2; \rho(#1,#2)
O3 0 2
Osequence_of_dist
mol@s#1#2; \rho(#1,#2)
R1 1 1
Ris_convergent_in_metrspace_to
i convergent to #2
not convergent to #2
R2 1 1
Rcontains_almost_all_sequence
h #1 contains almost all sequence #2
#1 does not contain almost all sequence #2
#METRIZTS
R1 1 2
Rseparates
h #1 separates #2,#3
#1 not separates #2,#3
V1 1
VLindelof
a Lindel\"of
#MIDSP_1
G1 2
GMidStr
mc#1#2; \langle #1, #2\rangle
J1 1
GMidStr
hol#1; midpoint algebra structure of #1
L1 0
GMidStr
ha midpoint algebra structure #0
midpoint algebra structures #0
M1 0
MMidSp
ha midpoint algebra #0
midpoint algebras #0
O1 0 0
OExample
mo; {\rm EX}
O2 0 1
OID
mow/1k#1; {\rm I}_{#1}
O3 0 1
Ovect
mol@s; \mathop{\rm vect} #1
O3 0 2
Ovect
mct#1#2; \overrightarrow{\lbrack #1,#2 \rbrack}
O4 0 1
Osetvect
mol@s; \mathop{\rm setvect} #1
O5 0 1
Oaddvect
mol@s; \mathop{\rm addvect} #1
O6 0 1
Ocomplvect
mol@s; \mathop{\rm complvect} #1
O7 0 1
Ozerovect
mol@s; \mathop{\rm zerovect} #1
O8 0 1
Ovectgroup
mol@s; \mathop{\rm vectgroup} #1
R1 2 2
R@@
m #1,#2 \equiv #3,#4
#1,#2 \not\equiv #3,#4
R2 1 1
R##
m #1 \equiv #2
#1 \not\equiv #2
U1 1
UMIDPOINT
hosl#1; midpoint operation of #1
midpoint operation
V1 1
VMidSp-like
a midpoint algebra-like
#MIDSP_2
G1 2
GAtlasStr
mc#1#2; \langle #1, #2\rangle
J1 1
GAtlasStr
hol#1; atlas structure of #1
L1 1
GAtlasStr
hn atlas structure #0 over #1
atlas structures #0 over #1
M1 1
MATLAS
hn atlas #0 of #1
atlases #0 of #1
O1 0 1
OHalf
mol@s; {1\over 2}#1
O2 0 1
OAtlas
mol@s; \mathop{\rm Atlas} #1
O3 0 1
OMidSp.
mol@s#1; \mathop{\rm MidSp}(#1)
R1 2 1
Rare_associated_wrp
h #1, #2 are associated w.r.t. #3
#1, #2 are not associated w.r.t. #3
R2 1 2
Ris_atlas_of
i an atlas of #2, #3
not an atlas of #2, #3
U1 1
Ualgebra
honl#1; algebra of #1
algebra
U2 1
Ufunction
hosl#1; function of #1
function
V1 1
Vmidpoint_operator
a midpoint operator
V2 1
VATLAS-like
n atlas-like
#MIDSP_3
G1 3
GReperAlgebraStr
mc#1#2#3; \langle #1, #2, #3\rangle
J1 1
GReperAlgebraStr
hol#1; structure of reper algebra of #1
L1 1
GReperAlgebraStr
ha structure of reper algebra #0 over #1
structures of reper algebra #0 over #1
M1 1
MReperAlgebra
ha reper algebra #0 of #1
reper algebras #0 of #1
R1 1 1
Rhas_property_of_zero_in
j property of zero in #2
not property of zero in #2
R2 1 1
Ris_semi_additive_in
i semi additive in #2
not semi additive in #2
R3 1 1
Ris_additive_in
i additive in #2
not additive in #2
R4 1 1
Ris_alternative_in
i alternative in #2
not alternative in #2
U1 1
Ureper
hosl#1; reper of #1
reper
V1 1
Vbeing_invariance
b invariance
#MODAL_1
M1 0
MMP-variable
ha variable #0
variables #0
M2 0
MMP-conective
ha connective #0
connectives #0
M3 1
MDOMAIN_DecoratedTree
ha non empty set #0 of trees decorated with elements of #1
non empty sets #0 of trees decorated with elements of #1
M4 0
MMP-wff
ha MP-formula #0
MP-formulae #0
O1 0 1
ORoot
hol; root of #1
O2 0 0
OMP-variables
mc; {\cal V}
O3 0 0
OMP-conectives
mc; {\cal C}
O4 0 0
OMP-WFF
mc; {\rm WFF}
O5 0 1
O?
mol@s; \lozenge #1
O5 1 0
O?
mor; #1 ?
V1 1
Vnecessitive
a necessitive
#MODCAT_1
M1 1
MLeftMod_DOMAIN
ha non empty set #0 of left-modules of #1
non empty sets #0 of left-modules of #1
M2 1
MLModMorphism_DOMAIN
ha non empty set #0 of morphisms of left-modules of #1
non empty sets #0 of morphisms of left-modules of #1
M2 2
MLModMorphism_DOMAIN
ha non empty set #0 of morphisms of left-modules from #1 into #2
non empty sets #0 of morphisms of left-modules from #1 into  #2
O1 0 2
OLModObjects
mol@s#1#2; \mathop{\rm LModObj}(#1,#2)
O2 0 1
Odom'
mol@s; \mathop{\rm dom'} #1
O3 0 1
Ocod'
mol@s; \mathop{\rm cod'} #1
O4 0 2
OLModCat
mol@s#1#2; \mathop{\rm LModCat}(#1,#2)
#MODELC_1
G1 4
GKripkeStr
mc#1#2#3#4; \langle #1,#2,#3,#4 \rangle
G2 7
GCTLModelStr
mc#1#2#3#4#5#6#7; \langle #1,#2,#3,#4,#5,#6,#7 \rangle
J1 1
GKripkeStr
hol#1; Kripke structure of #1
J2 1
GCTLModelStr
hol#1; CTL model structure of #1
L1 1
GKripkeStr
ha Kripke structure #0 over #1
Kripke structures #0 over #1
L2 0
GCTLModelStr
ha CTL model structure #0
CTL model structures #0
M1 0
MCTL-formula
ha CTL-formula #0
CTL-formulae #0
M2 1
MAssign
hn assignation #0 of #1
assignations #0 of #1
M3 1
Minf_path
hn infinity path #0 of #1
infinity paths #0 of #1
M4 0
MCTLModel
ha CTL Model #0
CTL Models #0
O1 0 3
Ok_id
mol#1#2#3; \mathop{\rm k.id}(#1,#2,#3)
O2 0 1
Ok_nat
mol; \mathop{\rm k.nat} #1
O3 0 3
OUnivF
mol#1#2#3; \mathop{\rm UnivF}(#1,#2,#3)
O4 0 1
OCastboolean
mol; \mathop{\rm Castboolean} #1
O5 0 2
OCastBool
mol#1#2; \mathop{\rm CastBool}(#1,#2)
O6 0 1
Oatom.
mol; \mathop{\rm atom.} #1
O7 0 1
OEX
mol; \mathop{\rm EX} #1
O8 0 1
OEG
mol; \mathop{\rm EG} #1
O9 1 1
OEU
moi; #1 \mathop{\rm EU} #2
O10 0 0
OCTL_WFF
mc; \mathop{\rm CTL\hbox{-}WFF}
O11 0 1
OCastCTLformula
mol; \mathop{\rm CastCTLformula} #1
O12 0 0
Oatomic_WFF
hol; atomic WFF
O13 0 6
OGraftEval
mol#1#2#3#4#5#6; \mathop{\rm GraftEval}(#1,#2,#3,#4,#5,#6)
O14 0 3
OEvalSet
mol#1#2#3; \mathop{\rm EvalSet}(#1,#2,#3)
O15 0 3
OCastEval
mol#1#2#3; \mathop{\rm CastEval}(#1,#2,#3)
O16 0 2
OEvalFamily
mol#1#2; \mathop{\rm EvalFamily}(#1,#2)
O17 0 2
OEvaluate
mol#1#2; \mathop{\rm Evaluate}(#1,#2)
O18 1 1
O|**
moq/2m#2; #1^{#2}
O19 0 1
OModelSP
mol; \mathop{\rm ModelSP} #1
O20 0 2
OFid
mol#1#2; \mathop{\rm Fid}(#1,#2)
O21 0 2
ONot_0
mol#1#2; \mathop{\rm Not}_0(#1,#2)
O22 0 1
ONot_
mol; \mathop{\rm Not} #1
O23 0 3
OEneXt_univ
mol#1#2#3; \mathop{\rm EneXt}_{\rm univ}(#1,#2,#3)
O24 0 2
OEneXt_0
mol#1#2; \mathop{\rm EneXt}_0(#1,#2)
O25 0 1
OEneXt_
mol; \mathop{\rm EneXt} #1
O26 0 3
OEGlobal_univ
mol#1#2#3; \mathop{\rm EGlobal}_{\rm univ}(#1,#2,#3)
O27 0 2
OEGlobal_0
mol#1#2; \mathop{\rm EGlobal}_0(#1,#2)
O28 0 1
OEGlobal_
mol; \mathop{\rm EGlobal} #1
O29 0 3
OAnd_0
mol#1#2#3; \mathop{\rm And}_0(#1,#2,#3)
O30 0 1
OAnd_
hol; and  #1
O31 0 4
OEUntill_univ
mol#1#2#3#4; \mathop{\rm EUntill}_{\rm univ}(#1,#2,#3,#4)
O32 0 3
OEUntill_0
mol#1#2#3; \mathop{\rm EUntill}_0(#1,#2,#3)
O33 0 1
OEUntill_
mol; \mathop{\rm EUntill} #1
O34 0 2
OF_LABEL
mol#1#2; \mathop{\rm F\hbox{-}LABEL}(#1,#2)
O35 0 1
OLabel_
mol; \mathop{\rm Label} #1
O36 0 3
OKModel
mol#1#2#3; \mathop{\rm KModel}(#1,#2,#3)
O37 0 2
OBASSModel
mol#1#2; \mathop{\rm BASS Model}(#1,#2)
O38 0 3
OPrePath
mol#1#2#3; \mathop{\rm PrePath}(#1,#2,#3)
O39 0 2
OPred
mol#1#2; \mathop{\rm Pred}(#1,#2)
O40 0 1
OSIGMA
mol; \mathop{\rm SIGMA} #1
O41 0 3
OTau
mol#1#2#3; \mathop{\rm Tau}(#1,#2,#3)
O42 0 2
OFax
mol#1#2; \mathop{\rm Fax}(#1,#2)
O43 0 4
OSigFaxTau
mol#1#2#3#4; \mathop{\rm SigFaxTau}(#1,#2,#3,#4)
O44 0 2
OPathShift
mol#1#2; \mathop{\rm PathShift}(#1,#2)
O45 0 4
OPathChange
mol#1#2#3#4; \mathop{\rm PathChange}(#1,#2,#3,#4)
O46 0 3
OPathConc
mol#1#2#3; \mathop{\rm PathConc}(#1,#2,#3)
O47 0 1
OTransEG
mol; \mathop{\rm TransEG} #1
O48 0 3
OFoax
mol#1#2#3; \mathop{\rm Foax}(#1,#2,#3)
O49 0 5
OSigFoaxTau
mol#1#2#3#4#5; \mathop{\rm SigFoaxTau}(#1,#2,#3,#4,#5)
O50 0 2
OTransEU
mol#1#2; \mathop{\rm TransEU}(#1,#2)
O51 0 0
OTrivialCTLModel
mol; \mathop{\rm Trivial CTL Model}
R1 1 1
Ris-Evaluation-for
i an evaluation for #2
not an evaluation for #2
R2 1 2
Ris-PreEvaluation-for
i a #2-pre-evaluation for #3
not a #2-pre-evaluation for #3
R3 1 1
R|/=
m #1 \not\models #2
#1 \models #2
R3 2 1
R|/=
m #1 \not\models_{#2} #3
#1 \models_{#2} #3
U2 1
UStarts
hopl#1; starts of #1
starts
U4 1
ULabel
hosl#1; label of #1
label
U6 1
UBasicAssign
hopl#1; basic assignations of #1
basic assignations
U9 1
UEneXt
hosl#1; next-operation of #1
next-operation
U10 1
UEGlobal
hosl#1; global-operation of #1
global-operation
U11 1
UEUntill
honl#1; until-operation of #1
until-operation
V1 1
VCTL-formula-like
a CTL-formula-like
V2 1
VExistNext
n exist-next-formula
V3 1
VExistGlobal
n exist-global-formula
V4 1
VExistUntill
n exist-until-formula
V5 1
Vwith_basic
x basic
#MODELC_2
G1 8
GLTLModelStr
mc#1#2#3#4#5#6#7#8; \langle #1,#2,#3,#4,#5,#6,#7,#8 \rangle
J1 1
GLTLModelStr
hol#1; LTL-model structure of #1
L1 0
GLTLModelStr
hn LTL-model structure #0
LTL-model structures #0
M1 0
MLTL-formula
hn LTL-formula #0
LTL-formulae #0
M2 0
MLTLModel
ha LTL Model #0
LTL Models #0
O1 0 1
OCastNat
mol; \mathop{\rm CastNat} #1
O2 0 1
O'X'
mol; \mathop{\cal X} #1
O3 1 1
O'U'
moi; #1 \mathbin{\cal U} #2
O4 1 1
O'R'
moi; #1 \mathbin{\cal R} #2
O5 0 0
OLTL_WFF
mow; {\rm WFF}_{\rm LTL}
O6 0 1
OCastLTL
mol; \mathop{\rm Cast}_{\rm LTL} #1
O7 0 0
Oatomic_LTL
mow; {\rm atomic}_{\rm LTL}
O7 0 1
Oatomic_LTL
mol; \mathop{\rm atomic}_{\rm LTL} #1
O8 0 1
OInf_seq
hol; infinite sequences of #1
O9 0 1
OCastSeq
mol; \mathop{\rm CastSeq} #1
O9 0 2
OCastSeq
mol#1#2; \mathop{\rm CastSeq}(#1,#2)
O10 0 2
ONext_univ
mol#1#2; \mathop{\rm Next\hbox{-}univ}(#1,#2)
O11 0 2
ONext_0
mol#1#2; \mathop{\rm Next}_0(#1,#2)
O12 0 1
ONext_
mol; \mathop{\rm Next} #1
O13 0 4
OUntil_univ
mol#1#2#3#4; \mathop{\rm Until\hbox{-}univ}(#1,#2,#3,#4)
O14 0 3
OUntil_0
mol#1#2#3; \mathop{\rm Until}_0(#1,#2,#3)
O15 0 1
OUntil_
mol; \mathop{\rm Until} #1
O16 0 1
OOr_
mow#1; \lor_{#1}
O17 0 1
ORelease_
mol; \mathop{\rm Release} #1
O18 0 2
OInf_seqModel
hol#1#2; infinite sequence of Model of (#1,#2)
O19 0 0
OAtomicFamily
mol; \mathop{\rm AtomicFamily}
O20 0 2
OAtomicFunc
mol#1#2; \mathop{\rm AtomicFunc}(#1,#2)
O21 0 1
OAtomicAsgn
mol; \mathop{\rm AtomicAsgn} #1
O22 0 0
OAtomicBasicAsgn
mol; \mathop{\rm AtomicBasicAsgn}
O23 0 0
OAtomicKai
mol; \mathop{\rm AtomicKai}
O24 0 0
OTrivialLTLModel
mol; \mathop{\rm Trivial LTL Model}
U2 1
UNEXT
hosl#1; next-operation of #1
next-operation
U3 1
UUNTIL
honl#1; until-operation of #1
until-operation
U4 1
URELEASE
hosl#1; release-operation of #1
release-operation
V1 1
VLTL-formula-like
a LTL-formula-like
V2 1
Vnext
x \textit{next} operator
V3 1
VUntil
x \textit{until} operator
V4 1
VRelease
x \textit{release} operator
#MODELC_3
G1 3
GLTLnode
mc#1#2#3; \langle #1,#2,#3 \rangle
G2 4
GBuchiAutomaton
mc#1#2#3#4; \langle #1,#2,#3,#4 \rangle
J1 1
GLTLnode
hol#1; LTL-node of #1
J2 1
GBuchiAutomaton
hol#1; Buchi automaton of #1
L1 1
GLTLnode
hn LTL-node #0 over #1
LTL-nodes #0 over #1
L2 1
GBuchiAutomaton
ha Buchi automaton #0 over #1
Buchi automatons #0 over #1
O1 0 1
OLTLNew1
mol; \mathop{\rm LTLNew}_1 #1
O1 0 2
OLTLNew1
mol#1#2; \mathop{\rm LTLNew}_1(#1,#2)
O2 0 1
OLTLNew2
mol; \mathop{\rm LTLNew}_2 #1
O2 0 2
OLTLNew2
mol#1#2; \mathop{\rm LTLNew}_2(#1,#2)
O3 0 1
OLTLNext
mol; \mathop{\rm LTLNext} #1
O4 0 2
OSuccNode1
mol#1#2; \mathop{\rm SuccNode}_1(#1,#2)
O5 0 2
OSuccNode2
mol#1#2; \mathop{\rm SuccNode}_2(#1,#2)
O6 0 1
OSeed
mol; \mathop{\rm Seed} #1
O7 0 1
OFinalNode
mol; \mathop{\rm FinalNode} #1
O8 0 2
OCastNode
mol#1#2; \mathop{\rm CastNode}(#1,#2)
O9 0 3
OLength_fun
hol#1#2#3; length of #1 w.r.t. #2 and #3
O10 0 2
OPartial_seq
hol#1#2; partial sequence of #1 w.r.t. #2
O11 0 1
OLTLNodes
mol; \mathop{\rm Nodes}_{\rm LTL} #1
O12 0 1
OLTLStates
mol; \mathop{\rm States}_{\rm LTL} #1
O13 0 2
Ochosen_formula
hol/1r@s#2; #1-chosen formula of #2
O14 0 4
Ochosen_succ
hol/3r@s#1#2#4; #3-chosen successor of #4 w.r.t. #1, #2
O15 0 3
Ochoice_succ_func
hol/3r@s#1#2; #3-choice successor function w.r.t. #1, #2
O16 0 1
ONeg_atomic_LTL
mol; \mathop{\rm NegAtomic}_{\rm LTL} #1
O17 0 1
OTran_LTL
mol; \mathop{\rm Tran}_{\rm LTL} #1
O18 0 1
OInitS_LTL
mol; \mathop{\rm InitS}_{\rm LTL} #1
O19 0 1
OFinalS_LTL
mol; \mathop{\rm FinalS}_{\rm LTL} #1
O19 0 2
OFinalS_LTL
mol#1#2; \mathop{\rm FinalS}_{\rm LTL}(#1,#2)
O20 0 1
OBAutomaton
mol; \mathop{\rm BAutomaton} #1
O21 0 4
Ochosen_succ_end_num
hol/3r@s#1#2#4; #3-chosen successor end number of #4 w.r.t. #1, #2
O22 0 4
Ochosen_next
hol/3r@s#1#2#4; #3-chosen next node to #4 w.r.t. #1, #2
O23 0 3
Ochosen_run
hol/3r@s#1#2; #3-chosen run w.r.t. #1, #2
R1 1 1
Ris_succ_of
i a successor of #2
not a successor of #2
R1 1 2
Ris_succ_of
i a successor of #2 and #3
not a successor of #2 and #3
R2 1 1
Ris_succ1_of
i a 1st successor of #2
not a 1st successor of #2
R3 1 1
Ris_succ2_of
i a 2nd successor of #2
not a 2nd successor of #2
R4 1 1
Ris_Finseq_for
i a successor sequence for #2
not a successor sequence for #2
R5 1 1
Ris_next_of
i next to #2
not next to #2
R6 1 2
Ris_succ_homomorphism
i a successor homomorphism from #2 to #3
not a succcessor homomorphism from #2 to #3
R7 1 1
Ris-accepted-by
i accepted by #2
not accepted by #2
U1 1
ULTLold
honl#1; old-component of #1
old-component
U2 1
ULTLnew
hosl#1; new-component of #1
new-component
U3 1
ULTLnext
hosl#1; next-component of #1
next-component
V1 1
Vfailure
a failure
V2 1
Velementary
n elementary
V3 1
Vneg-inner-most
a negation-inner-most
#MOD_2
G1 3
GLModMorphismStr
mc#1#2#3; \langle #1, #2, #3\rangle
J1 1
GLModMorphismStr
hol#1; left module morphism structure of #1
L1 1
GLModMorphismStr
ha left module morphism structure #0 over #1
left module morphism structures #0 over #1
M1 1
MLModMorphism
ha left module morphism #0 of #1
left module morphisms #0 of #1
O1 0 1
OTrivialLMod
mom#1; {}_{#1}\Theta
O2 0 0
Oadd3
mcw; \mathop{\rm add}_3
O3 0 0
Omult3
mcw; \mathop{\rm mult}_3
O4 0 0
Ocompl3
mcw; \mathop{\rm compl}_3
O5 0 0
Ounit3
mcw; \mathop{\rm unit}_3
O6 0 0
Ozero3
mcw; \mathop{\rm zero}_3
O7 0 0
OZ3
mcw; \mathop{\rm Z}_3
U1 1
UDom
hosl#1; dom\hbox{-}map of #1
dom\hbox{-}map
U2 1
UCod
hosl#1; cod\hbox{-}map of #1
cod\hbox{-}map
V1 1
VLModMorphism-like
a left module morphism-like
#MOD_3
V1 1
Vbase
a base
#MOD_4
M1 1
MEndomorphism
hn endomorphism #0 of #1
endomorphisms #0 of #1
M1 2
MEndomorphism
hn endomorphism #0 of #1 and #2
endomorphisms #0 of #1 and #2
M2 1
MAutomorphism
hn automorphism #0 of #1
automorphisms #0 of #1
V1 1
Vantimultiplicative
n antimultiplicative
V2 1
Vantilinear
n antilinear
V3 1
Vmonomorphism
a monomorphism
V4 1
Vantimonomorphism
n antimonomorphism
V5 1
Vepimorphism
n epimorphism
V6 1
Vantiepimorphism
n antiepimorphism
V7 1
Visomorphism
n isomorphism
V8 1
Vantiisomorphism
n antiisomorphism
V9 1
Vendomorphism
n endomorphism
V10 1
Vantiendomorphism
n antiendomorphism
V11 1
Vautomorphism
n automorphism
#MOEBIUS1
O1 0 0
OSCNAT
mol; \mathop{\rm SCNAT}
O2 0 1
OMoebius
mol#1; \mu(#1)
O3 0 1
ONatDivisors
mol; \mathop{\rm NatDivisors} #1
O4 0 1
OSMoebius
mol; \mathop{\rm SMoebius} #1
O5 0 1
OPFactors
mol; \mathop{\rm PFactors} #1
O6 0 1
ORadical
mol#1; \mathop{\rm Rad}(#1)
V1 1
Vsquare-containing
a square-containing
V2 1
Vsquare-free
a squarefree
#MONOID_0
M1 0
MMonoid
ha monoid #0
monoids #0
M2 1
MMonoidalExtension
ha monoidal extension #0 of #1
monoidal extensions #0 of #1
M3 1
MSubStr
ha subsystem #0 of #1
subsystems #0 of #1
M4 1
MMonoidalSubStr
ha monoidal subsystem #0 of #1
monoidal subsystems #0 of #1
O1 1 1
O(*)
moi@m; #1\circ #2
O1 1 2
O(*)
moi#2#3; #1 \circledast(#2,#3)
O2 0 0
O<REAL,+>
mc; \langle{\mathbb R},{+}\rangle
O3 0 0
O<NAT,+>
mc; \langle{\mathbb N},{+}\rangle
O4 0 0
O<NAT,+,0>
mc; \langle{\mathbb N},{+},0\rangle
O5 0 0
O<REAL,*>
mc; \langle{\mathbb R},{\cdot}\rangle
O6 0 0
O<NAT,*>
mc; \langle{\mathbb N},{\cdot}\rangle
O7 0 0
O<NAT,*,1>
mc; \langle{\mathbb N},{\cdot},1\rangle
O8 1 0
O*+^
mc/1q; \langle #1^\ast,{^\smallfrown}\rangle
O9 1 0
O*+^+<0>
mc/1q; \langle #1^\ast,{^\smallfrown},\varepsilon\rangle
O10 1 0
O-concatenation
hol; concatenation of #1
O11 0 1
OGPFuncs
hol; semigroup of partial functions onto #1
O12 0 1
OMPFuncs
hol; monoid of partial functions onto #1
O13 1 0
O-composition
hol; composition of #1
O14 0 1
OGFuncs
hol; semigroup of functions onto #1
O15 0 1
OMFuncs
hol; monoid of functions onto #1
O16 0 1
OGPerms
hol; group of permutations onto #1
V1 1
Vconstituted-Functions
a constituted functions
V2 1
Vconstituted-FinSeqs
a constituted finite sequences
V3 1
Vleft-invertible
a left invertible
V4 1
Vright-invertible
a right invertible
V5 1
Vleft-cancelable
a left cancelable
V6 1
Vright-cancelable
a right cancelable
V7 1
Vuniquely-decomposable
x uniquely decomposable unity
#MONOID_1
M1 1
MMultiset
ha multiset #0 over #1
multisets #0 over #1
O1 0 1
OMultiSet_over
mor{qrw}@s; #1^\otimes_\omega
O2 0 1
Ofinite-MultiSet_over
moq; #1^\otimes
O3 1 0
O.:^2
mok; {{}^\circ}#1
#MSAFREE
M1 1
MGeneratorSet
ha generator set #0 of #1
generator sets #0 of #1
O1 0 1
Ocoprod
mol#1; \mathop{\rm coprod}(#1)
O1 0 2
Ocoprod
mol#1#2; \mathop{\rm coprod}(#1,#2)
O2 0 1
OREL
mol#1; \mathop{\rm REL}(#1)
O2 0 2
OREL
mol#1#2; \mathop{\rm REL}(#1,#2)
O3 0 1
ODTConMSA
mol#1; \mathop{\rm DTConMSA}(#1)
O4 0 2
OSym
mol#1#2; \mathop{\rm Sym}(#1,#2)
O4 0 3
OSym
mol#1#2#3; \mathop{\rm Sym}(#1,#2,#3)
O5 0 1
OFreeSort
mol#1; \mathop{\rm FreeSorts}(#1)
O5 0 2
OFreeSort
mol#1#2; \mathop{\rm FreeSort}(#1,#2)
O6 0 2
ODenOp
mol#1#2; \mathop{\rm DenOp}(#1,#2)
O7 0 1
OFreeOper
mol#1; \mathop{\rm FreeOperations}(#1)
O8 0 1
OFreeMSA
mol#1; \mathop{\rm Free}(#1)
O9 0 1
OFreeGen
mol#1; \mathop{\rm FreeGenerator}(#1)
O9 0 2
OFreeGen
mol#1#2; \mathop{\rm FreeGenerator}(#1,#2)
O10 0 1
OReverse
mol#1; \mathop{\rm Reverse}(#1)
O10 0 2
OReverse
mol#1#2; \mathop{\rm Reverse}(#1,#2)
#MSAFREE1
O1 0 1
OFlatten
mol#1; \mathop{\rm Flatten}(#1)
O2 0 1
OSingleAlg
mol#1; \mathop{\rm SingleAlg}(#1)
#MSAFREE2
M1 1
MInputValues
hn input assignment #0 of #1
input assignments #0 of #1
O1 0 1
OSortsWithConstants
mol#1; \mathop{\rm SortsWithConstants}(#1)
O2 0 1
OInputVertices
mol#1; \mathop{\rm InputVertices}(#1)
O3 0 1
OInnerVertices
mol#1; \mathop{\rm InnerVertices}(#1)
O4 0 1
Oaction_at
hol#1; action at #1
O5 0 1
OFreeEnv
mol#1; \mathop{\rm FreeEnvelope}(#1)
O6 0 1
OEval
mol#1; \mathop{\rm Eval}(#1)
O7 0 1
Odepth
mol#1; \mathop{\rm depth}(#1)
O7 0 2
Odepth
mol#1#2; \mathop{\rm depth}(#1,#2)
V1 1
Vwith_input_V
x input vertices
V2 1
VCircuit-like
a circuit-like
V3 1
Vfinitely-generated
a finitely-generated
V4 1
Vmonotonic
a monotonic
#MSALIMIT
M1 2
MOrderedAlgFam
ha family #0 of algebras over #2 ordered by #1
families #0 of algebras over #2 ordered by #1
M2 1
MBinding
ha binding #0 of #1
bindings #0 of #1
O1 0 3
Obind
mol#1#2#3; \mathop{\rm bind}(#1,#2,#3)
O2 0 1
ONormalized
mol#1; \mathop{\rm Normalized}(#1)
O3 0 1
OInvLim
mol#1; \mathop{\underleftarrow{\rm lim}}{#1}
O4 0 0
OTrivialMSSign
mol; \mathop{\rm TrivialMSSign}
O5 0 1
OMSS_set
mol#1; \mathop{\rm MSS\hbox{-}set}(#1)
O6 0 2
OMSS_morph
mol#1#2; \mathop{\rm MSS\hbox{-}morph}(#1,#2)
V1 1
Vnormalized
a normalized
V2 1
VMSS-membered
a MSS-membered
#MSATERM
M1 2
MTerm
ha term #0 of #1 over #2
terms #0 of #1 over #2
M2 1
MArgumentSeq
hn argument sequence #0 of #1
argument sequences #0 of #1
M2 3
MArgumentSeq
hn argument sequence #0 of #1, #2, and #3
argument sequences #0 of #1, #2, and #3
M3 2
Mc-Term
ha term #0 of #1 over #2
terms #0 of #1 over #2
M4 2
MCompoundTerm
ha compound term #0 of #1 over #2
compound terms #0 of #1 over #2
M5 2
MSetWithCompoundTerm
ha set #0 with a compound term of #1 over #2
sets #0 with compound terms of #1 over #2
M6 1
MVariables
ha variables family #0 of #1
variables families #0 of #1
O1 1 1
O-Terms
moi#2; #1\mathop{\rm\hbox{-}Terms}(#2)
O1 1 2
O-Terms
moi#2#3; #1 \mathop{\rm\hbox{-}Terms}^{#3}(#2)
O2 1 1
O-term
mow#2; #1_{#2}
O2 1 2
O-term
mow#2#3; #1_{#2,#3}
R1 1 2
Ris_an_evaluation_of
i an evaluation of #2 w.r.t. #3
not an evaluation of #2 w.r.t. #3
#MSINST_1
O1 0 1
OMSSCat
mol#1; \mathop{\rm MSSCat}(#1)
O2 0 2
OMSAlg_set
mol#1#2; \mathop{\rm MSAlg\_set}(#1,#2)
O3 0 4
OMSAlg_morph
mol#1#2#3#4; \mathop{\rm MSAlg\_morph}(#1,#2,#3,#4)
O4 0 2
OMSAlgCat
mol#1#2; \mathop{\rm MSAlgCat}(#1,#2)
#MSSCYC_1
V1 1
Vdirected_cycle-less
a directed cycle-less
V2 1
Vwith_directed_cycle
x directed cycle
V3 1
Vwell-founded
a well-founded
V4 1
Vfinitely_operated
a finitely operated
#MSSCYC_2
O1 0 1
OInducedEdges
mol#1; \mathop{\rm InducedEdges}(#1)
O2 0 1
OInducedSource
mol#1; \mathop{\rm InducedSource}(#1)
O3 0 1
OInducedTarget
mol#1; \mathop{\rm InducedTarget}(#1)
O4 0 1
OInducedGraph
mol#1; \mathop{\rm InducedGraph}(#1)
#MSSUBFAM
M1 1
MMSSubsetFamily
ha subset family #0 of #1
subset families #0 of #1
V1 1
Vadditive
n additive
V2 1
Vabsolutely-additive
n absolutely-additive
V3 1
Vmultiplicative
a multiplicative
V4 1
Vabsolutely-multiplicative
n absolutely-multiplicative
V5 1
Vproperly-upper-bound
a properly upper bound
V6 1
Vproperly-lower-bound
a properly lower bound
#MSUALG_1
G1 4
GManySortedSign
mc#1#2#3#4; \langle #1,#2,#3,#4 \rangle
G2 1
Gmany-sorted
mc#1; \langle #1 \rangle
G3 2
GMSAlgebra
mc#1#2; \langle #1,#2 \rangle
J1 1
GManySortedSign
hol#1; many sorted signature of #1
J2 1
Gmany-sorted
hol#1; many-sorted structure of #1
J3 1
GMSAlgebra
hol#1; algebra of #1
L1 0
GManySortedSign
ha many sorted signature #0
many sorted signatures #0
L2 1
Gmany-sorted
ha many-sorted structure #0 over #1
many-sorted structures #0 over #1
L3 1
GMSAlgebra
hn algebra #0 over #1
algebras #0 over #1
M1 1
MSortSymbol
ha sort symbol #0 of #1
sort symbols #0 of #1
M2 1
MOperSymbol
hn operation symbol #0 of #1
operation symbols #0 of #1
O1 0 1
Othe_result_sort_of
hol#1; result sort of #1
O2 0 2
OArgs
mol#1#2; \mathop{\rm Args}(#1, #2)
O3 0 1
OResult
mol@s#1; {\rm Result}(#1)
O3 0 2
OResult
mol#1#2; \mathop{\rm Result}(#1,#2)
O4 0 2
ODen
mol#1#2; \mathop{\rm Den}(#1,\allowbreak #2)
O5 0 1
OMSSign
mol#1; \mathop{\rm MSSign}(#1)
O5 0 2
OMSSign
mol#1#2; \mathop{\rm MSSign}(#1, #2)
O6 0 1
OMSSorts
mol#1; \mathop{\rm MSSorts}(#1)
O7 0 1
OMSCharact
mol#1; \mathop{\rm MSCharact}(#1)
O8 0 1
OMSAlg
mol#1; \mathop{\rm MSAlg}(#1)
O8 0 2
OMSAlg
mol#1#2; \mathop{\rm MSAlg}(#1,#2)
O9 0 1
Othe_sort_of
hol#1; sort of #1
O9 0 2
Othe_sort_of
hosl#1#2; sort of #1 w.r.t. #2
O10 0 1
Othe_charact_of
mol#1; \mathop{\rm charact}(#1)
O11 0 1
O1-Alg
mol#1; \mathop{\rm Alg}_{\bf 1}(#1)
U1 1
UArity
honl#1; arity of #1
arity
U2 1
UResultSort
hosl#1; result sort of #1
result sort
U3 1
USorts
hopl#1; sorts of #1
sorts
U4 1
UCharact
hosl#1; characteristics of #1
characteristics
V1 1
Vsegmental
a segmental
#MSUALG_2
M1 1
MMSSubset
ha subset #0 of #1
subsets #0 of #1
M2 1
MMSSubAlgebra
ha subalgebra #0 of #1
subalgebras #0 of #1
O1 0 1
OSubSort
mol#1; \mathop{\rm SubSorts}(#1)
O1 0 2
OSubSort
mol#1#2; \mathop{\rm SubSort}(#1,#2)
O2 0 1
OMSSubSort
mol#1; \mathop{\rm MSSubSort}(#1)
O3 0 1
OGenMSAlg
mol#1; \mathop{\rm Gen}(#1)
O4 0 1
OMSSub
mol#1; \mathop{\rm Subalgebras}(#1)
O5 0 1
OMSAlg_join
mol#1; \mathop{\rm MSAlgJoin}(#1)
O6 0 1
OMSAlg_meet
mol#1; \mathop{\rm MSAlgMeet}(#1)
O7 0 1
OMSSubAlLattice
hol#1; lattice of subalgebras of #1
V1 1
Vall-with_const_op
w constant operations
#MSUALG_3
R1 1 2
Ris_homomorphism
i a homomorphism of #2 into #3
not a homomorphism of #2 into #3
R2 1 2
Ris_epimorphism
i an epimorphism of #2 onto #3
not an epimorphism of #2 onto #3
R3 1 2
Ris_monomorphism
i a monomorphism of #2 into #3
not a monomorphism of #2 into #3
R4 1 2
Ris_isomorphism
i an isomorphism of #2 and #3
not an isomorphism of #2 and #3
V1 1
V"1-1"
a ``1-1"
V2 1
V"onto"
n onto
#MSUALG_4
M1 1
MManySortedRelation
ha many sorted relation #0 indexed by #1
many sorted relations #0 indexed by #1
M1 2
MManySortedRelation
ha many sorted relation #0 between #1 and #2
many sorted relations #0 between #1 and #2
M2 1
MMSCongruence
ha congruence #0 of #1
congruences #0 of #1
O1 0 1
OQuotRes
mol#1; \mathop{\rm QuotRes}(#1)
O1 0 2
OQuotRes
mol#1#2; \mathop{\rm QuotRes}(#1,#2)
O2 0 1
OQuotArgs
mol#1; \mathop{\rm QuotArgs}(#1)
O2 0 2
OQuotArgs
mol#1#2; \mathop{\rm QuotArgs}(#1,#2)
O3 0 1
OQuotCharact
mol#1; \mathop{\rm QuotCharact}(#1)
O3 0 2
OQuotCharact
mol#1#2; \mathop{\rm QuotCharact}(#1,#2)
O4 0 2
OQuotMSAlg
moi@m; #1/#2
O5 0 2
OMSNat_Hom
mol#1#2; \mathop{\rm MSNatHom}(#1,#2)
O5 0 3
OMSNat_Hom
mol#1#2#3; \mathop{\rm MSNatHom}(#1,#2,#3)
O6 0 1
OMSCng
mol#1; \mathop{\rm Congruence}(#1)
O6 0 2
OMSCng
mol#1#2; \mathop{\rm Congruence}(#1,#2)
O7 0 1
OMSHomQuot
mol#1; \mathop{\rm MSHomQuot}(#1)
O7 0 2
OMSHomQuot
mol#1#2; \mathop{\rm MSHomQuot}(#1,#2)
V1 1
VRelation-yielding
a binary relation yielding
V2 1
VMSEquivalence_Relation-like
n equivalence
V3 1
VMSEquivalence-like
n equivalence
V4 1
VMSCongruence-like
a MSCongruence-like
#MSUALG_5
O1 0 1
OEqCl
mol#1; \mathop{\rm EqCl}(#1)
O1 0 2
OEqCl
mol#1#2; \mathop{\rm EqCl}(#1,#2)
O2 0 1
OEqRelLatt
mol#1; \mathop{\rm EqRelLatt}(#1)
O3 0 1
OCongrLatt
mol#1; \mathop{\rm CongrLatt}(#1)
#MSUALG_6
M1 3
MTranslation
ha translation #0 in #1 from #2 into #3
translations #0 in #1 from #2 into #3
M2 1
MEquationalTheory
hn equational theory #0 of #1
equational theories #0 of #1
O1 0 1
OTranslationRel
mosl#1; \mathop{\rm TranslRel}(#1)
O2 0 1
OInvCl
mosl#1; \mathop{\rm InvCl}(#1)
O3 0 1
OStabCl
mosl#1; \mathop{\rm StabCl}(#1)
O4 0 1
OTRS
mosl#1; \mathop{\rm TRS}(#1)
O5 0 1
OEqTh
mosl#1; \mathop{\rm EqTh}(#1)
R1 1 3
Ris_e.translation_of
i an elementary translation in #2 from #3 into #4
not an elementary translation in #2 from #3 into #4
V1 1
Vfeasible
a feasible
V2 1
Vcompatible
a compatible
V3 1
Vinvariant
n invariant
#MSUALG_7
O1 0 2
ORealSubLatt
mol#1#2; \mathop{\rm RealSubLatt}(#1,#2)
V1 1
V/\-inheriting
a $\bigsqcap$-inheriting
V2 1
V\/-inheriting
a $\bigsqcup$-inheriting
#MSUALG_8
O1 0 1
OCongrCl
mol#1; \mathop{\rm CongrCl}(#1)
O2 0 2
OEqRelSet
mol#1#2; \mathop{\rm EqRelSet}(#1,#2)
#MSUALG_9
O1 0 1
OMpr1
mol#1; \mathop{\rm Mpr1}(#1)
O2 0 1
OMpr2
mol#1; \mathop{\rm Mpr2}(#1)
#MSUHOM_1
O1 1 1
OOver
mci; (#1\mathop{\rm over} #2)
#MULTOP_1
M1 1
MTriOp
ha ternary operation #0 on #1
ternary operations #0 on #1
M2 1
MQuaOp
ha quadrary operation #0 on #1
quadrary operations #0 on #1
#NAGATA_1
M1 1
MFamilySequence
ha family sequence #0 of #1
family sequences #0 of #1
R1 1 1
Ris_a_pseudometric_of
i a pseudometric of
not a pseudometric of
V1 1
Vsigma_discrete
a sigma-discrete
V2 1
Vsigma_locally_finite
a sigma-locally-finite
V3 1
Vuncountable
n uncountable
V4 1
VBasis_sigma_discrete
a Basis-sigma-discrete
V5 1
VBasis_sigma_locally_finite
a Basis-sigma-locally finite
#NAGATA_2
O1 0 0
OPairFunc
mcl; \mathop{\rm PairFunc}
#NATTRA_1
M1 2
Mtransformation
ha transformation #0 from #1 to #2
transformations #0 from #1 to #2
M2 2
Mnatural_transformation
ha natural transformation #0 from #1 to #2
natural transformations #0 from #1 to #2
M3 2
Mnatural_equivalence
ha natural equivalence #0 of #1 and #2
natural equivalences #0 of #1 and #2
M4 2
MNatTrans-DOMAIN
ha set #0 of natural transformations from #1 to #2
sets #0 of natural transformations from #1 to #2
O1 1 1
O`*`
moi; #1\mathbin{^{_{\circ}}}#2
O1 2 0
O`*`
mow#1#2; (#2)_{#1}
O2 0 2
ONatTrans
mol@s#1#2; \mathop{\rm NatTrans}(#1,#2)
O3 0 2
OFunctors
moq#1; #2^{#1}
O4 0 1
OIdCat
mol@s; \mathop{\rm IdCat} #1
R1 1 1
Ris_naturally_transformable_to
i naturally transformable to #2
not naturally transformable to #2
R2 2 0
Rare_naturally_equivalent
h #1 and #2 are naturally equivalent
#1 and #2 are not naturally equivalent
R3 1 1
R~=
m #1\cong #2
#1\ncong #2
V1 1
Vdiscrete
a discrete
#NAT_1
M1 0
MNat
ha natural number #0
natural numbers #0
M1 1
MNat
ha natural number #0 of #1
natural numbers #0 of #1
M2 1
Msequence
ha sequence #0 of #1
sequences #0 of #1
O1 0 1
Omin*
mol; {\rm min}^\ast #1
O2 1 1
O^\
moi@m; #1 \mathbin{\uparrow} #2
#NAT_3
O1 1 1
O|-count
moi#2; #1\mathop{\rm \hbox{-}count}(#2)
O2 0 1
Oprime_exponents
mol#1; \mathop{\rm PrimeExponents}(#1)
O3 0 1
Opfexp
mol#1; \mathop{\rm PFExp}(#1)
O4 0 1
Oprime_factorization
mol#1; \mathop{\rm PrimeFactorization}(#1)
O5 0 1
Oppf
mol#1; \mathop{\rm PPF}(#1)
#NAT_5
O1 0 1
OEXP
mol; \mathop{\rm EXP} #1
O2 0 0
OEuler_phi
mc; \mathop{\phi}
#NAT_LAT
M1 0
MNatPlus
ha positive natural number #0
positive natural numbers #0
M2 1
MSubLattice
ha sublattice #0 of #1
sublattices #0 of #1
O1 0 0
Ohcflat
mow; \mathop{\rm hcf}_{\mathbb N}
O2 0 0
Olcmlat
mow; \mathop{\rm lcm}_{\mathbb N}
O3 0 0
ONat_Lattice
mow; {\mathbb L}_{\mathbb N}
O4 0 0
O0_NN
mow; {\bf 0}_{{\mathbb L}_{\mathbb N}}
O5 0 0
O1_NN
mow; {\bf 1}_{{\mathbb L}_{\mathbb N}}
O6 0 0
ONATPLUS
moq; {\mathbb N}^{+}
O7 0 0
Ohcflatplus
mcw; \mathop{\rm hcf}_{{\mathbb N}^+}
O8 0 0
Olcmlatplus
mcw; \mathop{\rm lcm}_{{\mathbb N}^+}
O9 0 0
ONatPlus_Lattice
mow; {\mathbb L}_{{\mathbb N}^+}
#NDIFF_2
O1 0 3
OGateaux_diff
mcl@s/3k#1#2#3; \mathop{\rm GateauxDiff}_{#3}(#1,#2)
R1 1 2
Ris_Gateaux_differentiable_in
i Gateaux differentiable in #2, #3
not Gateaux differentiable in #2, #3
#NECKLACE
O1 1 0
O-SuccRelStr
mor#1; #1 \mathop{\rm \hbox{-}SuccRelStr}
O2 0 1
OSymRelStr
mol#1; \mathop{\rm SymRelStr} #1
O3 0 1
OComplRelStr
mol#1; \mathop{\rm ComplRelStr} #1
O4 0 1
ONecklace
mol#1; \mathop{\rm Necklace} #1
R1 1 1
Rembeds
h #1 embeds #2
#1 does not embed #2
R2 1 1
Ris_equimorphic_to
i equimorphic to #2
not equimorphic to #2
V1 1
Vparallel
a parallel
#NECKLA_2
O1 0 2
Ounion_of
mol#1#2; \mathop{\rm UnionOf} (#1,#2)
O2 0 2
Osum_of
mol#1#2; \mathop{\rm SumOf} (#1,#2)
O3 0 0
Ofin_RelStr
mol; \mathop{\rm FinRelStr}
O4 0 0
Ofin_RelStr_sp
mol; \mathop{\rm FinRelStrSp}
V1 1
VN-free
n N-free
#NECKLA_3
M1 1
Mpath
ha path #0 of #1
paths #0 of #1
O1 0 1
Ocomponent
mcl@s#1; \mathop{\rm component}(#1)
V1 1
Vpath-connected
a path-connected
#NET_1
M1 0
MPnet
ha Petri net #0
Petri nets #0
O1 0 1
OFlow
mol; \mathop{\rm Flow} #1
O2 0 1
OElements
mcl@s#1; {\rm Elements}(#1)
O3 0 1
OPre
mol#1; \mathop{\rm Pre}\: #1
O3 0 2
OPre
mcl@s#1#2; {\rm Pre}(#1,#2)
O4 0 1
OPost
mol#1; \mathop{\rm Post}\: #1
O4 0 2
OPost
mcl@s#1#2; {\rm Post}(#1,#2)
O5 0 2
Oenter
mcl@s#1#2; {\rm enter}(#1,#2)
O6 0 2
Oexit
mc#1#2; {\rm exit}(#1,#2)
O7 0 2
OPrec
mcl@s#1#2; {\rm Prec}(#1,#2)
O8 0 2
OPostc
mcl@s#1#2; {\rm Postc}(#1,#2)
O9 0 2
OEntr
mcl@s#1#2; {\rm Entr}(#1,#2)
O10 0 2
OExt
mcl@s#1#2; {\rm Ext}(#1,#2)
O11 0 1
OInput
mol; \mathop{\rm Input} #1
O11 0 2
OInput
mcl@s#1#2; {\rm Input}(#1,#2)
O12 0 1
OOutput
mol; \mathop{\rm Output} #1
O12 0 2
OOutput
mcl@s#1#2; {\rm Output}(#1,#2)
R1 0 3
Rpre
h #2 is a pre-element of #3 in #1
#2 is not a pre-element of #3 in #1
R2 0 3
Rpost
h #2 is a post-element of #3 in #1
#2 is not a post-element of #3 in #1
V1 1
VPetri
a Petri
#NEWTON
M1 0
MPrime
ha prime number #0
prime numbers #0
O1 1 1
O|^
moq(1)/2m#2; {#1}^{#2}
O1 1 2
O|^
moq(1)#2#3; {#1}^{#2,#3}
O2 2 1
OIn_Power
mc/1q/2q#3; \langle {{#3} \choose 0}#1^{0}#2^{#3}, \dots, {{#3} \choose {#3}}#1^{#3}#2^{0}\rangle
O3 0 1
ONewton_Coeff
mc#1; \langle {{#1} \choose 0}, \dots, {{#1} \choose {#1}}\rangle
O4 0 0
OSetPrimes
mc; \mathop{\rm Prime}
O5 0 1
OSetPrimenumber
mol@s#1; \mathop{\rm Prime}(#1)
O6 0 1
Oprimenumber
mol@s#1; \mathop{\rm pr}(#1)
#NFCONT_1
R1 1 1
Ris_Lipschitzian_on
i Lipschitzian on #2
not Lipschitzian on #2
#NFCONT_2
R1 1 1
Ris_uniformly_continuous_on
i uniformly continuous on #2
not uniformly continuous on #2
#NORMFORM
O1 0 1
OFinPairUnion
mow/1k#1; \mathop{\rm FinUnion}_{#1}
O1 0 2
OFinPairUnion
mcl@s#1#2; \mathop{\rm FinUnion}(#1,#2)
O2 0 1
ODISJOINT_PAIRS
mcl@s#1; \mathop{\rm DP}(#1)
O3 0 1
ONormal_forms_on
hol; normal forms over #1
O4 0 1
Omi
mcl@9; \mu #1
O5 0 1
ONormForm
hol; lattice of normal forms over #1
#NORMSP_0
G1 2
GN-Str
mc#1#2; \langle #1,#2 \rangle
G2 3
GN-ZeroStr
mc#1#2#3; \langle #1,#2,#3 \rangle
J1 1
GN-Str
hol#1; $N$-structure of #1
J2 1
GN-ZeroStr
hol#1; $N$-zero structure of #1
L1 0
GN-Str
ha $N$-structure #0
$N$-structures #0
L2 0
GN-ZeroStr
ha $N$-zero structure #0
$N$-zero structures #0
U1 1
UnormF
hosl#1; normed of #1
normed 
#NORMSP_1
G1 5
GNORMSTR
mc#1#2#3#4#5; \langle #1, #2, #3, #4, #5\rangle
J1 1
GNORMSTR
hol#1; normed structure of #1
K1 1 L1 vNORMSP_1
K||.
L.||
mc#1; \mathopen{\Vert} #1 \mathclose{\Vert}
L1 0
GNORMSTR
ha normed structure #0
normed structures #0
M1 0
MRealNormSpace
ha real normed space #0
real normed spaces #0
V1 1
VRealNormSpace-like
a real normed space-like
#NORMSP_2
O1 0 1
Odistance_by_norm_of
hol; distance by norm of #1
O2 0 1
OMetricSpaceNorm
mol; \mathop{\rm MetricSpaceNorm} #1
O3 0 1
OTopSpaceNorm
mol; \mathop{\rm TopSpaceNorm} #1
O4 0 1
OLinearTopSpaceNorm
mol; \mathop{\rm LinearTopSpaceNorm} #1
#NUMBERS
O1 0 0
ONAT
mc; {\mathbb N}
O2 0 0
OREAL
mc; {\mathbb R}
O2 0 1
OREAL
moq#1; {\cal R}^{#1}
O3 0 0
OCOMPLEX
mc; {\mathbb C}
O3 0 1
OCOMPLEX
moq/1m#1; {\mathbb C}^{#1}
O4 0 0
ORAT
mc; {\mathbb Q}
O4 0 2
ORAT
mol#1#2; \rbrack #1,#2 \lbrack{}_{\mathbb Q}
O5 0 0
OINT
mc; {\mathbb Z}
O6 0 0
OExtREAL
mc; \overline{\mathbb R}
#NUMERAL1
O1 0 2
Ovalue
mol#1#2; \mathop{\rm value}(#1,#2)
O2 0 2
Odigits
mol#1#2; \mathop{\rm digits}(#1,#2)
#OPENLATT
O1 0 1
OTopology_of
mol#1; \mathop{\rm Topology}(#1)
O2 0 1
OTop_Union
mol#1; \mathop{\rm TopUnion}(#1)
O3 0 1
OTop_Meet
mol#1; \mathop{\rm TopMeet}(#1)
O4 0 1
OOpen_setLatt
mol#1; \mathop{\rm OpenSetLatt}(#1)
O5 0 1
OF_primeSet
mol#1; \mathop{\rm PrimeFilters}(#1)
O6 0 1
OStoneH
mol#1; \mathop{\rm StoneH}(#1)
O7 0 1
OStoneS
mol#1; \mathop{\rm StoneS}(#1)
O8 0 1
OSF_have
mol#1; \mathop{\rm Filters}(#1)
O9 0 1
OSet_Union
mol#1; \mathop{\rm SetUnion}(#1)
O10 0 1
OSet_Meet
mol#1; \mathop{\rm SetMeet}(#1)
O11 0 1
OStoneLatt
mol#1; \mathop{\rm StoneLatt}(#1)
O12 0 1
OHTopSpace
mol#1; \mathop{\rm HTopSpace}(#1)
#OPOSET_1
M1 0
MQuasiPureOrthoRelStr
ha QuasiPureOrthoRelStr #0
QuasiPureOrthoRelStrs #0
M2 0
MPureOrthoRelStr
ha PureOrthoRelStr #0
PureOrthoRelStrs #0
M3 0
MPreOrthoPoset
ha PreOrthoPoset #0
PreOrthoPosets #0
M4 0
MQuasiOrthoPoset
ha QuasiOrthoPoset #0
QuasiOrthoPosets #0
M5 0
MOrthoPoset
hn orthoposet #0
orthoposets #0
O1 0 0
OTrivOrthoRelStr
mol; \mathop{\rm TrivOrthoRelStr}
O2 0 0
OTrivPoset
mol; \mathop{\rm TrivPoset}
O3 0 0
OTrivAsymOrthoRelStr
mol; \mathop{\rm TrivAsymOrthoRelStr}
R1 1 1
RQuasiOrthoComplement_on
i QuasiOrthoComplement on #2
not QuasiOrthoComplement on #2
R2 1 1
ROrthoComplement_on
i OrthoComplement on #2
not OrthoComplement on #2
V2 1
Vinvolutive
n involutive
V3 1
VDneg
a Dneg
V4 1
VSubReFlexive
a SubReFlexive
V10 1
VSubQuasiOrdered
a SubQuasiOrdered
V11 1
VSubPreOrdered
a SubPreOrdered
V12 1
VQuasiOrdered
a QuasiOrdered
V13 1
VPreOrdered
a PreOrdered
V14 1
VQuasiPure
a QuasiPure
V16 1
VPartialOrdered
a PartialOrdered
V17 1
VPure
a Pure
V19 1
VStrictPartialOrdered
a StrictPartialOrdered
V20 1
VStrictOrdered
a StrictOrdered
V21 1
VOrderinvolutive
n Orderinvolutive
V22 1
VOrderInvolutive
n OrderInvolutive
V23 1
VQuasiOrthocomplemented
a QuasiOrthocomplemented
V24 1
VOrthocomplemented
n Orthocomplemented
#OPPCAT_1
M1 2
MContravariant_Functor
ha contravariant functor #0 from #1 into #2
contravariant functors #0 from #1 into #2
O1 0 1
Oid*
mcl@s#1; \mathop{\rm id}^{\rm op}(#1)
O2 0 1
O*id
mok#1; \mathop{^{\rm op}\rm id}(#1)
#ORDERS_1
M1 1
MChoice_Function
ha choice function #0 of #1
choice functions #0 of #1
M2 1
MOrder
hn order #0 in #1
orders #0 in #1
O1 0 1
OBOOL
mor/1m#1; 2_+^{#1}
R1 1 1
Rquasi_orders
h #1 quasi orders #2
#1 does not quasi order #2
R2 1 1
Rpartially_orders
h #1 partially orders #2
#1 does not partially order #2
R3 1 1
Rlinearly_orders
h #1 linearly orders #2
#1 does not linearly order #2
R4 1 1
Rhas_upper_Zorn_property_wrt
j the upper Zorn property w.r.t. #2
not the upper Zorn property w.r.t. #2
R5 1 1
Rhas_lower_Zorn_property_wrt
j the lower Zorn property w.r.t. #2
not the lower Zorn property w.r.t. #2
R6 1 1
Ris_maximal_in
i maximal in #2
not maximal in #2
R7 1 1
Ris_minimal_in
i minimal in #2
not minimal in #2
R8 1 1
Ris_superior_of
i superior of #2
not superior of #2
R9 1 1
Ris_inferior_of
i inferior of #2
not inferior of #2
V1 1
Vbeing_quasi-order
b quasi-order
V2 1
Vbeing_partial-order
b partial-order
V3 1
Vbeing_linear-order
b linear-order
#ORDERS_2
G1 2
GRelStr
mc#1#2; \langle #1,#2 \rangle
J1 1
GRelStr
hol#1; relational structure of #1
L1 0
GRelStr
ha relational structure #0
relational structures #0
M1 0
MPoset
ha poset #0
posets #0
M2 1
MInitial_Segm
hn initial segment #0 of #1
initial segments #0 of #1
O1 0 1
OUpperCone
mol@s; \mathop{\rm UpperCone} #1
O2 0 1
OLowerCone
mol@s; \mathop{\rm LowerCone} #1
O3 0 2
OInitSegm
mcl@s#1#2; \mathop{\rm InitSegm}(#1,#2)
O4 0 1
OChains
mol@s; \mathop{\rm Chains} #1
O4 0 2
OChains
mol#2; #1\hbox{-}\mathop{\rm Chains}(#2)
U1 1
UInternalRel
honl#1; internal relation of #1
internal relation
#ORDERS_3
M1 0
MPOSet_set
ha set #0 of posets
sets #0 of posets
O1 0 2
OMonFuncs
mor(2){qrw}#1; {#2}^{#1}_\leq
O2 0 1
OCarr
mol#1; \mathop{\rm Carr}(#1)
O3 0 1
OPOSCat
mol#1; \mathop{\rm POSCat}(#1)
O4 0 1
OPOSAltCat
mol#1; \mathop{\rm POSAltCat}(#1)
V1 1
Vdisconnected
a disconnected
V2 1
VPOSet_set-like
a poset-membered
#ORDERS_4
R1 2 1
Rform_upper_lower_partition_of
h #1,#2 form upper lower partition of #3
#1,#2 does not form upper lower partition of #3
#ORDINAL1
M1 0
Mnumber
ha number #0
numbers #0
M2 0
MOrdinal
hn ordinal number #0
ordinal numbers #0
M2 1
MOrdinal
hn ordinal #0 of #1
ordinals #0 of #1
M3 0
MT-Sequence
ha transfinite sequence #0
transfinite sequences #0
M3 1
MT-Sequence
ha transfinite sequence #0 of elements of #1
transfinite sequences #0 of elements of #1
O1 0 1
Osucc
mol@s; \mathop{\rm succ} #1
O1 0 2
Osucc
mol#1#2; \mathop{\rm succ}(#1,#2)
O1 1 0
Osucc
mol@s; \mathop{\rm Succ} #1
O1 1 1
Osucc
mol(2)/1k#1#2; \mathop{\rm succ}_{#1}(#2)
O2 0 1
OOn
mol@s; \mathop{\rm On} #1
O2 0 2
OOn
mol#1#2; \mathop{\rm On}(#1,#2)
O3 0 1
OLim
mol@s; \mathop{\rm Lim} #1
O4 0 0
Oomega
mc; \omega
O4 0 1
Oomega
mol#1; \omega(#1)
V1 1
Vepsilon-transitive
a transitive
V2 1
Vepsilon-connected
a connected
V3 1
Vordinal
n ordinal
V4 1
Vlimit_ordinal
a limit ordinal
V5 1
VT-Sequence-like
a transfinite sequence-like
V6 1
Vc=-linear
a $\subseteq$-linear
V7 1
Vnatural
a natural
#ORDINAL2
M1 0
MOrdinal-Sequence
ha sequence #0 of ordinal numbers
sequences #0 of ordinal numbers
M1 1
MOrdinal-Sequence
ha transfinite sequence #0 of ordinals of #1
transfinite sequences #0 of ordinals of #1
O1 0 1
Olast
mol@s; \mathop{\rm last} #1
O2 0 1
Oinf
mol@s; \mathop{\rm inf} #1
O3 0 1
Osup
mol@s; \mathop{\rm sup} #1
O4 0 1
Olim_sup
mol@s; \mathop{\rm lim\, sup} #1
O5 0 1
Olim_inf
mol@s; \mathop{\rm lim\, inf} #1
O6 0 1
Olim
mol@s; \mathop{\rm lim} #1
O6 0 2
Olim
mol@s/2k#2; {\mathop{\rm lim}_{#2}} #1
O7 1 1
O+^
moi@a; #1+#2
O8 1 1
O*^
moi@m; #1 \cdot #2
O9 0 0
Oexp
mc; \mathop{\rm exp}
O9 0 1
Oexp
mol; \mathop{\rm exp} #1
O9 0 2
Oexp
moq#2; #1^{#2}
R1 1 1
Ris_limes_of
i the limit of #2
not the limit of #2
R2 1 1
Ris_cofinal_with
i cofinal with #2
not cofinal with #2
V1 1
VOrdinal-yielding
n ordinal yielding
V2 1
Vincreasing
n increasing
V3 1
Vcontinuous
a continuous
#ORDINAL3
O1 1 1
O-^
moi@a; #1-#2
O2 1 1
Odiv^
moi@a; #1 \div #2
O3 1 1
Omod^
moi@a; #1 \mathbin{\rm\,mod\,} #2
#ORDINAL4
O1 0 1
O^
mct#1; \hat{#1}
O1 1 0
O^
mo{kqmw}@s/1t#1; {1 \over {#1}}
O1 1 1
O^
moi@m/1q/2k; #1\mathbin{^\smallfrown}#2
O1 1 2
O^
mow#2#3; \hat{#1}_{#2,#3}
O2 0 1
O0-element_of
mow/1k#1; {\bf 0}_{#1}
O3 0 1
O1-element_of
mow/1k#1; {\bf 1}_{#1}
#ORDINAL5
O1 1 1
O|^|^
moi@s; #1 \mathop{\uparrow\uparrow} #2
O2 0 1
Ofirst_epsilon_greater_than
hol#1; first $\varepsilon$ greater than #1
O3 0 1
Oepsilon_
mow#1; \varepsilon_{#1}
O4 0 1
OSum^
mol#1; \sum #1
O5 1 1
O-exponent
moi#2; #1{\rm\hbox{-}exponent}(#2)
V1 1
Vepsilon
n epsilon
V2 1
VCantor-component
a Cantor component
V3 1
VCantor-normal-form
a Cantor normal form
#ORTSP_1
M1 1
MOrtSp
hn orthogonality space #0 over #1
orthogonality spaces #0 over #1
V1 1
VOrtSp-like
n orthogonality space-like
#OSAFREE
M1 1
MOSGeneratorSet
hn order sorted generator set #0 of #1
order sorted generator sets #0 of #1
M2 2
MMinTerm
ha minimal term #0 of #1,#2
minimal terms #0 of #1,#2
O1 0 1
OOSREL
mol#1; \mathop{\rm OSREL} #1
O2 0 1
ODTConOSA
mol#1; \mathop{\rm DTConOSA} #1
O3 0 2
OOSSym
mol#1#2; \mathop{\rm OSSym}(#1,#2)
O4 0 1
OParsedTerms
mol#1; \mathop{\rm ParsedTerms} #1
O4 0 2
OParsedTerms
mol#1#2; \mathop{\rm ParsedTerms}(#1,#2)
O5 0 2
OPTDenOp
mol#1#2; \mathop{\rm PTDenOp}(#1,#2)
O6 0 1
OPTOper
mol#1; \mathop{\rm PTOper} #1
O7 0 1
OParsedTermsOSA
mol#1; \mathop{\rm ParsedTermsOSA} #1
O8 0 1
OLeastSort
mol#1; \mathop{\rm LeastSort} #1
O9 0 1
OLeastSorts
mol#1; \mathop{\rm LeastSorts} #1
O10 0 1
OLCongruence
mol#1; \mathop{\rm LCongruence} #1
O11 0 1
OFreeOSA
mol#1; \mathop{\rm FreeOSA} #1
O12 0 1
OPTClasses
mol#1; \mathop{\rm PTClasses} #1
O13 0 1
OPTCongruence
mol#1; \mathop{\rm PTCongruence} #1
O14 0 1
OPTVars
mol#1; \mathop{\rm PTVars} #1
O14 0 2
OPTVars
mol#1#2; \mathop{\rm PTVars}(#1,#2)
O15 0 1
OOSFreeGen
mol#1; \mathop{\rm OSFreeGen} #1
O15 0 2
OOSFreeGen
mol#1#2; \mathop{\rm OSFreeGen}(#1,#2)
O16 0 1
ONHReverse
mol#1; \mathop{\rm NHReverse} #1
O16 0 2
ONHReverse
mol#1#2; \mathop{\rm NHReverse}(#1,#2)
O17 0 1
OPTMin
mol#1; \mathop{\rm PTMin} #1
O18 0 1
OMinTerms
mol#1; \mathop{\rm MinTerms} #1
V1 1
Vosfree
n osfree
#OSALG_1
G1 5
GOverloadedMSSign
mc#1#2#3#4#5; \langle #1,#2,#3,#4,#5 \rangle
G2 5
GRelSortedSign
mc#1#2#3#4#5; \langle #1,#2,#3,#4,#5 \rangle
G3 6
GOverloadedRSSign
mc#1#2#3#4#5#6; \langle #1,#2,#3,#4,#5,#6 \rangle
J1 1
GOverloadedMSSign
hol#1; overloaded many sorted signature of #1
J2 1
GRelSortedSign
hol#1; RelSortedSign of #1
J3 1
GOverloadedRSSign
hol#1; overloaded relation sorted signature of #1
L1 0
GOverloadedMSSign
hn overloaded many sorted signature #0
overloaded many sorted signatures #0
L2 0
GRelSortedSign
ha relation sorted signature #0
relation sorted signatures #0
L3 0
GOverloadedRSSign
hn overloaded relation sorted signature #0
overloaded relation sorted signatures #0
M1 0
MOrderSortedSign
hn order sorted signature #0
order sorted signatures #0
M2 1
MOrderSortedSet
hn order sorted set #0 of #1
order sorted sets #0 of #1
M3 1
MOSAlgebra
hn order sorted algebra #0 of #1
order sorted algebras #0 of #1
M4 1
MOperName
hn OperName #0 of #1
OperNames #0 of #1
O1 0 1
OOSSign
mol#1; \mathop{\rm OSSign} #1
O2 0 2
OConstOSSet
mol#1#2; \mathop{\rm ConstOSSet}(#1,#2)
O3 0 3
OConstOSA
mol#1#2#3; \mathop{\rm ConstOSA}(#1,#2,#3)
O4 0 1
OOSAlg
mol#1; \mathop{\rm OSAlg} #1
O5 0 3
OTrivialOSA
mol#1#2#3; \mathop{\rm TrivialOSA}(#1,#2,#3)
O6 0 1
OOperNames
mol#1; \mathop{\rm OperNames} #1
O7 0 1
OName
mol#1; \mathop{\rm Name} #1
R1 1 2
Rhas_least_args_for
j least args for #2,#3
not least args for #2,#3
R2 1 2
Rhas_least_sort_for
j least sort for #2,#3
not least sort for #2,#3
R3 1 2
Rhas_least_rank_for
j least rank for #2,#3
not least rank for #2,#3
U1 1
UOverloading
honl#1; overloading of #1
overloading
V1 1
Vorder-sorted
n order-sorted
V2 1
Vdiscernable
a discernable
V3 1
Vop-discrete
n op-discrete
#OSALG_2
M1 1
MOrderSortedSubset
hn Order sorted subset #0 of #1
order sorted subsets #0 of #1
M2 1
MOSSubset
hn OSSubset #0 of #1
OSSubsets #0 of #1
M3 1
MOSSubAlgebra
hn OSSubAlgebra #0 of #1
OSSubAlgebras #0 of #1
O1 0 1
OOSConstants
mol#1; \mathop{\rm OSConstants} #1
O1 0 2
OOSConstants
mol#1#2; \mathop{\rm OSConstants}(#1,#2)
O2 0 1
OOSCl
mol#1; \mathop{\rm OSCl} #1
O3 0 1
OOSbool
mol#1; \mathop{\rm OSbool} #1
O4 0 1
OOSSubSort
mol#1; \mathop{\rm OSSubSort} #1
O4 0 2
OOSSubSort
mol#1#2; \mathop{\rm OSSubSort}(#1,#2)
O5 0 1
OOSMSubSort
mol#1; \mathop{\rm OSMSubSort} #1
O6 0 1
OGenOSAlg
mol#1; \mathop{\rm OSGen} #1
O7 1 1
O"\/"_os
moi@a; #1 \sqcup_{os} #2
O8 0 1
OOSSub
mol#1; \mathop{\rm OSSub} #1
O9 0 1
OOSAlg_join
mol#1; \mathop{\rm OSAlgJoin} #1
O10 0 1
OOSAlg_meet
mol#1; \mathop{\rm OSAlgMeet} #1
O11 0 1
OOSSubAlLattice
mol#1; \mathop{\rm OSSubAlLattice} #1
#OSALG_3
R1 2 0
Rare_os_isomorphic
h #1 and #2 are os-isomorphic
#1 and #2 are not os-isomorphic
#OSALG_4
M1 1
MOrderSortedRelation
hn order sorted relation #0 of #1
order sorted relations #0 of #1
M1 2
MOrderSortedRelation
hn order sorted relation #0 of #1,#2
order sorted relations #0 of #1,#2
M2 1
MOSCongruence
hn order sorted congruence #0 of #1
order sorted congruences #0 of #1
O1 0 1
OPath_Rel
mol#1; \mathop{\rm PathRel} #1
O2 0 2
OCompClass
mol#1#2; \mathop{\rm CompClass}(#1,#2)
O3 0 1
OOSClass
mol#1; \mathop{\rm OSClass} #1
O3 0 2
OOSClass
mol#1#2; \mathop{\rm OSClass}(#1,#2)
O4 1 1
O#_os
moi#1#2; #1 #_os #2
O5 0 1
OOSQuotRes
mol#1; \mathop{\rm OSQuotRes} #1
O5 0 2
OOSQuotRes
mol#1#2; \mathop{\rm OSQuotRes}(#1,#2)
O6 0 1
OOSQuotArgs
mol#1; \mathop{\rm OSQuotArgs} #1
O6 0 2
OOSQuotArgs
mol#1#2; \mathop{\rm OSQuotArgs}(#1,#2)
O7 0 1
OOSQuotCharact
mol#1; \mathop{\rm OSQuotCharact} #1
O7 0 2
OOSQuotCharact
mol#1#2; \mathop{\rm OSQuotCharact}(#1,#2)
O8 0 2
OQuotOSAlg
mol#1#2; \mathop{\rm QuotOSAlg}(#1,#2)
O9 0 2
OOSNat_Hom
mol#1#2; \mathop{\rm OSNatHom}(#1,#2)
O9 0 3
OOSNat_Hom
mol#1#2#3; \mathop{\rm OSNatHom}(#1,#2,#3)
O10 0 1
OOSCng
mol#1; \mathop{\rm OSCng} #1
O11 0 1
OOSHomQuot
mol#1; \mathop{\rm OSHomQuot} #1
O11 0 2
OOSHomQuot
mol#1#2; \mathop{\rm OSHomQuot}(#1,#2)
O11 0 3
OOSHomQuot
mol#1#2#3; \mathop{\rm OSHomQuot}(#1,#2,#3)
V1 1
Vos-compatible
n os-compatible
V2 1
Vlocally_directed
a locally directed
#O_RING_1
V1 1
Vbeing_a_square
b a square
V2 1
Vbeing_a_Sum_of_squares
b sequence of sums of squares
V3 1
Vbeing_a_sum_of_squares
b a sum of squares
V4 1
Vbeing_a_Product_of_squares
b sequence of products of squares
V5 1
Vbeing_a_product_of_squares
b a product of squares
V6 1
Vbeing_a_Sum_of_products_of_squares
b sequence of sums of products of squares
V7 1
Vbeing_a_sum_of_products_of_squares
b a sum of products of squares
V8 1
Vbeing_an_Amalgam_of_squares
b sequence of amalgams of squares
V9 1
Vbeing_an_amalgam_of_squares
b an amalgam of squares
V10 1
Vbeing_a_Sum_of_amalgams_of_squares
b sequence of sums of amalgams of squares
V11 1
Vbeing_a_sum_of_amalgams_of_squares
b a sum of amalgams of squares
V12 1
Vbeing_a_generation_from_squares
b a generation from squares
V13 1
Vgenerated_from_squares
a generated from squares
#PARSP_1
G1 2
GParStr
mc#1#2; \langle #1, #2\rangle
J1 1
GParStr
hol#1; parallelity structure of #1
L1 0
GParStr
ha parallelity structure #0
parallelity structures #0
M1 1
MRelation4
ha 4-ary relation #0 over #1
4-ary relations #0 over #1
M2 0
MParSp
ha parallelity space #0
parallelity spaces #0
O1 0 1
Oc3add
mow/1k#1; {\bf +}_{#1}
O2 0 1
Oc3compl
mow/1k#1; {\bf -}_{#1}
O3 0 1
OC3
moq#1; {#1}^{\bf 3}
O4 0 1
O4C3
moq#1; ({#1}^{\bf 3})^{\bf 4}
O5 0 1
OPRs
mow/1k#1; {\bf Par'}_{#1}
O6 0 1
OPR
mow/1k#1; {\bf Par}_{#1}
O7 0 1
OMPS
mow/1q; {\rm Aff}_{{#1}^3}
R1 1 1
R'||'
m #1 \vert\vert #2
#1 \not\vert\not\vert #2
R1 2 2
R'||'
m #1, #2 \bfparallel #3, #4
#1, #2 \nbfparallel #3, #4
U1 1
U4_arg_relation
hosl#1; parallelity of #1
parallelity
V1 1
VParSp-like
a parallelity space-like
#PARSP_2
M1 0
MFanodesSp
ha Fano-Desarques space #0
Fano-Desarques spaces #0
R1 3 0
Ris_collinear
h #1, #2 and #3 are collinear
#1, #2 and #3 are not collinear
R2 0 4
Rparallelogram
h #1, #2, #3, #4 form a parallelogram
#1, #2, #3, #4 do not form a parallelogram
R3 0 4
Rcongr
h #1, #2 are congruent to #3, #4
#1, #2 are not congruent to #3, #4
R3 2 2
Rcongr
h #1,#2 congr #3,#4
#1,#2 not congr #3,#4
V1 1
VFanodesSp-like
a Fano-Desarques space-like
#PARTFUN1
K1 1 L1 vPARTFUN1
K<:
L:>
mol@s; \prod^\ast #1
K1 2 L1 vPARTFUN1
K<:
L:>
mc#1#2; \langle #1, #2\rangle
K1 3 L1 vPARTFUN1
K<:
L:>
mow(1)/3l@w/2r@w#2#3;  #1_{\restriction  #2 \dot\to #3}
M1 1
MPartFunc
ha partial function #0 on #1
partial functions #0 on #1
M1 2
MPartFunc
ha partial function #0 from #1 to #2
partial functions #0 from #1 to #2
O1 0 2
OPFuncs
mox@a; #1 \dot\to #2
O2 0 1
OTotFuncs
mol@s; \mathop{\rm TotFuncs} #1
O3 1 1
O/.
mow(1)#2; #1_{#2}
R1 1 1
Rtolerates
m #1 \approx #2
#1 \not\approx #2
V1 1
Vtotal
a total
#PARTFUN3
V1 1
Vpositive-yielding
a positive yielding
V2 1
Vnegative-yielding
a negative yielding
V3 1
Vnonpositive-yielding
a non-positive yielding
V4 1
Vnonnegative-yielding
a non-negative yielding
#PARTIT1
O1 0 1
OPARTITIONS
mol#1; \mathop{\rm PARTITIONS}(#1)
O2 0 1
O'/\'
mol#1; \bigwedge #1
O2 1 1
O'/\'
moi#1#2; #1 \wedge #2
O3 0 1
O'\/'
mol#1; \bigvee #1
O3 1 1
O'\/'
moi#1#2; #1 \vee #2
O4 0 1
OERl
mow#1; {\equiv_{#1}}
O5 0 1
ORel
mol#1; \mathop{\rm Rel}(#1)
O6 0 1
O%I
mol#1; {\cal I}(#1)
O7 0 1
O%O
mol#1; {\cal O}(#1)
R1 1 1
R'<'
m #1 \Subset #2
#1 \not\Subset #2
R2 1 1
R'>'
m #1 \Supset #2
#1 \not\Supset #2
R3 1 1
Ris_a_dependent_set_of
i a dependent set of #2
not a dependent set of #2
R4 1 2
Ris_min_depend
i a minimal dependent set of #2 and #3
not a minimal dependent set of #2 and #3
#PASCH
V1 1
Vsatisfying_Int_Par_Pasch
s inner invariancy of betweenness relation under parallel projections
V2 1
Vsatisfying_Ext_Par_Pasch
s outer invariancy of betweenness relation under parallel projections
V3 1
Vsatisfying_Gen_Par_Pasch
s general invariancy of betweenness relation under parallel projections
V4 1
Vsatisfying_Ext_Bet_Pasch
s outer form of Pasch' Axiom
V5 1
Vsatisfying_Int_Bet_Pasch
s inner form of Pasch' Axiom
#PBOOLE
K1 2 L1 vPBOOLE
K[|
L|]
mc#1#2; \mathopen{[\![} #1,#2 \mathclose{]\!]}
M1 1
MManySortedSet
ha many sorted set #0 indexed by #1
many sorted sets #0 indexed by #1
M1 2
MManySortedSet
ha pair #0 of many sorted sets indexed by #1 and #2
pairs #0 of many sorted sets indexed by #1 and #2
M2 1
MManySortedFunction
ha many sorted function #0 indexed by #1
many sorted functions #0 indexed by #1
M2 2
MManySortedFunction
ha many sorted function #0 from #1 into #2
many sorted functions #0 from #1 into #2
M3 1
MComponent
ha component #0 of #1
components #0 of #1
M4 1
MManySortedSubset
ha many sorted subset #0 indexed by #1
many sorted subsets #0 indexed by #1
O1 0 1
O[[0]]
mol; {\bf 0.}#1
O2 1 0
O#
moq; #1^\#
O2 1 1
O#
moi@m; #1 \hash #2
O3 0 1
O*-->
moi(0,1)@a; \square \longmapsto #1
O4 0 2
OMSFuncs
mol#1#2; \mathop{\rm MSFuncs}(#1,#2)
O5 1 1
O.:.:
moi@s/1q/2k; #1 \mathbin{^\circ} #2
O6 0 1
Odown
mol; \mathop{\rm down} #1
R1 1 1
Roverlaps
h #1 overlaps #2
#1 does not overlap #2
R2 1 1
R[=
m #1 \sqsubseteq #2
#1 \not\sqsubseteq #2
#PCOMPS_1
O1 0 1
Oclf
mol@s; \mathop{\rm clf} #1
O2 0 1
OFamily_open_set
hol; open set family of #1
O3 0 1
OTopSpaceMetr
mow; #1_{\rm top}
O4 0 2
OSpaceMetr
mcl@s; \mathop{\rm MetrSp}(#1,#2)
R1 1 1
Ris_metric_of
i a metric of #2
not a metric of #2
V1 1
Vlocally_finite
a locally finite
V2 1
Vparacompact
a paracompact
V3 1
Vmetrizable
a metrizable
#PCOMPS_2
O1 0 2
OPartUnion
mol@s#1#2; \bigcup_{\beta{<_{#2}}#1}\beta
O2 0 2
ODisjointFam
hol; disjoint family of #1, #2
O3 0 2
OPartUnionNat
mol@s/2r@s#1; \bigcup_{\kappa<#1}#2(\kappa)
#PCS_0
G1 2
GTolStr
mc#1#2; \langle #1,#2 \rangle
G2 3
Gpcs-Str
mc#1#2#3; \langle #1,#2,#3 \rangle
J1 1
GTolStr
honl#1; alternative relational structure of #1
J2 1
Gpcs-Str
hol#1; pcs structure of #1
K1 2 L1 vPCS_0
K[^
L^]
mc#1#2; [\hat{\ }#1,#2\hat{\ }]
L1 0
GTolStr
hn alternative relational structure #0
alternative relational structures #0
L2 0
Gpcs-Str
ha pcs structure #0
pcs structures #0
M1 0
Mpcs
ha pcs #0
pcs's #0
M2 0
Manti-pcs
hn anti-pcs #0
anti-pcs's #0
M3 1
Mpcs-Chain
ha pcs-chain #0 of #1
pcs-chains #0 of #1
O1 0 1
Opcs-InternalRels
mol; \mathop{\rm pcs\hbox{-}InternalRels} #1
O2 0 0
OemptyTolStr
mol; \mathop{\rm emptyTolStr}
O3 0 1
Opcs-ToleranceRels
mol; \mathop{\rm pcs\hbox{-}ToleranceRels} #1
O4 1 0
O^`1
mor; #1 ^`1
O5 1 0
O^`2
mor; #1 ^`2
O6 0 1
Opcs-total
mol; \mathop{\rm TotalPCS} #1
O7 0 0
Opcs-empty
mol; \mathop{\rm EmptyPCS}
O8 0 1
Opcs-singleton
mol; \mathop{\rm SingletonPCS} #1
O9 0 1
Opcs-union
mol; \bigcup #1
O10 0 2
OMSSet
mol#1#2; \mathop{\rm MSSet}(#1,#2)
O11 0 2
Opcs-sum
moi@a; #1\oplus #2
O12 0 2
Opcs-extension
mor#2; #1_{#2}
O13 0 1
Opcs-reverse
mol; \mathopen\updownarrow #1
O14 1 1
Opcs-times
moi@m; #1 \otimes #2
O15 0 2
Opcs-general-power-IR
mol#1#2; {\cal P}_{\rm IR}(#1,#2)
O16 0 2
Opcs-general-power-TR
mol#1#2; {\cal P}_{\rm TR}(#1,#2)
O17 0 1
Opcs-general-power
mol#1; {\cal P}(#1)
O17 0 2
Opcs-general-power
mol#1#2; {\cal P}(#1,#2)
O18 0 1
Opcs-coherent-power
mol; \mathop{\rm pcs\hbox{-}coherent\hbox{-}power} #1
O19 0 1
Opcs-power
mol#1; {\cal P}(#1)
R1 1 1
R(--)
m #1 \sim #2
#1 \not\sim #2
U1 1
UToleranceRel
honl#1; alternative relation of #1
alternative relation
V1 1
Vtransitive-yielding
a transitive-yielding
V2 1
Vpcs-tol-total
a $\beta$-total
V3 1
Vpcs-tol-reflexive
a $\beta$-reflexive
V4 1
Vpcs-tol-irreflexive
a $\beta$-irreflexive
V5 1
Vpcs-tol-symmetric
a $\beta$-symmetric
V6 1
VTolStr-yielding
n alternative relational structure yielding
V7 1
Vpcs-tol-reflexive-yielding
a $\beta$-reflexive yielding
V8 1
Vpcs-tol-irreflexive-yielding
a $\beta$-irreflexive yielding
V9 1
Vpcs-tol-symmetric-yielding
a $\beta$-symmetric yielding
V10 1
Vpcs-compatible
a compatible
V11 1
Vpcs-like
a pcs-like
V12 1
Vanti-pcs-like
n anti-pcs-like
V13 1
Vpcs-Str-yielding
a pcs structure yielding
V14 1
Vpcs-yielding
a pcs-yielding
V15 1
Vpcs-chain-like
a chain-like
V16 1
Vpcs-self-coherent
a self-coherent
V17 1
Vpcs-self-coherent-membered
a self-coherent-membered
#PDIFF_1
O1 0 1
O<>*
mc#1; \langle #1\rangle
O2 0 2
Oreproj
mol#1#2; \mathop{\rm reproj}(#1,#2)
O3 0 3
Opartdiff
mol#1#2#3; \mathop{\rm partdiff}(#1,#2,#3)
O3 0 4
Opartdiff
mol#1#2#3#4; \mathop{\rm partdiff}(#1,#2,#3,#4)
O4 1 2
O`partial|
moi#2#3; #1{\upharpoonright}^{#3}#2
R1 1 2
Ris_partial_differentiable_in
i partially differentiable in #2 w.r.t. #3
not partially differentiable in #2 w.r.t. #3
R1 1 3
Ris_partial_differentiable_in
i partially differentiable in #2 w.r.t. #3 and #4
not partially differentiable in #2 w.r.t. #3 and #4
R2 1 2
Ris_partial_differentiable_on
i partially differentiable on #2 w.r.t. #3
not partially differentiable on #2 w.r.t. #3
#PDIFF_2
O1 0 3
OSVF1
mol#1#2#3; \mathop{\rm SVF1}(#1,#2,#3)
O2 1 1
O`partial1|
mow#2; {#1}^{\rm 1st}_{{\upharpoonright} #2}
O3 1 1
O`partial2|
mow#2; #1^{\rm 2nd}_{{\upharpoonright} #2}
R1 1 1
Ris_partial_differentiable`1_on
i partial differentiable w.r.t. 1st coordinate on #2
not partial differentiable w.r.t. 1st coordinate on #2
R2 1 1
Ris_partial_differentiable`2_on
i partial differentiable w.r.t. 2nd coordinate on #2
not partial differentiable w.r.t. 2nd coordinate on #2
#PDIFF_3
O1 0 2
Opdiff1
mol#1#2; \mathop{\rm pdiff1}(#1,#2)
O2 0 2
Ohpartdiff11
mol#1#2; \mathop{\rm hpartdiff11}(#1,#2)
O3 0 2
Ohpartdiff12
mol#1#2; \mathop{\rm hpartdiff12}(#1,#2)
O4 0 2
Ohpartdiff21
mol#1#2; \mathop{\rm hpartdiff21}(#1,#2)
O5 0 2
Ohpartdiff22
mol#1#2; \mathop{\rm hpartdiff22}(#1,#2)
O6 1 1
O`hpartial11|
mow#2; {#1}^{\rm 1st-1st}_{{\upharpoonright} #2}
O7 1 1
O`hpartial12|
mow#2; {#1}^{\rm 1st-2nd}_{{\upharpoonright} #2}
O8 1 1
O`hpartial21|
mow#2; {#1}^{\rm 2nd-1st}_{{\upharpoonright} #2}
O9 1 1
O`hpartial22|
mow#2; {#1}^{\rm 2nd-2nd}_{{\upharpoonright} #2}
R1 1 1
Ris_hpartial_differentiable`11_in
i partial differentiable on 1st-1st coordinate in #2
not partial differentiable on 1st-1st coordinate in #2
R2 1 1
Ris_hpartial_differentiable`12_in
i partial differentiable on 1st-2nd coordinate in #2
not partial differentiable on 1st-2nd coordinate in #2
R3 1 1
Ris_hpartial_differentiable`21_in
i partial differentiable on 2nd-1st coordinate in #2
not partial differentiable on 2nd-1st coordinate in #2
R4 1 1
Ris_hpartial_differentiable`22_in
i partial differentiable on 2nd-2nd coordinate in #2
not partial differentiable on 2nd-2nd coordinate in #2
R5 1 1
Ris_hpartial_differentiable`11_on
i partial differentiable on 1st-1st coordinate on #2
not partial differentiable on 1st-1st coordinate on #2
R6 1 1
Ris_hpartial_differentiable`12_on
i partial differentiable on 1st-2nd coordinate on #2
not partial differentiable on 1st-2nd coordinate on #2
R7 1 1
Ris_hpartial_differentiable`21_on
i partial differentiable on 2nd-1st coordinate on #2
not partial differentiable on 2nd-1st coordinate on #2
R8 1 1
Ris_hpartial_differentiable`22_on
i partial differentiable on 2nd-2nd coordinate on #2
not partial differentiable on 2nd-2nd coordinate on #2
#PDIFF_4
O1 1 1
O`partial3|
mow#2; #1^{\rm 3rd}_{{\upharpoonright} #2}
O2 0 2
Ograd
mol#1#2; \mathop{\rm grad}(#1,#2)
O3 0 3
ODirectiondiff
mol#1#2#3; \mathop{\rm Directiondiff}(#1,#2,#3)
O4 0 1
Ounitvector
mol; \mathop{\rm unitvector} #1
O5 0 4
Ocurl
mol#1#2#3#4; \mathop{\rm curl}(#1,#2,#3,#4)
R1 1 1
Ris_partial_differentiable`3_on
i partially differentiable w.r.t. 3rd coordinate on #2
not partially differentiable w.r.t. 3rd coordinate on #2
#PDIFF_5
O1 0 2
Ohpartdiff13
mol#1#2; \mathop{\rm hpartdiff13}(#1,#2)
O2 0 2
Ohpartdiff23
mol#1#2; \mathop{\rm hpartdiff23}(#1,#2)
O3 0 2
Ohpartdiff31
mol#1#2; \mathop{\rm hpartdiff31}(#1,#2)
O4 0 2
Ohpartdiff32
mol#1#2; \mathop{\rm hpartdiff32}(#1,#2)
O5 0 2
Ohpartdiff33
mol#1#2; \mathop{\rm hpartdiff33}(#1,#2)
O6 1 1
O`hpartial13|
mow#2; {#1}^{\rm 1st-3rd}_{{\upharpoonright} #2}
O7 1 1
O`hpartial23|
mow#2; {#1}^{\rm 2nd-3rd}_{{\upharpoonright} #2}
O8 1 1
O`hpartial31|
mow#2; {#1}^{\rm 3rd-1st}_{{\upharpoonright} #2}
O9 1 1
O`hpartial32|
mow#2; {#1}^{\rm 3rd-2nd}_{{\upharpoonright} #2}
O10 1 1
O`hpartial33|
mow#2; {#1}^{\rm 3rd-3rd}_{{\upharpoonright} #2}
R1 1 1
Ris_hpartial_differentiable`13_in
i partial differentiable on 1st-3rd coordinate in #2
not partial differentiable on 1st-3rd coordinate in #2
R2 1 1
Ris_hpartial_differentiable`23_in
i partial differentiable on 2nd-3rd coordinate in #2
not partial differentiable on 2nd-3rd coordinate in #2
R3 1 1
Ris_hpartial_differentiable`31_in
i partial differentiable on 3rd-1st coordinate in #2
not partial differentiable on 3rd-1st coordinate in #2
R4 1 1
Ris_hpartial_differentiable`32_in
i partial differentiable on 3rd-2nd coordinate in #2
not partial differentiable on 3rd-2nd coordinate in #2
R5 1 1
Ris_hpartial_differentiable`33_in
i partial differentiable on 3rd-3rd coordinate in #2
not partial differentiable on 3rd-3rd coordinate in #2
R6 1 1
Ris_hpartial_differentiable`13_on
i partial differentiable on 1st-3rd coordinate on #2
not partial differentiable on 1st-3rd coordinate on #2
R7 1 1
Ris_hpartial_differentiable`23_on
i partial differentiable on 2nd-3rd coordinate on #2
not partial differentiable on 2nd-3rd coordinate on #2
R8 1 1
Ris_hpartial_differentiable`31_on
i partial differentiable on 3rd-1st coordinate on #2
not partial differentiable on 3rd-1st coordinate on #2
R9 1 1
Ris_hpartial_differentiable`32_on
i partial differentiable on 3rd-2nd coordinate on #2
not partial differentiable on 3rd-2nd coordinate on #2
R10 1 1
Ris_hpartial_differentiable`33_on
i partial differentiable on 3rd-3rd coordinate on #2
not partial differentiable on 3rd-3rd coordinate on #2
#PENCIL_1
M1 1
MBlock
ha block #0 of #1
blocks #0 of #1
M2 0
MPLS
ha PLS #0
PLS #0
O1 0 1
OSegre_Blocks
mol#1; \mathop{\rm SegreBlocks} #1
O2 0 1
OSegre_Product
mol#1; \mathop{\rm SegreProduct} #1
R1 2 0
Rare_collinear
h #1,#2 are collinear
#1,#2 are not collinear
V1 1
Vclosed_under_lines
a closed under lines
V2 1
Vstrong
a strong
V3 1
Vwith_non_trivial_blocks
x non trivial blocks
V4 1
Videntifying_close_blocks
n identifying close blocks
V5 1
Vtruly-partial
a truly-partial
V6 1
Vwithout_isolated_points
xn no isolated points
V7 1
VTopStruct-yielding
a TopStruct-yielding
V8 1
Vnon-void-yielding
a non-void-yielding
V9 1
Vtrivial-yielding
a trivial-yielding
V10 1
Vnon-Trivial-yielding
a non-Trivial-yielding
V11 1
VPLS-yielding
a PLS-yielding
V12 1
VSegre-like
a Segre-like
#PENCIL_2
M1 1
MSegre-Coset
ha Segre coset #0 of #1
Segre cosets #0 of #1
M2 1
MCollineation
ha collineation #0 of #1
collineations #0 of #1
R1 2 0
Rare_joinable
h #1 and #2 are joinable
#1 and #2 are not joinable
#PENCIL_3
O1 0 1
Opermutation_of_indices
mol#1; {\rm IndPerm}(#1)
O2 0 2
Ocanonical_embedding
mol#1#2; {\rm CanEmb}(#1, #2)
#PENCIL_4
O1 0 2
Osegment
mol#1#2; \mathop{\rm segment}(#1,#2)
O2 0 2
Opencil
mol#1#2; \mathop{\rm pencil}(#1,#2)
O2 0 3
Opencil
mol#1#2#3; \mathop{\rm pencil}(#1,#2,#3)
O3 1 1
OPencils_of
Hoi#1#2; #1 pencils of #2
O4 0 2
OPencilSpace
mol#1#2; \mathop{\rm PencilSpace}(#1,#2)
O5 0 3
OSubspaceSet
mol#1#2#3; \mathop{\rm SubspaceSet}(#1,#2,#3)
O6 0 3
OGrassmannSpace
mol#1#2#3; \mathop{\rm GrassmannSpace}(#1,#2,#3)
O7 0 1
OPairSet
mol; \mathop{\rm PairSet} #1
O7 0 2
OPairSet
mol#1#2; \mathop{\rm PairSet}(#1,#2)
O8 0 1
OPairSetFamily
mol; \mathop{\rm PairSetFamily} #1
O9 0 1
OVeroneseSpace
mol; \mathop{\rm VeroneseSpace} #1
#PEPIN
O1 0 3
OCrypto
mol#1#2#3; \mathop{\rm Crypto}(#1,#2,#3)
O2 0 1
Oorder
mol; \mathop{\rm order} #1
O2 0 2
Oorder
mol#1#2; \mathop{\rm order}(#1,#2)
O3 0 1
OFermat
mol#1; \mathop{\rm Fermat} #1
#PETRI
G1 4
GPT_net_Str
mc#1#2#3#4; \langle #1, #2, #3, #4\rangle
J1 1
GPT_net_Str
hol#1; place/transition net structure of #1
L1 0
GPT_net_Str
ha place/transition net structure #0
place/transition net structures #0
M1 1
Mplace
ha place #0 of #1
places #0 of #1
M2 1
Mplaces
ha% place #0 of #1
places #0 of #1
M3 1
Mtransition
ha transition #0 of #1
transitions #0 of #1
M4 1
Mtransitions
ha% transition #0 of #1
transitions #0 of #1
M5 1
MS-T_arc
hn S-T arc #0 of #1
S-T arcs #0 of #1
M6 1
MT-S_arc
ha T-S arc #0 of #1
T-S arcs #0 of #1
O1 0 0
OTrivialPetriNet
mol; \mathop{\rm Trivial Petri Net}
U1 1
US-T_Arcs
hopl#1; S-T arcs of #1
S-T arcs
U2 1
UT-S_Arcs
hopl#1; T-S arcs of #1
T-S arcs
V1 1
VDeadlock-like
a deadlock-like
V2 1
VWith_Deadlocks
x deadlocks
V3 1
VTrap-like
a trap-like
V4 1
VWith_Traps
x traps
V5 1
Vwith_S-T_arc
x $S$-$T$ arc
V6 1
Vwith_T-S_arc
x $T$-$S$ arc
#PETRI_2
G1 6
GColored_PT_net_Str
mc#1#2#3#4#5#6; \langle #1,#2,#3,#4,#5,#6 \rangle
J1 1
GColored_PT_net_Str
hol#1; colored place/transition net structure of #1
L1 0
GColored_PT_net_Str
ha colored place/transition net structure #0
colored place/transition net structures #0
M1 2
Mthin_cylinder
ha thin cylinder #0 of #1 and #2
thin cylinder(s) #0 of #1 and #2
M2 0
MColored-PT-net
ha colored place/transition net #0
colored place/transition nets #0
M3 2
Mconnecting-mapping
ha connecting mapping #0 of #1 and #2
connecting mappings #0 of #1 and #2
M4 3
Mconnecting-firing-rule
ha connecting firing rule #0 of #1, #2, and #3
connecting-firing-rules #0 of #1, #2, and #3
M5 0
MColored_Petri_net
ha colored Petri net #0
colored Petri nets #0
O1 0 4
Ocylinder0
mol#1#2#3#4; \mathop{\rm cylinder}_0(#1,#2,#3,#4)
O2 0 2
Othin_cylinders
hopl#1#2; thin cylinders of #1 and #2
O3 0 4
OExtcylinders
mol#1#2#3#4; \mathop{\rm Extcylinders}(#1,#2,#3,#4)
O4 0 4
ORistcylinders
mol#1#2#3#4; \mathop{\rm Ristcylinders}(#1,#2,#3,#4)
O5 0 1
Oloc
mol; \mathop{\rm loc} #1
O6 0 9
OCylinderFunc
mol#1#2#3#4#5#6#7#8#9; \mathop{\rm CylinderFunc}(#1,#2,#3,#4,#5,#6,#7,#8,#9)
O7 0 1
OOutbds
mol; \mathop{\rm Outbds} #1
O8 0 4
Osynthesis
mol#1#2#3#4; \mathop{\rm synthesis}(#1,#2,#3,#4)
O9 0 0
OTrivialColoredPetriNet
mol; \mathop{\rm Trivial Colored Petri Net}
U1 1
UColoredSet
hosl#1; colored set of #1
colored set
U2 1
Ufiring-rule
hosl#1; firing-rule of #1
firing-rule
V1 1
Voutbound
n outbound
V2 1
VColored-PT-net-like
a colored-PT-net-like
#PNPROC_1
M1 1
Mmarking
ha marking #0 of #1
markings #0 of #1
M2 0
MPetri_net
ha petri net #0
petri nets #0
M2 1
MPetri_net
ha Petri net #0 over #1
Petri nets #0 over #1
M3 1
Mfiring-sequence
ha firing-sequence #0 of #1
firing-sequences #0 of #1
M4 1
Mprocess
ha process #0 in #1
processes #0 in #1
O1 1 1
Omultitude_of
hoi#1; #1 multitude of #2
O2 0 1
O{$}
mol#1; \{\}_{#1}
O3 0 1
Ofire
mol; \mathop{\rm fire}\: #1
O3 0 2
Ofire
mol#1#2; \mathop{\rm fire}(#1,#2)
O4 1 1
Obefore
moi; #1 \mathop{\rm before} #2
O5 1 1
Oconcur
moi; #1 \mathop{\rm concur} #2
O6 0 1
ONeutralProcess
hol; neutral process in #1
O7 0 1
OElementaryProcess
hol; elementary process with #1
#POLYALG1
M1 1
MSubalgebra
ha subalgebra #0 of #1
subalgebras #0 of #1
O1 0 1
OFormal-Series
mol#1; \mathop{\rm Formal\hbox{-}Series} #1
O2 0 1
OGenAlg
mol#1; \mathop{\rm GenAlg} #1
O3 0 1
OPolynom-Algebra
mol#1; \mathop{\rm Polynom\hbox{-}Algebra} #1
V1 1
Vmix-associative
a mix-associative
#POLYEQ_1
O1 0 3
OPolynom
mol#1#2#3; \mathop{\rm Polynom}(#1,#2,#3)
O1 0 4
OPolynom
mol#1#2#3#4; \mathop{\rm Polynom}(#1,#2,#3,#4)
O1 0 5
OPolynom
mol#1#2#3#4#5; \mathop{\rm Polynom}(#1,#2,#3,#4,#5)
O1 0 6
OPolynom
mol#1#2#3#4#5#6; \mathop{\rm Polynom}(#1,#2,#3,#4,#5,#6)
O1 0 7
OPolynom
mol#1#2#3#4#5#6#7; \mathop{\rm Polynom}(#1,#2,#3,#4,#5,#6,#7)
O2 0 4
OQuard
mol#1#2#3#4; \mathop{\rm Quard}(#1,#2,#3,#4)
O3 0 5
OTri
mol#1#2#3#4#5; \mathop{\rm Tri}(#1,#2,#3,#4,#5)
#POLYEQ_2
O1 0 6
OFour0
mol#1#2#3#4#5#6; \mathop{\rm Four0}(#1,#2,#3,#4,#5,#6)
#POLYEQ_3
O1 1 0
O^3
mor; #1{}^{3}
#POLYEQ_5
O1 1 1
O-real-root
mol#1#2; #2^{1/#1}
O2 0 3
O1_root_of_cubic
mol#1#2#3; \mathop{\rho_{1}}(#1,#2,#3)
O3 0 3
O2_root_of_cubic
mol#1#2#3; \mathop{\rho_{2}}(#1,#2,#3)
O4 0 3
O3_root_of_cubic
mol#1#2#3; \mathop{\rho_{3}}(#1,#2,#3)
O5 0 4
O1_root_of_quartic
mol#1#2#3#4; \mathop{\rho_{1}}(#1,#2,#3,#4)
O6 0 4
O2_root_of_quartic
mol#1#2#3#4; \mathop{\rho_{2}}(#1,#2,#3,#4)
O7 0 4
O3_root_of_quartic
mol#1#2#3#4; \mathop{\rho_{3}}(#1,#2,#3,#4)
O8 0 4
O4_root_of_quartic
mol#1#2#3#4; \mathop{\rho_{4}}(#1,#2,#3,#4)
#POLYFORM
G1 2
GPolyhedronStr
mc#1#2; \langle #1,#2 \rangle
J1 1
GPolyhedronStr
hol#1; polyhedron structure of #1
L1 0
GPolyhedronStr
ha polyhedron structure of #0
polyhedron structures of #0
M1 2
Mincidence-matrix
hn incidence matrix #0 of #1 and #2
incidence matrices #0 of #1 and #2
M2 0
Mpolyhedron
ha polyhedron #0
polyhedrons #0
O1 1 1
O-polytopes
mow#1#2; P_{#1,#2}
O2 0 2
Oeta
mow#1#2; \eta_{#1,#2}
O3 1 1
O-polytope-seq
mow#1#2; S_{#1,#2}
O4 0 2
Onum-polytopes
mow#1#2; N_{#1,#2}
O5 0 1
Onum-vertices
mow#1; V_{#1}
O6 0 1
Onum-edges
mow#1; E_{#1}
O7 0 1
Onum-faces
mow#1; F_{#1}
O8 1 2
O-th-polytope
mor#1#2#3; P_{#2,#3}^{#1}
O9 0 2
Oincidence-value
mol#2; #1(#2)
O10 1 1
O-chain-space
mow#1#2; C_{#1,#2}
O11 1 1
O-chains
moi; #1\mathop{\rm\hbox{-}chains} #2
O12 0 2
Oincidence-sequence
mor/2l@m#1; #2(#1)
O13 0 1
OBoundary
mol; \partial #1
O14 1 1
O-boundary
mor(2)#1; \partial_{#1}#2
O15 1 1
O-circuit-space
mow#1#2; Z_{#1,#2}
O16 1 1
O-circuits
moc#1#2; \mathopen\vert Z_{#1,#2}\mathclose\vert
O17 1 1
O-bounding-chain-space
mow#1#2; B_{#1,#2}
O18 1 1
O-bounding-chains
moc#1#2; \mathopen\vert B_{#1,#2}\mathclose\vert
O19 1 1
O-bounding-circuit-space
mow#1#2; \mathop{\rm BZ}_{#1,#2}
O20 1 1
O-bounding-circuits
moi; #1 \mathop{\rm\hbox{-}bounding\hbox{-}circuits} #2
O21 0 1
Oalternating-f-vector
mct#1; \widehat{#1}
O22 0 1
Oalternating-proper-f-vector
mct#1; \bar{#1}
O23 0 1
Oalternating-semi-proper-f-vector
mct#1; \overline{#1}
U1 1
UPolytopsF
hosl#1; polytops of #1
polytops
U2 1
UIncidenceF
hosl#1; incidence of #1
incidence
V1 1
Vpolyhedron_1
a polyhedron${}_1$
V2 1
Vpolyhedron_2
a polyhedron${}_2$
V3 1
Vpolyhedron_3
a polyhedron${}_3$
V4 1
Vsimply-connected
a being a homology sphere
V5 1
Veulerian
n Eulerian
#POLYNOM1
M1 2
MSeries
ha series #0 of #1,#2
series #0 of #1,#2
M2 1
MPolynomial
ha polynomial #0 of #1
polynomials #0 of #1
M2 2
MPolynomial
ha polynomial #0 of #1,#2
polynomials #0 of #1,#2
O1 0 1
OSupport
mol; \mathop{\rm Support} #1
O1 0 2
OSupport
mol#1#2; \mathop{\rm Support}(#1,#2)
O2 0 2
O0_
mol#1; 0_{#1} #2
O3 0 1
OPolynom-Ring
mol; \mathop{\rm Polynom\hbox{-}Ring} #1
O3 0 2
OPolynom-Ring
mol#1#2; \mathop{\rm Polynom\hbox{-}Ring}(#1,#2)
#POLYNOM2
O1 0 2
Oeval
mol#1#2; \mathop{\rm eval}(#1,#2)
O2 0 2
OPolynom-Evaluation
mol#1#2; \mathop{\rm Polynom\hbox{-}Evaluation}(#1,#2)
O2 0 3
OPolynom-Evaluation
mol#1#2#3; \mathop{\rm Polynom\hbox{-}Evaluation}(#1,#2,#3)
#POLYNOM3
O1 0 1
OTuplesOrder
mol; \mathop{\rm TuplesOrder} #1
O2 0 2
ODecomp
mol#1#2; \mathop{\rm Decomp}(#1,#2)
O3 0 4
OprodTuples
mol#1#2#3#4; \mathop{\rm prodTuples}(#1,#2,#3,#4)
O4 0 1
O0_.
mol; \mathop{\bf 0.} #1
O5 0 1
O1_.
mol; \mathop{\bf 1.} #1
#POLYNOM4
O1 0 1
OLeading-Monomial
mol#1; \mathop{\rm Leading\hbox{-}Monomial} #1
#POLYNOM5
O1 1 1
O`^
moq(1)/2m#2; #1^{#2}
O2 0 1
ORoots
mol; \mathop{\rm Roots} #1
O3 0 1
ONormPolynomial
mol; \mathop{\rm NormPolynomial} #1
O4 0 2
OFPower
mol#1#2; \mathop{\rm FPower}(#1,#2)
O5 0 2
OPolynomial-Function
mol#1#2; \mathop{\rm Polynomial\hbox{-}Function}(#1,#2)
R1 1 1
Ris_a_root_of
h #1 is a root of #2
#1 is not a root of #2
V1 1
Vwith_roots
x roots
V2 1
Valgebraic-closed
n algebraic-closed
#POLYNOM6
O1 0 1
OCompress
mol; \mathop{\rm Compress} #1
#POLYNOM7
M1 2
MMonomial
ha monomial #0 of #1,#2
monomials #0 of #1,#2
M2 2
MConstPoly
ha constant polynomial #0 of #1,#2
constant polynomials #0 of #1,#2
O1 0 2
OMonom
mol#1#2; \mathop{\rm Monom}(#1,#2)
O2 0 1
Ocoefficient
mol; \mathop{\rm coefficient} #1
V1 1
Vunivariate
n univariate
V2 1
Vmonomial-like
a monomial-like
V3 1
VConstant
a constant
#POLYNOM8
O1 0 2
Oemb
mow#2; #1_{#2}
O2 0 2
Opow
moq(1)/2m#2; #1^{#2}
O3 0 2
OmConv
mol#1#2; \mathop{\rm mConv}(#1,#2)
O4 0 1
OaConv
mol; \mathop{\rm aConv} #1
O5 0 3
ODFT
mol#1#2#3; \mathop{\rm DFT}(#1,#2,#3)
O6 0 2
OVandermonde
mol#1#2; \mathop{\rm Vandermonde}(#1,#2)
O7 0 2
OVM
mol#1#2; \mathop{\rm VM}(#1,#2)
R1 1 1
Ris_primitive_root_of_degree
i primitive root of degree #2
not primitive root of degree #2
#POLYRED
O1 0 2
OPolyRedRel
mol#1#2; \mathop{\rm PolyRedRel}(#1,#2)
R1 1 3
Rreduces_to
h #1 reduces to #2,#3,#4
#1 does not reduce to #2,#3,#4
R1 1 4
Rreduces_to
h #1 reduces to #2,#3,#4,#5
#1 does not reduce to #2,#3,#4,#5
R2 1 2
Ris_reducible_wrt
i reducible w.r.t. #2,#3
not reducible w.r.t. #2,#3
R3 1 2
Ris_irreducible_wrt
i irreducible w.r.t. #2,#3
not irreducible w.r.t. #2,#3
R4 1 2
Ris_in_normalform_wrt
i in normal form w.r.t. #2,#3
not in normal form w.r.t. #2,#3
R5 1 3
Rtop_reduces_to
h #1 top reduces to #2,#3,#4
#1 does not top reduce to #2,#3,#4
R6 1 2
Ris_top_reducible_wrt
i top reducible w.r.t. #2,#3
not top reducible w.r.t. #2,#3
#POSET_1
O1 0 2
OiterSet
mol#1#2; \mathop{\rm iterSet}(#1,#2)
O2 0 1
Oiter_min
mol; \mathop{\rm iter\hbox{-}min} #1
O3 0 2
OConFuncs
mol#1#2; \mathop{\rm ConFuncs}(#1,#2)
O4 0 2
OConRelat
mol#1#2; \mathop{\rm ConRelat}(#1,#2)
O5 0 2
OConPoset
mol#1#2; \mathop{\rm ConPoset}(#1,#2)
O6 0 1
Osup_func
mol; \mathop{\rm sup\hbox{-}func} #1
O7 0 2
Omin_func
mol#1#2; \mathop{\rm min\hbox{-}func}(#1,#2)
O8 0 1
Oleast_fix_point
hol; least fixpoint of #1
O9 0 1
Ofix_func
mol; \mathop{\rm fix\hbox{-}func} #1
O10 1 1
O-image
moi#2; #1{\rm\hbox{-}image}(#2)
V1 1
Vchain-complete
a chain-complete
#POWER
O1 1 1
O-root
mc{w}@9#1#2; \sqrt[#1]{#2}
O2 1 1
Oto_power
moq#2; #1^{#2}
O2 2 1
Oto_power
moi(1,2)@a#3; (#1\setminus #2)^{#3}
O3 0 2
Olog
mol(2)@s/1k#1; {\mathop{\rm log}_{#1}#2}
O4 0 0
Onumber_e
mc; {\it e}
#PRALG_1
K1 1 L1 vPRALG_1
K[[:
L:]]
mc#1; \rceil\!\rceil #1 \lceil\!\lceil
K1 2 L1 vPRALG_1
K[[:
L:]]
mc#1; \rceil\!\rceil #1,#2 \lceil\!\lceil
M1 1
MManySortedOperation
ha many sorted operation #0 of #1
many sorted operations #0 of #1
O1 0 1
OInv
mol#1; \mathop{\rm Inv} #1
O1 0 2
OInv
mol#1#2; \mathop{\rm Inv}(#1,#2)
O2 0 1
OTrivialOp
mol#1; \mathop{\rm TrivOp}(#1)
O3 0 1
OTrivialOps
mol#1; \mathop{\rm TrivOps}(#1)
O4 0 1
OTrivial_Algebra
hol#1; trivial algebra of #1
O5 0 1
OComSign
mol#1; \mathop{\rm ComSign}(#1)
O6 0 1
OComAr
mol#1; \mathop{\rm ComAr}(#1)
O7 0 1
OEmptySeq
mow#1; \varepsilon_{#1}
O8 0 2
OProdOp
mol#1#2; \mathop{\rm ProdOp}(#1,#2)
O9 0 1
OProdOpSeq
mol#1; \mathop{\rm ProdOpSeq}(#1)
O10 0 1
OProdUnivAlg
mol#1; \mathop{\rm ProdUnivAlg}(#1)
V1 1
VUniv_Alg-yielding
a universal algebra yielding
V2 1
V1-sorted-yielding
a 1-sorted yielding
V3 1
Vequal-signature
n equal signature
V4 1
Vequal-arity
n equal arity
#PRALG_2
M1 2
MMSAlgebra-Family
hn algebra family #0 of #1 over #2
algebra families #0 of #1 over #2
O1 0 1
OCommute
mol#1; \blacksquare\!\mathop{\rm commute}(#1)
O2 0 1
OSORTS
mol#1; \mathop{\rm SORTS}(#1)
O3 0 1
OOPER
mol#1; \mathop{\rm OPER}(#1)
O4 1 1
O?.
mor(1)@9#2; #1(#2)
O5 0 1
OOPS
mol#1; \mathop{\rm OPS}(#1)
#PRALG_3
M1 2
MMSAlgebra-Class
ha MSAlgebra-Class #0 of #1,#2
MSAlgebra-Classes #0 of #1,#2
O1 0 2
Oconst
mol#1#2; \mathop{\rm const}(#1,#2)
O1 1 1
Oconst
mol(2)/1k#1#2; \mathop{\rm const}_{#1}(#2)
#PRELAMB
G1 4
Gtypealg
mc#1#2#3#4; \langle #1, #2, #3, #4\rangle
G2 5
Gtypestr
mc#1#2#3#4#5; \langle #1, #2, #3, #4, #5\rangle
J1 1
Gtypealg
hol#1; structure of the type algebra of #1
J2 1
Gtypestr
hol#1; type structure of #1
L1 0
Gtypealg
ha structure of the type algebra #0
structures of the type algebra #0
L2 0
Gtypestr
ha type structure #0
type structures #0
M1 1
Mtype
ha type #0 of #1
types #0 of #1
M2 1
MPreProof
ha preproof #0 of #1
preproofs #0 of #1
M3 1
MProof
ha proof #0 of #1
proofs #0 of #1
M4 2
MModel
ha model #0 of #1
models #0 of #1
M5 0
MSynTypes_Calculus
ha calculus #0 of syntactic types
calculuses #0 of syntactic types
O1 0 1
Orepr_of
hol; representation of #1
O2 0 1
Osize_w.r.t.
hol; size w.r.t. #1
O3 0 1
Ocutdeg
hol; cut degree of #1
R1 1 1
Rrepresents
h #1 represents #2
#1 does not represent #2
R2 1 1
Rdoes_not_represent
h #1 does not represent #2
#1 represents #2
R3 1 1
R==>.
m #1 \longrightarrow #2
#1 \not\longrightarrow #2
R3 1 2
R==>.
m #1 \Rightarrow_{#3} #2
#1 \not\Rightarrow_{#3} #2
R3 2 3
R==>.
m #1,#2 \Rightarrow_{#5} #3,#4
#1,#2 \not\Rightarrow_{#5} #3,#4
R4 1 1
R<==>.
m #1 \longleftrightarrow #2
#1 \not\longleftrightarrow #2
U1 1
Uleft_quotient
hosl#1; left quotient of #1
left quotient
U2 1
Uright_quotient
hosl#1; right quotient of #1
right quotient
U3 1
Uinner_product
honl#1; inner product of #1
inner product
U4 1
Uderivability
hosl#1; derivability of #1
derivability
V1 1
Vcorrect
a correct
V2 1
Vleft
a left
V3 1
Vright
a right
V4 1
Vmiddle
a middle
V5 1
Vprimitive
a primitive
V6 1
Vfree
a free
V7 1
Vcut-free
a cut-free
V8 1
VSynTypes_Calculus-like
a calculus of syntactic types-like
#PREPOWER
M1 0
MRational_Sequence
ha rational sequence #0
rational sequences #0
O1 1 0
OGeoSeq
mow/1q; (#1^\kappa)_{\kappa\in \mathbb N}
O2 1 1
O-Root
mo{kw}#1#2; \mathop{\rm root}_{#1}(#2)
O3 0 1
O#Z
mor{qrw}@m#1; {\square}^{#1}
O3 1 1
O#Z
mor{qrw}@s#2; #1^{#2}
O4 1 1
O#Q
mor{qrw}@s#2; #1^{#2}_{\mathbb Q}
O5 0 1
O#R
mor{qrw}@s#1; {\square}^{#1}
O5 1 1
O#R
mor{qrw}@s#2; #1^{#2}
#PRE_FF
O1 0 1
OFib
mcl#1; \mathop{\rm Fib}(#1)
O2 0 1
OFusc
mcl#1; \mathop{\rm Fusc}(#1)
#PRE_POLY
M1 1
Mbag
ha bag #0 of #1
bags #0 of #1
O1 0 1
OFlattenSeq
mc#1; \mathop{\rm Flat}(#1)
O2 0 2
OSgmX
mol#1#2; \mathop{\rm SgmX}(#1,#2)
O3 0 2
O^^
mol#1#2; \mathop\uparrow(#1,#2)
O3 0 3
O^^
mol#1#2#3; \mathop\uparrow(#1,#2,#3)
O3 1 1
O^^
moi@m/1q/2k; #1 \mathbin{^\frown} #2
O4 0 1
Osupport
mol@s; \mathop{\rm support} #1
O5 0 1
OBags
mol; \mathop{\rm Bags} #1
O6 0 1
OEmptyBag
mol; \mathop{\rm EmptyBag} #1
O7 0 1
OBagOrder
mol; \mathop{\rm BagOrder} #1
O8 0 1
ONatMinor
mol; \mathop{\rm NatMinor} #1
O9 0 1
Odivisors
mol; \mathop{\rm divisors} #1
O10 0 1
Odecomp
mol; \mathop{\rm decomp} #1
V1 1
VFinSequence-yielding
a finite sequence-yielding
V2 1
Vfinite-support
a finite-support
#PRE_TOPC
G1 2
GTopStruct
mc#1#2; \langle #1,\allowbreak #2\rangle
J1 1
GTopStruct
hol#1; topological structure of #1
L1 0
GTopStruct
ha topological structure #0
topological structures #0
M1 0
MTopSpace
ha topological space #0
topological spaces #0
M2 1
MPoint
ha point #0 of #1
points #0 of #1
M3 1
MSubSpace
ha subspace #0 of #1
subspaces #0 of #1
O1 0 1
OCl
mct#1; \overline{#1}
U1 1
Utopology
hosl#1; topology of #1
topology
V1 1
VTopSpace-like
a topological space-like
V2 1
VT_0
a {\Tzero}
V3 1
VT_1
a $T_1$
V4 1
VT_2
a $T_2$
V5 1
Vnormal
a normal
V6 1
VT_3
a $T_3$
V7 1
VT_4
a $T_4$
#PRGCOR_1
O1 0 2
Oidiv1_prg
mol#1#2; \mathop{\rm Idiv1Prg}(#1,#2)
O2 0 2
Oidiv_prg
mol#1#2; \mathop{\rm IdivPrg}(#1,#2)
#PRGCOR_2
O1 0 1
OFS2XFS
mol#1; \mathop{\rm FS2XFS}(#1)
O2 0 1
OXFS2FS
mol#1; \mathop{\rm XFS2FS}(#1)
O3 0 2
OFS2XFS*
mol#1#2; \mathop{\rm FS2XFS}^{\star}(#1,#2)
O4 0 1
OXFS2FS*
mol#1; \mathop{\rm XFS2FS}^{\star}(#1)
O5 0 5
OIFLGT
mol#1#2#3#4#5; \mathop{\rm IFLGT}(#1,#2,#3,#4,#5)
O6 0 2
Oinner_prd_prg
mol#1#2; \mathop{\rm InnerPrdPrg}(#1,#2)
R1 1 1
Ris_an_xrep_of
h #1 is an xrep of #2
#1 is not an xrep of #2
R2 1 3
Rscalar_prd_prg
h #1 scalar prd prg of #2,#3,#4
not #1 scalar prd prg of #2,#3,#4
R3 1 2
Rvector_minus_prg
h #1 vector minus prg of #2,#3
not #1 vector minus prg of #2,#3
R4 1 3
Rvector_add_prg
h #1 vector add prg of #2,#3,#4
not #1 vector add prg of #2,#3
R5 1 3
Rvector_sub_prg
h #1 vector sub prg of #2,#3,#4
not #1 vector sub prg of #2,#3,#4
#PROB_1
M1 1
MField_Subset
ha field #0 of subsets of #1
fields #0 of subsets of #1
M2 0
MSetSequence
ha set sequence #0
set sequences #0
M2 1
MSetSequence
ha sequence #0 of subsets of #1
sequences #0 of subsets of #1
M3 1
MSigmaField
ha \FMsig-field #0 of subsets of #1
\FMsig-fields #0 of subsets of #1
M4 1
MProbability
ha probability #0 on #1
probabilities #0 on #1
O1 0 1
OComplement
mol@s; \mathop{\rm Complement} #1
O2 0 1
Osigma
mol#1; \sigma(#1)
O2 0 2
Osigma
mol#1#2; \mathop{\sigma_{#1}}(#2)
O3 0 1
Ohalfline
mcl@s#1; \mathop{\rm halfline}(#1)
O3 0 2
Ohalfline
mcl@s#1#2; \mathop{\rm halfline}(#1,#2)
O4 0 0
OFamily_of_halflines
mc; \mathop{\rm Halflines}
O5 0 0
OBorel_Sets
ho; Borel sets
V1 1
Vcompl-closed
a closed for complement operator
V2 1
Vnon-ascending
a non ascending
V3 1
Vnon-descending
a non descending
V4 1
Vsigma-multiplicative
a \fmsig-multiplicative
#PROB_2
O1 0 1
O@Intersection
mol@s; \bigcap #1
O2 0 1
O@Complement
moq; #1 \mathclose{^{\bf c}}
O3 1 1
O.|.
mci@7; (#1|#2)
R1 2 1
Rare_independent_respect_to
h #1 and #2 are independent w.r.t. #3
#1 and #2 are not independent w.r.t. #3
R1 3 1
Rare_independent_respect_to
h #1, #2 and #3 are independent w.r.t. #4
#1, #2 and #3 are not independent w.r.t. #4
V1 1
Vdisjoint_valued
a disjoint valued
#PROB_3
M1 1
MMonotoneClass
ha monotone class #0 of #1
monotone classes #0 of #1
O1 0 1
OPartial_Intersection
hopl; partial intersections of #1
O2 0 1
OPartial_Union
hopl; partial unions of #1
O3 0 1
OPartial_Diff_Union
hopl; partial diff-unions of #1
O4 0 1
O@Partial_Intersection
hol; partial Intersection of #1
O5 0 1
O@Partial_Union
hol; partial Union of #1
O6 0 1
O@Partial_Diff_Union
hol; partial Diff Union of #1
O7 0 1
Omonotoneclass
mol#1; \mathop{\rm monotone\hbox{-}class}(#1)
V1 1
Vnon-decreasing-closed
a non-decreasing-union-closed
V2 1
Vnon-increasing-closed
a non-increasing-intersection-closed
#PROB_4
O1 0 1
OP2M
mol; \mathop{\rm P2M} #1
O2 0 1
OM2P
mol; \mathop{\rm M2P} #1
O3 0 1
OP_COM2M_COM
mol; \mathop{\rm P_{COM}2M_{COM}} #1
O4 0 1
OProbPart
mol; \mathop{\rm ProbPart} #1
#PROJDES1
R1 4 0
Rare_coplanar
h #1, #2, #3, #4 are coplanar
#1, #2, #3, #4 are not coplanar
R2 4 0
Rconstitute_a_quadrangle
h #1, #2, #3, and #4 constitute a quadrangle
#1, #2, #3, and #4 do not constitute a quadrangle
#PROJPL_1
M1 0
MIncProjectivePlane
hn incidence projective plane #0
incidence projective planes #0
M2 1
MQuadrangle
ha quadrangle #0 of #1
quadrangles #0 of #1
R1 1 1
R|'
mn #21 \nmid #2
#1 \mid #2
R1 2 1
R|'
m #1,#2 \nmid #3
#1,#2 \mid #3
R2 3 0
Ris_a_triangle
h #1,#2,#3 form a triangle
#1,#2,#3 do not form a triangle
R3 4 0
Ris_a_quadrangle
h #1,#2,#3,#4 form a quadrangle
#1,#2,#3,#4 do not form a quadrangle
V1 1
Vconfiguration
a configuration
#PROJRED1
O1 0 3
OIncProj
mcl/1r@w/3r@w/2k#1#2#3; \pi_{#2}(#1 \to #3)
#PROJRED2
M1 1
MProjection
ha projection #0 of #1
projections #0 of #1
O1 0 1
OCHAIN
mol@s#1; \mathop{\rm chain}(#1)
R1 3 0
Rare_concurrent
h #1, #2, #3 are concurrent
#1, #2, #3 are not concurrent
#PRVECT_1
M1 0
MDomain-Sequence
ha sequence #0 of non empty sets
sequences #0 of non empty sets
M2 1
MBinOps
ha family #0 of binary operations of #1
families #0 of binary operations of #1
M3 1
MUnOps
ha family #0 of unary operations of #1
families #0 of unary operations of #1
M4 0
MGroup-Sequence
ha sequence #0 of groups
sequences #0 of groups
O1 1 1
O-Group_over
moq(2)#1; #2^{#1}
O2 1 1
O-Mult_over
mor{qrw}@s#1#2; {\cdot}^{#1}_{#2}
O3 1 1
O-VectSp_over
hol(2); #1-dimension vector space over #2
O4 0 1
Oaddop
mow#1; \langle{+}_{{#1}_i}\rangle_{i}
O5 0 1
Ocomplop
mow#1; \langle{-}_{{#1}_i}\rangle_{i}
O6 0 1
Ozeros
mow#1; \langle{0}_{{#1}_i}\rangle_{i}
V1 1
VAbGroup-yielding
n Abelian group yielding
#PRVECT_2
M1 2
MMultOps
ha multi-operation #0 of #1 and #2
multi-operations #0 of #1 and #2
M2 0
MRealLinearSpace-Sequence
ha real linear space-sequence #0
real linear space-sequences #0
M3 0
MRealNormSpace-Sequence
ha real norm space-sequence #0
real norm space-sequences #0
O1 0 1
Omultop
mol; \mathop{\rm multop} #1
O2 0 2
Onormsequence
mol#1#2; \mathop{\rm normsequence}(#1,#2)
O3 0 1
Oproductnorm
mol; \mathop{\rm productnorm} #1
V1 1
VRealLinearSpace-yielding
a real-linear-space-yielding
V2 1
VRealNormSpace-yielding
a real-norm-space-yielding
#PSCOMP_1
M1 1
MRealMap
ha real map #0 of #1
real maps #0 of #1
O1 0 1
OW-bound
mol#1; \mathop{\rm W\hbox{-}bound}(#1)
O2 0 1
ON-bound
mol#1; \mathop{\rm N\hbox{-}bound}(#1)
O3 0 1
OE-bound
mol#1; \mathop{\rm E\hbox{-}bound}(#1)
O4 0 1
OS-bound
mol#1; \mathop{\rm S\hbox{-}bound}(#1)
O5 0 1
OSW-corner
mol#1; \mathop{\rm SW\hbox{-}corner}(#1)
O6 0 1
ONW-corner
mol#1; \mathop{\rm NW\hbox{-}corner}(#1)
O7 0 1
ONE-corner
mol#1; \mathop{\rm NE\hbox{-}corner}(#1)
O8 0 1
OSE-corner
mol#1; \mathop{\rm SE\hbox{-}corner}(#1)
O9 0 1
OW-most
mol#1; \mathop{\rm W_{most}}(#1)
O10 0 1
ON-most
mol#1; \mathop{\rm N_{most}}(#1)
O11 0 1
OE-most
mol#1; \mathop{\rm E_{most}}(#1)
O12 0 1
OS-most
mol#1; \mathop{\rm S_{most}}(#1)
O13 0 1
OW-min
mol#1; \mathop{\rm W_{min}}(#1)
O14 0 1
OW-max
mol#1; \mathop{\rm W_{max}}(#1)
O15 0 1
ON-min
mol#1; \mathop{\rm N_{min}}(#1)
O16 0 1
ON-max
mol#1; \mathop{\rm N_{max}}(#1)
O17 0 1
OE-max
mol#1; \mathop{\rm E_{max}}(#1)
O18 0 1
OE-min
mol#1; \mathop{\rm E_{min}}(#1)
O19 0 1
OS-max
mol#1; \mathop{\rm S_{max}}(#1)
O20 0 1
OS-min
mol#1; \mathop{\rm S_{min}}(#1)
V1 1
Vwith_max
x maximum
V2 1
Vwith_min
x minimum
V3 1
Vpseudocompact
a pseudocompact
#PUA2MSS1
M1 1
MIndexedPartition
hn indexed partition #0 of #1
indexed partitions #0 of #1
O1 1 1
O-index_of
hosi#1#2; #1-index of #2
O2 0 1
ODomRel
mol#1; \mathop{\rm DomRel}(#1)
O3 0 1
OLimDomRel
mol#1; \mathop{\rm LimDomRel}(#1)
R1 1 1
Ris_partitable_wrt
i partitable w.r.t. #2
not partitable w.r.t. #2
R2 1 1
Ris_exactly_partitable_wrt
i exactly partitable w.r.t. #2
not exactly partitable w.r.t. #2
R3 2 2
Rform_morphism_between
h #1 and #2 form morphism between #3 and #4
#1 and #2 do not form morphism between #3 and #4
R4 1 1
Ris_rougher_than
i rougher than #2
not rougher than #2
R5 1 1
Rcan_be_characterized_by
h #1 can be characterized by #2
#1 cannot be characterized by #2
R5 1 3
Rcan_be_characterized_by
h #1 can be characterized by #2, #3, and #4
#1 cannot be characterized by #2, #3, and #4
#PYTHTRIP
M1 0
MPythagorean_triple
ha Pythagorean triple #0
Pythagorean triples #0
V1 1
Vsquare
a square
V2 1
Vdegenerate
a degenerate
V3 1
Vsimplified
a simplified
#PZFMISC1
R1 1 1
Ris_transformable_to
i transformable to #2
not transformable to #2
#QC_LANG1
M1 0
MQC-variable
ha variable #0
variables #0
M2 0
MQC-pred_symbol
ha predicate symbol #0
predicate symbols #0
M2 1
MQC-pred_symbol
ha #1-ary predicate symbol #0
#1-ary predicate symbols #0
M3 0
Mbound_QC-variable
ha bound variable #0
bound variables #0
M4 0
Mfixed_QC-variable
ha fixed variable #0
fixed variables #0
M5 0
Mfree_QC-variable
ha free variable #0
free variables #0
M6 1
MQC-variable_list
ha list of variables #0 of the length #1
lists of variables #0 of the length #1
M7 0
MQC-formula
ha formula #0
formulae #0
O1 0 0
OQC-variables
mc; \mathop{\rm Var}
O2 0 0
Obound_QC-variables
mc; \mathop{\rm BoundVar}
O3 0 0
Ofixed_QC-variables
mc; \mathop{\rm FixedVar}
O4 0 0
Ofree_QC-variables
mc; \mathop{\rm FreeVar}
O5 0 0
OQC-pred_symbols
mc; \mathop{\rm PredSym}
O6 1 0
O-ary_QC-pred_symbols
mow/1k#1; {\mathop{\rm PredSym}_{#1}}
O7 0 0
OQC-WFF
mc; \mathop{\rm WFF}
O8 0 1
O@
mok@w; \mathopen{^@} #1
O8 0 2
O@
mok@w#1#2; \mathopen{^@}(#1,#2)
O8 0 3
O@
mol(1)@s/2r@w/3l@w; #1(#2\leftarrow #3)
O8 1 0
O@
moq; #1^{\rm T}
O8 1 1
O@
moi@6; #1{^@}#2
O8 1 2
O@
mow#1#2#3; [\![#1]\!]_{#3}(#2)
O8 2 0
O@
moq{}/2k#1; #2^@
O9 0 0
OVERUM
mc; \mathop{\rm VERUM}
O10 0 1
Othe_pred_symbol_of
mcl@s#1; \mathop{\rm PredSym}(#1)
O11 0 1
Othe_arguments_of
mcl@s#1; \mathop{\rm Args}(#1)
O12 0 1
Ostill_not-bound_in
mcl@s#1; \mathop{\rm snb}(#1)
V1 1
VQC-closed
a closed
#QC_LANG2
O1 0 0
OFALSUM
mc; \mathop{\rm FALSUM}
O2 0 1
Othe_left_disjunct_of
mcl@s#1; \mathop{\rm LeftDisj}(#1)
O3 0 1
Othe_right_disjunct_of
mcl@s#1; \mathop{\rm RightDisj}(#1)
#QC_LANG3
O1 0 1
Oa.
mow/1k#1; {\bf a}_{#1}
O2 0 0
OVars
mol; \mathop{\rm Vars}
O2 0 2
OVars
mcl@s/2k#1#2; \mathop{\rm Vars}_{#2}(#1)
O3 0 1
OFixed
mol@s; \mathop{\rm Fixed} #1
#QC_LANG4
M1 1
MSubformula
ha subformula #0 of #1
subformulae #0 of #1
M2 1
MEntry_Point_in_Subformula_Tree
hn entry point #0 in subformula tree of #1
entry points #0 in subformula tree of #1
O1 0 1
Olist_of_immediate_constituents
hol#1; list of immediate constituents of #1
O2 0 1
Otree_of_subformulae
hol#1; tree of subformulae of #1
O3 1 1
O-entry_points_in_subformula_tree_of
hol(2)#1#2; #1-entry points in subformula tree of #2
O4 0 1
Oentry_points_in_subformula_tree
hol#1; entry points in subformula tree of #1
#QMAX_1
G1 3
GQM_Str
mc#1#2#3; \langle #1, #2, #3\rangle
G2 3
GOrthoRelStr
mc#1#2#3; \langle #1,#2,#3 \rangle
J1 1
GQM_Str
hol#1; quantum mechanics structure of #1
J2 1
GOrthoRelStr
hol#1; OrthoRelStr of #1
L1 0
GQM_Str
ha quantum mechanics structure #0
quantum mechanics structures #0
L2 0
GOrthoRelStr
hn orthorelational structure #0
orthorelational structures #0
M1 0
MQuantum_Mechanics
ha quantum mechanics #0
quantum mechanics' #0
O1 0 1
OProbabilities
mol@s; \mathop{\rm probabilities} #1
O2 0 1
OObs
mol@s; \mathop{\rm Obs} #1
O3 0 1
OSts
mol@s; \mathop{\rm Sts} #1
O4 0 2
OMeas
mcl@s#1#2; \mathop{\rm Meas}( #1, #2)
O5 0 1
OProp
mol@s; \mathop{\rm Prop} #1
O6 0 1
OPropRel
mol@s; \mathop{\rm PropRel} #1
O7 0 1
OOrdRel
mol@s; \mathop{\rm OrdRel} #1
O8 0 1
OInvRel
mol@s; \mathop{\rm InvRel} #1
R1 1 0
Ris_an_involution
i an involution in #2
not an involution in #2
R2 1 0
Ris_a_Quantum_Logic
i a quantum logic on #2
not a quantum logic on #2
U1 1
UObservables
hopl#1; observables of #1
observables
U2 1
UStates
hopl#1; control states of #1
control states
U3 1
UQuantum_Probability
hosl#1; probability of #1
probability
V1 1
VQuantum_Mechanics-like
a quantum mechanics-like
#QUANTAL1
G1 4
GQuantaleStr
mc#1#2#3#4; \langle #1,#2,#3,#4 \rangle
G2 5
GQuasiNetStr
mc#1#2#3#4#5; \langle #1,#2,#3,#4,#5 \rangle
G3 6
GGirard-QuantaleStr
mc#1#2#3#4#5#6; \langle #1,#2,#3,#4,#5,#6 \rangle
J1 1
GQuantaleStr
hol#1; quantale structure of #1
J2 1
GQuasiNetStr
hol#1; quasinet structure of #1
J3 1
GGirard-QuantaleStr
hol#1; Girard quantale structure of #1
L1 0
GQuantaleStr
ha quantale structure #0
quantale structures #0
L2 0
GQuasiNetStr
ha quasinet structure #0
quasinet structures #0
L3 0
GGirard-QuantaleStr
ha Girard quantale structure #0
Girard quantale structures #0
M1 0
MQuantale
ha quantale #0
quantales #0
M2 0
MQuasiNet
ha quasinet #0
quasinets #0
M3 0
MBlikleNet
ha Blikle net #0
Blikle nets #0
M4 0
MGirard-Quantale
ha Girard quantale #0
Girard quantales #0
O1 1 1
O-r>
mox@a; #1 \to_r #2
O2 1 1
O-l>
mox@a; #1 \to_l #2
O3 0 1
ONegation
mol#1; \mathop{\rm Negation}(#1)
U1 1
Uabsurd
honl#1; absurd of #1
absurd
V1 1
Vwith_left-zero
x left-zero
V2 1
Vwith_right-zero
x right-zero
V3 1
Vwith_zero
x zero
V4 1
Vtimes-additive
a \ox-additive
V5 1
Vtimes-continuous
a \ox-continuous
V6 1
Vinflationary
n inflationary
V7 1
Vdeflationary
a deflationary
V8 1
Vtimes-monotone
a \ox-monotone
V9 1
Vdualizing
a dualizing
V10 1
Vdualized
a dualized
#QUATERN2
O1 0 0
Ocompquaternion
mow; \mathop{\rm compl}_{\mathbb H}
O2 0 0
Oaddquaternion
mow; +_{\mathbb H}
O3 0 0
Odiffquaternion
mow; -_{\mathbb H}
O4 0 0
Omultquaternion
mow; \cdot_{\mathbb H}
O5 0 0
Odivquaternion
mow; /_{\mathbb H}
O6 0 0
Oinvquaternion
mo; {{}^{-1}_{\mathbb H}}
O7 0 0
OG_Quaternion
mow; {\mathbb H}_{\rm G}
O8 0 0
OR_Quaternion
mow; {\mathbb H}_{\rm R}
#QUATERNI
O1 0 0
OQUATERNION
mol; \mathop{\mathbb H}
O2 0 0
O<j>
mo@7; j
O3 0 0
O<k>
mo@7; k
O4 0 1
ORea
mol#1; \Re(#1)
O5 0 1
OIm1
mol#1; \Im_1(#1)
O6 0 1
OIm2
mol#1; \Im_2(#1)
O7 0 1
OIm3
mol#1; \Im_3(#1)
O8 0 0
O0q
mow; 0_{\mathbb H}
O9 0 0
O1q
mow; 1_{\mathbb H}
V1 1
Vquaternion
a quaternion
#QUOFIELD
O1 0 1
OQ.
mosl#1; \mathop{\rm Q}(#1)
O2 0 2
Opadd
moi; #1+#2
O3 0 2
Opmult
moi; #1\cdot #2
O4 0 1
OQClass.
mosl#1; \mathop{\rm QClass}(#1)
O5 0 1
OQuot.
mosl#1; \mathop{\rm Quot}(#1)
O6 0 2
Oqadd
moi; #1 +_{\rm q} #2
O7 0 2
Oqmult
moi; #1 \cdot_{\rm q} #2
O8 0 1
Oq0.
mol#1; 0_{\rm q}(#1)
O9 0 1
Oq1.
mol#1; 1_{\rm q}(#1)
O10 0 1
Oqaddinv
mol; -_{\rm q} #1
O11 0 1
Oqmultinv
moq; {#1}^{-1}_{\rm q}
O12 0 1
Oquotadd
mol#1; +_{\rm q}(#1)
O13 0 1
Oquotmult
mol#1; \cdot_{\rm q}(#1)
O14 0 1
Oquotaddinv
mol#1; -_{\rm q}(#1)
O15 0 1
Oquotmultinv
mol#1; {}^{-1}_{\rm q}(#1)
O16 0 1
Othe_Field_of_Quotients
hol#1; field of quotients of #1
O17 0 1
OcanHom
hosl#1; canonical homomorphism of #1 into quotient field
R1 1 1
Ris_embedded_in
h #1 is embedded in #2
#1 is not embedded in #2
R2 1 1
Ris_ringisomorph_to
h #1 is ring isomorphic to #2
#1 is not ring isomorphic to #2
R3 1 2
Rhas_Field_of_Quotients_Pair
h #2 is a field of quotients for #1 via #3
#2 is not a field of quotients for #1 via #3
V1 1
VRingHomomorphism
ax ring homomorphism
V2 1
VRingEpimorphism
ax ring epimorphism
V3 1
VRingMonomorphism
ax ring monomorphism
V4 1
Vembedding
nx embedding
V5 1
VRingIsomorphism
ax ring isomorphism
#RADIX_1
O1 0 1
ORadix
mol; \mathop{\rm Radix} #1
O2 1 0
O-SD
mor; #1 \mathop{\rm -SD}
O3 0 2
ODigA
mol#1#2; \mathop{\rm DigA}(#1,#2)
O4 0 2
ODigB
mol#1#2; \mathop{\rm DigB}(#1,#2)
O5 0 3
OSubDigit
mol#1#2#3; \mathop{\rm SubDigit}(#1,#2,#3)
O6 0 1
ODigitSD
mol#1; \mathop{\rm DigitSD} #1
O7 0 1
OSDDec
mol#1; \mathop{\rm SDDec} #1
O8 0 3
ODigitDC
mol#1#2#3; \mathop{\rm DigitDC}(#1,#2,#3)
O9 0 3
ODecSD
mol#1#2#3; \mathop{\rm DecSD}(#1,#2,#3)
O10 0 1
OSD_Add_Carry
mol#1; \mathop{\rm SD\_Add\_Carry} #1
O11 0 2
OSD_Add_Data
mol#1#2; \mathop{\rm SD\_Add\_Data}(#1,#2)
O12 0 4
OAdd
mol#1#2#3#4; \mathop{\rm Add}(#1,#2,#3,#4)
O13 1 1
O'+'
moi#1#2; #1 '+' #2
R1 1 2
Ris_represented_by
h #1 is represented by #2,#3
#1 is not represented by #2,#3
#RADIX_2
O1 0 3
OSubDigit2
mol#1#2#3; \mathop{\rm SubDigit2}(#1,#2,#3)
O2 0 2
ODigitSD2
mol#1#2; \mathop{\rm DigitSD2}(#1,#2)
O3 0 2
OSDDec2
mol#1#2; \mathop{\rm SDDec2}(#1,#2)
O4 0 3
ODigitDC2
mol#1#2#3; \mathop{\rm DigitDC2}(#1,#2,#3)
O5 0 3
ODecSD2
mol#1#2#3; \mathop{\rm DecSD2}(#1,#2,#3)
O6 0 4
OTable1
mol#1#2#3#4; \mathop{\rm Table1}(#1,#2,#3,#4)
O7 0 4
OMul_mod
mol#1#2#3#4; \mathop{\rm Mul\_mod}(#1,#2,#3,#4)
O8 0 4
OTable2
mol#1#2#3#4; \mathop{\rm Table2}(#1,#2,#3,#4)
O9 0 4
OPow_mod
mol#1#2#3#4; \mathop{\rm Pow\_mod}(#1,#2,#3,#4)
#RADIX_3
O1 1 0
O-SD_Sub_S
mor; #1 \mathop{\rm -SD\_Sub\_S}
O2 1 0
O-SD_Sub
mor; #1 \mathop{\rm -SD\_Sub}
O3 0 2
OSDSub_Add_Carry
mol#1#2; \mathop{\rm SDSubAddCarry}(#1,#2)
O4 0 2
OSDSub_Add_Data
mol#1#2; \mathop{\rm SDSubAddData}(#1,#2)
O5 0 2
ODigA_SDSub
mol#1#2; \mathop{\rm DigA\_SDSub}(#1,#2)
O6 0 3
OSD2SDSubDigit
mol#1#2#3; \mathop{\rm SD2SDSubDigit}(#1,#2,#3)
O7 0 3
OSD2SDSubDigitS
mol#1#2#3; \mathop{\rm SD2SDSubDigitS}(#1,#2,#3)
O8 0 1
OSD2SDSub
mol; \mathop{\rm SD2SDSub} #1
O9 0 2
ODigB_SDSub
mol#1#2; \mathop{\rm DigB\_SDSub}(#1,#2)
O10 0 3
OSDSub2INTDigit
mol#1#2#3; \mathop{\rm SDSub2INTDigit}(#1,#2,#3)
O11 0 1
OSDSub2INT
mol#1; \mathop{\rm SDSub2INT} #1
O12 0 1
OSDSub2IntOut
mol#1; \mathop{\rm SDSub2IntOut} #1
#RADIX_4
O1 0 4
OSDSubAddDigit
mol#1#2#3#4; \mathop{\rm SDSubAddDigit}(#1,#2,#3,#4)
#RADIX_5
O1 0 3
OSDMinDigit
mol#1#2#3; \mathop{\rm SDMinDigit}(#1,#2,#3)
O2 0 3
OSDMin
mol#1#2#3; \mathop{\rm SDMin}(#1,#2,#3)
O3 0 3
OSDMaxDigit
mol#1#2#3; \mathop{\rm SDMaxDigit}(#1,#2,#3)
O4 0 3
OSDMax
mol#1#2#3; \mathop{\rm SDMax}(#1,#2,#3)
O5 0 3
OFminDigit
mol#1#2#3; \mathop{\rm FminDigit}(#1,#2,#3)
O6 0 3
OFmin
mol#1#2#3; \mathop{\rm Fmin}(#1,#2,#3)
O7 0 3
OFmaxDigit
mol#1#2#3; \mathop{\rm FmaxDigit}(#1,#2,#3)
O8 0 3
OFmax
mol#1#2#3; \mathop{\rm Fmax}(#1,#2,#3)
#RADIX_6
O1 0 2
OM0Digit
mol#1#2; \mathop{\rm M0Digit}(#1,#2)
O2 0 1
OM0
mol#1; \mathop{\rm M0}(#1)
O3 0 2
OMmaxDigit
mol#1#2; \mathop{\rm MmaxDigit}(#1,#2)
O4 0 1
OMmax
mol#1; \mathop{\rm Mmax}(#1)
O5 0 2
OMminDigit
mol#1#2; \mathop{\rm MminDigit}(#1,#2)
O6 0 1
OMmin
mol#1; \mathop{\rm Mmin}(#1)
O7 0 2
OMmaskDigit
mol#1#2; \mathop{\rm MmaskDigit}(#1,#2)
O8 0 1
OMmask
mol#1; \mathop{\rm Mmask}(#1)
O9 0 3
OFSDMinDigit
mol#1#2#3; \mathop{\rm FSDMinDigit}(#1,#2,#3)
O10 0 3
OFSDMin
mol#1#2#3; \mathop{\rm FSDMin}(#1,#2,#3)
R1 1 2
Rneeds_digits_of
h #1 needs digits of #2,#3
#1 does not need digits of #2,#3
R2 1 1
Ris_Zero_over
i zero over #2
not zero over #2
#RAMSEY_1
O1 1 1
O||^
moi; #1 ||^ #2
R1 1 1
Ris_homogeneous_for
i homogeneous for #2
!not homogeneous for #2
#RANDOM_1
M1 1
MReal-Valued-Random-Variable
ha real-valued random variable #0 of #1
real-valued random variables #0 of #1
O1 0 1
OTrivial-SigmaField
hol; trivial $\sigma$-field of #1
O2 0 1
OTrivial-Probability
hol; trivial probability of #1
O3 0 2
Oexpect
mol#1#2; E_{#2}\{#1\}
#RANDOM_2
O1 0 2
Ovariance
mol#1#2; \mathop{\rm variance}(#1,#2)
O2 0 1
OReal-Valued-Random-Variables-Set
mol; \mathop{\rm Real-Valued-Random-Variables-Set} #1
O3 0 1
OR_Algebra_of_Real-Valued-Random-Variables
hol; r algebra of real-valued-random-variables #1
O4 0 4
OProduct-Probability
mol#1#2#3#4; \mathop{\rm Product-Probability}(#1,#2,#3,#4)
#RANKNULL
M1 2
Mlinear-transformation
ha linear transformation #0 from #1 to #2
linear transformations #0 from #1 to #2
O1 0 1
Oim
mol; \mathop{\rm im} #1
O2 0 1
Orank
mol; \mathop{\rm rank} #1
O3 0 1
Onullity
mol; \mathop{\rm nullity} #1
#RAT_1
M1 0
MRational
ha rational number #0
rational numbers #0
V1 1
Vrational
a rational
#RCOMP_1
M1 1
MNeighbourhood
ha neighbourhood #0 of #1
neighbourhoods #0 of #1
V1 1
Vcompact
a compact
V2 1
Vclosed
a closed
V3 1
Vopen
n open
#RCOMP_3
M1 1
MIntervalCover
hn interval cover #0 of #1
interval covers #0 of #1
M2 1
MIntervalCoverPts
ha chain #0 of rivets in interval cover #1
chains #0 of rivets in interval cover #1
#REALSET1
M1 1
MPreserv
ha set #0 closed w.r.t. #1
sets #0 closed w.r.t. #1
M2 2
MPresv
ha binary operation #0 of #1 preserving #2
binary operations #0 of #1 preserving #2
M3 2
MDnT
ha binary operation #0 of #2 preserving #2 $\setminus$ \{#1\}
binary operations #0 of #2 preserving #2 $\setminus$ \{#1\}
M4 1
MOnePoint
hn one-element subset #0 of #1
one-element subsets #0 of #1
O1 1 1
O||
moi@m; #1 \restriction #2
O2 1 1
O|||
moi@m; #1 \restriction #2
O3 1 0
O!
mor@s; #1!
O3 1 1
O!
mor@s#2; #1 \lbrack #2 \rbrack
O3 1 2
O!
moi(1,2)@m/3k#3; #1 \restriction_{#3} #2
R1 1 1
Ris_in
i in #2
not in #2
R2 1 1
Ris_Bin_Op_Preserv
i binary operation preserving #2
not binary operation preserving #2
#REALSET2
O1 0 0
Oadd_2
mol; +_{{\mathbb Z}_2}
O2 0 0
Omult_2
mol; \cdot_{{\mathbb Z}_2}
O3 0 0
OdL-Z_2
mol; {\mathbb Z_2}
O4 0 1
Oomf
mow/1k#1; {\bf \cdot}_{#1}
O5 0 1
Orevf
mo{kqmw}@s#1; {^{-1}_{#1}}
V1 1
VField-like
a field-like
#REALSET3
O1 0 1
Oosf
mol@s; \mathop{\rm osf} #1
O2 0 1
Oovf
mol@s; \mathop{\rm ovf} #1
#REAL_1
M1 0
MReal
ha real number #0
real numbers #0
#REAL_3
M1 0
MInteger_Sequence
hn integer sequence #0
integer sequences #0
O1 0 2
OmodSeq
mol#1#2; \mathop{\rm modSeq}(#1,#2)
O2 0 2
OdivSeq
mol#1#2; \mathop{\rm divSeq}(#1,#2)
O3 0 1
Oremainders_for_scf
hol; remainders for s.c.f. of #1
O4 0 1
Orfs
mol; \mathop{\rm rfs} #1
O5 0 1
OSimpleContinuedFraction
hol; simple continued fraction of #1
O6 0 1
Oscf
mol; \mathop{\rm scf} #1
O7 0 1
Oconvergent_numerators
hol; convergent numerators of #1
O8 0 1
Oconvergent_denominators
hol; convergent denominators of #1
O9 0 1
Oc_n
mol; \mathop{cn} #1
O10 0 1
Oc_d
mol; \mathop{cd} #1
O11 0 1
Oconvergents_of_continued_fractions
hol; convergents of continued fractions of #1
O12 0 1
Ococf
mol; \mathop{\rm cocf} #1
O13 0 1
ObackContinued_fraction
hol; back continued fraction of #1
O14 0 1
Obcf
mol; \mathop{\rm bcf} #1
V1 1
Vinteger-yielding
n integer-yielding
#REAL_LAT
O1 0 0
Ominreal
mow; \mathop{\rm min}_{\mathbb R}
O2 0 0
Omaxreal
mow; \mathop{\rm max}_{\mathbb R}
O3 0 0
OReal_Lattice
mow; {\mathbb R}_{\rm L}
O4 0 1
Omaxfuncreal
mow/1m#1; \mathop{\bf max}_{{\mathbb R}^{#1}}
O5 0 1
Ominfuncreal
mow/1m#1; \mathop{\bf min}_{{\mathbb R}^{#1}}
O6 0 1
ORealFunc_Lattice
mcr@s/1m#1; {\mathbb R}_{\rm L}^{#1}
#REAL_NS1
O1 0 1
OEuclid_add
mow#1; +_{{\cal E}^{#1}}
O2 0 1
OEuclid_mult
mow#1; \cdot_{{\cal E}^{#1}}
O3 0 1
OEuclid_norm
mow#1; \Vert\cdot\Vert_{{\cal E}^{#1}}
O4 0 1
OREAL-NS
mc; \langle{\cal E}^{#1},\Vert\cdot\Vert\rangle
O5 0 1
OEuclid_scalar
mow#1; \otimes_{{\cal E}^{#1}}
O6 0 1
OREAL-US
mc; \langle{\cal E}^{#1},(\cdot\vert\cdot)\rangle
#REARRAN1
M1 1
MRearrangmentGen
ha rearrangement generator #0 of #1
rearrangement generators #0 of #1
O1 0 1
OCo_Gen
mol#1; \mathop{\rm co\hbox{-}Gen}(#1)
O2 0 2
ORland
mol{qrw}#2; #1_{#2}^\land
O3 0 2
ORlor
mol{qrw}#2; #1_{#2}^\lor
V1 1
Vterms've_same_card_as_number
w cardinality by index
V2 1
Vascending
n ascending
V3 1
Vlenght_equal_card_of_set
w length by cardinality
#RECDEF_2
O1 1 0
O`1_3
mow; {#1_{{\bf 1},3}}
O2 1 0
O`2_3
mow; {#1_{{\bf 2},3}}
O3 1 0
O`3_3
mow; {#1_{{\bf 3},3}}
O4 1 0
O`1_4
mow; {#1_{{\bf 1},4}}
O5 1 0
O`2_4
mow; {#1_{{\bf 2},4}}
O6 1 0
O`3_4
mow; {#1_{{\bf 3},4}}
O7 1 0
O`4_4
mow; {#1_{{\bf 4},4}}
O8 1 0
O`1_5
mow; {#1_{{\bf 1},5}}
O9 1 0
O`2_5
mow; {#1_{{\bf 2},5}}
O10 1 0
O`3_5
mow; {#1_{{\bf 3},5}}
O11 1 0
O`4_5
mow; {#1_{{\bf 4},5}}
O12 1 0
O`5_5
mow; {#1_{{\bf 5},5}}
#RELAT_1
M1 0
MRelation
ha binary relation #0
binary relations #0
M1 1
MRelation
ha binary relation #0 on #1
binary relations #0 on #1
M1 2
MRelation
ha relation #0 between #1 and #2
relations #0 between #1 and #2
O1 0 0
Oproj1
mc; \mathop{\rm proj1}
O1 0 1
Oproj1
mcl@s#1; \pi_1(#1)
O2 0 1
Odom
mol@s; \mathop{\rm dom} #1
O2 1 1
Odom
moi; #1 \mathop{\rm dom} #2
O3 0 0
Oproj2
mc; \mathop{\rm proj2}
O3 0 1
Oproj2
mcl@s#1; \pi_2(#1)
O4 0 1
Orng
mol@s; \mathop{\rm rng} #1
O5 0 1
Ofield
mol@s; \mathop{\rm field} #1
O5 0 2
Ofield
mcl@s#1#2; {\rm field}(#1,#2)
O6 0 1
O~
mol@s; \mathopen{\curvearrowleft} #1
O6 1 0
O~
moq; #1 \mathclose{^\smallsmile}
O6 1 1
O~
moi#1#2; #1{\sim}#2
O7 0 0
O*
mc; \ast
O7 0 1
O*
moi@m; \cdot #1
O7 0 2
O*
mol#1#2; \mathopen{\cdot} (#1,#2)
O7 1 0
O*
moq; {{#1}^\ast}
O7 1 1
O*
moi@m; #1 \cdot #2
O7 1 2
O*
mow/1r@s#2#3; #1_{#2,#3}
O8 0 1
Oid
mow/1k#1; \mathord{\rm id}_{#1}
O8 0 2
Oid
mol#1#2; \mathord{\rm id}(#1,#2)
O8 0 3
Oid
mol#1#2#3; \mathop{\rm id}(#1,#2,#3)
O9 1 1
O|
moi@m; #1{\upharpoonright}#2
O9 1 2
O|
moi#2#3; #1 {\upharpoonright}(#2,#3)
O9 1 3
O|
moi@m#3#4; #1{\upharpoonright}_{(#3,#4)}#2
O10 0 1
O.:
mok; {{}^\circ}#1
O10 0 2
O.:
moq#2; #1^{#2}
O10 1 0
O.:
moq; #1^\circ
O10 1 1
O.:
moi@s/1q/2k; #1 ^\circ #2
O10 1 2
O.:
mo@s/1q#2#3; #1^\circ (#2,\allowbreak\,#3)
O10 2 1
O.:
mor(1){qrw}@s/1q#3; #1^\circ_{#3}
O11 0 1
O"
mok; {^{-1}}#1
O11 1 0
O"
moq; #1 \mathclose{^{-1}}
O11 1 1
O"
moi@s/1q/2k#2; #1{^{-1}}(#2)
O12 0 1
OIm
mcl@s#1; \Im(#1)
O12 0 2
OIm
moi@s/1q/2k; #1 ^\circ #2
O13 0 2
OCoim
mol#1#2; \mathop{\rm Coim}(#1,#2)
V1 1
VRelation-like
a relation-like
V2 1
Vnon-empty
a non-empty
V3 1
Vempty-yielding
n empty yielding
V4 2
V-defined
a #1-defined
V5 2
V-valued
a #1-valued
#RELAT_2
R1 1 1
Ris_reflexive_in
i reflexive in #2
not reflexive in #2
R2 1 1
Ris_irreflexive_in
i irreflexive in #2
not irreflexive in #2
R3 1 1
Ris_symmetric_in
i symmetric in #2
not symmetric in #2
R4 1 1
Ris_antisymmetric_in
i antisymmetric in #2
not antisymmetric in #2
R5 1 1
Ris_asymmetric_in
i asymmetric in #2
not asymmetric in #2
R6 1 1
Ris_connected_in
i connected in #2
not connected in #2
R7 1 1
Ris_strongly_connected_in
i strongly connected in #2
not strongly connected in #2
R8 1 1
Ris_transitive_in
i transitive in #2
not transitive in #2
V1 1
Vreflexive
a reflexive
V2 1
Virreflexive
n irreflexive
V3 1
Vsymmetric
a symmetric
V4 1
Vantisymmetric
n antisymmetric
V5 1
Vasymmetric
n asymmetric
V6 1
Vconnected
a connected
V7 1
Vstrongly_connected
a strongly connected
V8 1
Vtransitive
a transitive
#RELOC
O1 0 2
OReloc
mol#1#2; \mathop{\rm Reloc}(#1,#2)
#RELSET_2
K1 1 L1 vRELSET_2
K{_{
L}_}
mc@3#1; \{\{\ast\}:\ast\in#1\}
O1 1 1
O.:^
mol/1r#2; #1[#2]
#REWRITE1
M1 1
MRedSequence
ha reduction sequence #0 w.r.t. #1
reduction sequences #0 w.r.t. #1
M2 1
MCompletion
ha completion #0 of #1
completions #0 of #1
O1 1 1
O$^
moi@m/1q/2k; #1 \mathbin{^{\$\smallfrown}} #2
O2 0 2
Onf
mol#1#2; \mathop{\rm nf}_{#2}(#1)
R1 1 2
Rreduces
h #1 reduces #2 to #3
#1 does not reduce #2 to #3
R2 2 1
Rare_convertible_wrt
h #1 and #2 are convertible w.r.t. #3
#1 and #2 are not convertible w.r.t. #3
R3 1 1
Ris_a_normal_form_wrt
i a normal form w.r.t. #2
not a normal form w.r.t. #2
R4 1 2
Ris_a_normal_form_of
i a normal form of #2 w.r.t. #3
not a normal form of #2 w.r.t. #3
R5 2 1
Rare_convergent_wrt
h #1 and #2 are convergent w.r.t. #3
#1 and #2 are not convergent w.r.t. #3
R6 2 1
Rare_divergent_wrt
h #1 and #2 are divergent w.r.t. #3
#1 and #2 are not divergent w.r.t. #3
R7 2 1
Rare_convergent<=1_wrt
h #1 and #2 are convergent at most in 1 step w.r.t. #3
#1 and #2 are not convergent at most in 1 step w.r.t. #3
R8 2 1
Rare_divergent<=1_wrt
h #1 and #2 are divergent at most in 1 step w.r.t. #3
#1 and #2 are not divergent at most in 1 step w.r.t. #3
R9 1 1
Rhas_a_normal_form_wrt
h #1 has a normal form w.r.t. #2
#1 has not a normal form w.r.t. #2
R10 1 1
Rcommutes-weakly_with
h #1 commutes-weakly with #2
#1 does not commute-weakly with #2
R11 1 1
Rcommutes_with
h #1 commutes with #2
#1 does not commute with #2
R12 2 0
Rare_equivalent
h #1 and #2 are equivalent
#1 and #2 are not equivalent
R13 2 1
Rare_critical_wrt
h #1 and #2 are critical w.r.t. #3
#1 and #2 are not critical w.r.t. #3
V1 1
Vco-well_founded
a reversely well founded
V2 1
Vweakly-normalizing
a weakly-normalizing
V3 1
Vstrongly-normalizing
a strongly-normalizing
V4 1
Vwith_UN_property
x unique normal form property
V5 1
Vwith_NF_property
x normal form property
V6 1
Vsubcommutative
a subcommutative
V7 1
Vconfluent
a confluent
V8 1
Vwith_Church-Rosser_property
x Church-Rosser property
V9 1
Vlocally-confluent
a locally-confluent
V10 1
Vcomplete
a complete
#REWRITE2
M1 1
Msemi-Thue-system
ha semi-Thue-system #0 of #1
semi-Thue-systems #0 of #1
M2 1
MThue-system
ha Thue-system #0 of #1
Thue-systems #0 of #1
O1 1 1
O^+
moi@a; #1+#2
O2 0 1
O==>.-relation
moq#1; {\Rightarrow_{#1}}
R1 1 2
R-->.
m #1 \rightarrow_{#3} #2
#1 \not\rightarrow_{#3} #2
R1 2 2
R-->.
m #1,#2 \rightarrow_{#4} #3
#1,#2 \not\rightarrow_{#4} #3
R2 1 2
R==>*
m #1 \Rightarrow^\ast_{#3} #2
#1 \not\Rightarrow^\ast_{#3} #2
R2 2 2
R==>*
m #1,#2 \Rightarrow^\ast_{#4} #3
#1,#2 \not\Rightarrow^\ast_{#4} #3
R2 2 3
R==>*
m #1,#2 \Rightarrow^\ast_{#5} #3,#4
#1,#2 \not\Rightarrow^\ast_{#5} #3,#4
V1 1
VXFinSequence-yielding
a finite-0-sequence-yielding
#REWRITE3
G1 2
Gtransition-system
mc#1#2; \langle #1,#2 \rangle
J1 1
Gtransition-system
hol#1; transition-system of #1
L1 1
Gtransition-system
ha transition-system #0 over #1
transition-systems #0 over #1
O1 0 2
Odim2
mol#1#2; \mathop{\rm dim}_2(#1,#2)
V1 1
Vdeterministic
a deterministic
#RFINSEQ
O1 1 1
O/^
mow(1)#2; #1_{\downharpoonright #2}
O2 0 1
OMIM
mol@s#1; {\rm MIM}(#1)
#RFINSEQ2
O1 0 1
Omax_p
mol@s; \mathop{\rm max_p} #1
O2 0 1
Omin_p
mol@s; \mathop{\rm min_p} #1
O3 0 1
Osort_d
mol@s; \mathop{\rm sort_d} #1
O4 0 1
Osort_a
mol@s; \mathop{\rm sort_a} #1
#RFUNCT_3
M1 2
MPartFunc-set
ha set #0 of partial functions from #1 to #2
sets #0 of partial functions from #1 to #2
M2 2
MPFUNC_DOMAIN
ha non empty set #0 of partial functions from #1 to #2
non empty sets #0 of partial functions from #1 to #2
O1 0 1
Omax+
mol@s#1; \mathop{\rm max}_+(#1)
O2 0 1
Omax-
mol@s#1; \mathop{\rm max}_-(#1)
O3 0 1
Oaddpfunc
mow#1; +_{#1\dot\to{\mathbb R}}
O4 0 2
OCHI
mol@s#1#2; {\rm CHI}(#1,#2)
O5 0 2
OFinS
mol@s#1#2; {\rm FinS}(#1,#2)
R1 1 1
Ris_common_for_dom
h #1 is common for dom #2
#1 is not common for dom #2
R2 1 1
Ris_convex_on
h #1 is convex on #2
#1 is not convex on #2
#RFUNCT_4
R1 1 1
Ris_strictly_convex_on
h #1 is strictly convex on #2
#1 is not strictly convex on #2
R2 1 1
Ris_quasiconvex_on
h #1 is quasiconvex on #2
#1 is not quasiconvex on #2
R3 1 1
Ris_strictly_quasiconvex_on
h #1 is strictly quasiconvex on #2
#1 is not strictly quasiconvex on #2
R4 1 1
Ris_strongly_quasiconvex_on
h #1 is strongly quasiconvex on #2
#1 is not strongly quasiconvex on #2
R5 1 1
Ris_upper_semicontinuous_in
h #1 is upper semicontinuous in #2
#1 is not upper semicontinuous in #2
R6 1 1
Ris_upper_semicontinuous_on
h #1 is upper semicontinuous on #2
#1 is not upper semicontinuous on #2
R7 1 1
Ris_lower_semicontinuous_in
h #1 is lower semicontinuous in #2
#1 is not lower semicontinuous in #2
R8 1 1
Ris_lower_semicontinuous_on
h #1 is lower semicontinuous on #2
#1 is not lower semicontinuous on #2
#RINFSUP1
O1 0 1
Oinferior_realsequence
hol; inferior realsequence #1
O2 0 1
Osuperior_realsequence
hol; superior realsequence #1
#RINGCAT1
G1 3
GRingMorphismStr
mc#1#2#3; \langle #1, #2, #3\rangle
J1 1
GRingMorphismStr
hol#1; ring morphisms structure of #1
L1 0
GRingMorphismStr
ha ring morphisms structure #0
ring morphisms structures #0
M1 0
MRingMorphism
ha morphism #0 of rings
morphisms #0 of rings
M2 0
MRing_DOMAIN
ha non empty set #0 of rings
non empty sets #0 of rings
M3 0
MRingMorphism_DOMAIN
ha non empty set #0 of morphisms of rings
non empty sets #0 of morphisms of rings
M3 2
MRingMorphism_DOMAIN
ha non empty set #0 of morphisms from #1 into #2
non empty sets #0 of morphisms from #1 into #2
O1 0 1
ORingObjects
mol@s#1; \mathop{\rm RingObj}(#1)
O2 0 1
ORingCat
mol@s#1; \mathop{\rm RingCat}(#1)
V1 1
VRingMorphism-like
a morphism of rings-like
V2 1
VRing_DOMAIN-like
a non empty set of rings-like
V3 1
VRingMorphism_DOMAIN-like
a non empty set of morphisms of rings-like
#RING_1
O1 0 2
OQuotientRing
mol#1#2; {}^{\textstyle #1}\!/\!_{\textstyle #2}
V1 1
Vquasi-prime
a quasi-prime
V2 1
Vquasi-maximal
a quasi-maximal
#RLAFFIN1
O1 0 1
OAffin
mol; \mathop{\rm Affin} #1
V1 1
Vaffinely-independent
n affinely independent
#RLAFFIN2
O1 0 1
Ocenter_of_mass
hol; center of mass #1
#RLSUB_1
M1 1
MSubspace
ha subspace #0 of #1
subspaces #0 of #1
M2 1
MCoset
ha coset #0 of #1
cosets #0 of #1
O1 0 1
O(0).
mow/1k#1; {{\bf 0}_{#1}}
O2 0 1
O(Omega).
mow/1k#1; {\Omega_{#1}}
V1 1
Vlinearly-closed
a linearly closed
#RLSUB_2
M1 1
MLinear_Compl
ha linear complement #0 of #1
linear complements #0 of #1
O1 0 1
OSubspaces
mol@s; \mathop{\rm Subspaces} #1
O2 0 1
OSubJoin
mol@s; \mathop{\rm SubJoin} #1
O3 0 1
OSubMeet
mol@s; \mathop{\rm SubMeet} #1
R1 1 2
Ris_the_direct_sum_of
i the direct sum of #2 and #3
not the direct sum of #2 and #3
#RLTOPSP1
G1 5
GRLTopStruct
mc#1#2#3#4#5; \langle #1,#2,#3,#4,#5 \rangle
J1 1
GRLTopStruct
hol#1; real linear topological structure of #1
L1 0
GRLTopStruct
ha real linear topological structure #0
real linear topological structures #0
M1 0
MLinearTopSpace
ha linear topological space #0
linear topological spaces #0
M2 1
Mlocal_base
ha local base #0 of #1
local bases #0 of #1
O1 0 2
OLSeg
mol@s#1#2; {\cal L}(#1,#2)
O2 0 2
Otransl
mol#1#2; \mathop{\rm transl}(#1,#2)
O2 0 4
Otransl
mor#2#3#4; #1^{#4}_{#2}(#3,-)
V1 1
Vconvex-membered
a convex-membered
V2 1
Vcircled
a circled
V3 1
Vcircled-membered
a circled-membered
V4 1
Vadd-continuous
n add-continuous
V5 1
VMult-continuous
a mult-continuous
V6 1
Vlocally-convex
a locally-convex
#RLVECT_1
G1 4
GRLSStruct
mc#1#2#3#4; \langle #1, #2, #3, #4\rangle
J1 1
GRLSStruct
hol#1; RLS structure of #1
L1 0
GRLSStruct
hn RLS structure #0
RLS structures #0
M1 1
MVECTOR
ha vector #0 of #1
vectors #0 of #1
M2 0
MRealLinearSpace
ha real linear space #0
real linear spaces #0
O1 0 0
OTrivial-RLSStruct
mol; \mathop{\rm Trivial\hbox{-}RLSStruct}
U1 1
UMult
honl#1; external multiplication of #1
external multiplication
V1 1
VAbelian
n Abelian
V2 1
Vadd-associative
n add-associative
V3 1
Vright_zeroed
a right zeroed
V5 1
Vscalar-distributive
a scalar distributive
V6 1
Vvector-distributive
a vector distributive
V7 1
Vscalar-associative
a scalar associative
V8 1
Vscalar-unital
a scalar unital
#RLVECT_2
M1 1
MLinear_Combination
ha linear combination #0 of #1
linear combinations #0 of #1
O1 0 2
Ovector
moq(2)/1m#1; #2^{#1}
O2 0 1
OCarrier
hol@w; support of #1
O2 0 2
OCarrier
mol#1#2; \mathop{\rm Carrier}(#1,#2)
O3 0 1
OZeroLC
mow/1k#1; {\bf 0}_{{\rm LC}_{#1}}
O4 0 1
OLinComb
mow/1k#1; \mathop{\rm LC}_{#1}
O5 0 1
OLCAdd
mow/1k#1; {+}_{{\rm LC}_{#1}}
O6 0 1
OLCMult
mow/1k#1; {\cdot}_{{\rm LC}_{#1}}
O7 0 1
OLC_RLSpace
mow/1k#1; {\mathbb L\mathbb C}_{#1}
#RLVECT_3
M1 1
MBasis
ha basis #0 of #1
bases #0 of #1
O1 0 1
OLin
mcl@s#1; {\rm Lin}(#1)
V1 1
Vlinearly-independent
a linearly independent
V2 1
Vlinearly-dependent
a linearly dependent
#RLVECT_5
O1 0 1
Odim
mol#1; \mathop{\rm dim}(#1)
O2 1 1
OSubspaces_of
mol(2)#1#2; \mathop{\rm Sub}_{#1}(#2)
V1 1
Vfinite-dimensional
a finite dimensional
#RMOD_2
M1 1
MSubmodule
ha submodule #0 of #1
submodules #0 of #1
#RMOD_3
O1 0 1
OSubmodules
mcl@s#1; \mathop{\rm Sub}(#1)
#ROBBINS1
G1 2
GComplStr
mc#1#2; \langle #1,#2 \rangle
G2 3
GComplLLattStr
mc#1#2#3; \langle #1,#2,#3 \rangle
G3 3
GComplULattStr
mc#1#2#3; \langle #1,#2,#3 \rangle
G4 4
GOrthoLattStr
mc#1#2#3#4; \langle #1,#2,#3,#4 \rangle
J1 1
GComplStr
hol#1; ComplStr of #1
J2 1
GComplLLattStr
hol#1; complemented L-lattice structure of #1
J3 1
GComplULattStr
hol#1; complemented U-lattice structure of #1
J4 1
GOrthoLattStr
hol#1; ortholattice structure of #1
L1 0
GComplStr
ha ComplStr #0
ComplStr #0
L2 0
GComplLLattStr
ha complemented L-lattice structure #0
complemented L-lattice structures #0
L3 0
GComplULattStr
ha complemented U-lattice structure #0
complemented U-lattice structures #0
L4 0
GOrthoLattStr
hn ortholattice structure #0
ortholattice structures #0
M1 0
MpreOrthoLattice
ha pre-ortholattice #0
pre-ortholattices #0
O1 0 0
OTrivComplLat
mol; \mathop{\rm TrivComplLat}
O2 0 0
OTrivOrtLat
mol; \mathop{\rm TrivOrtLat}
O3 0 1
OBot
mow#1; \bot^{\rm C}_{#1}
O4 0 1
OCLatt
mol#1; \mathop{\rm CLatt} #1
O5 0 2
O\delta
mol#1#2; \delta(#1,#2)
O6 0 2
OExpand
mol#1#2; \mathop{\rm Expand}(#1,#2)
O7 1 0
O_0
mor#1; #1 _0
O8 0 1
ODouble
mol@s; 2#1
O9 1 0
O_1
mor#1; #1 _1
O10 1 0
O_2
mor#1; #1 _2
O11 1 0
O_3
mor#1; #1 _3
O12 1 0
O_4
mor#1; #1 _4
O13 0 1
O\beta
mol#1; \beta (#1)
U1 1
UCompl
hosl#1; complement operation of #1
complement operation
V1 1
VRobbins
a Robbins
V2 1
VHuntington
a Huntington
V3 1
Vjoin-idempotent
a join-idempotent
V4 1
Vwell-complemented
a well-complemented
V5 1
Vwith_idempotent_element
x idempotent element
V6 1
Vde_Morgan
a de Morgan
#ROBBINS2
V1 1
Vsatisfying_DN_1
s $({\rm DN}_1)$
V2 1
Vsatisfying_MD_1
s $({\rm Meredith}_1)$
V3 1
Vsatisfying_MD_2
s $({\rm Meredith}_2)$
#ROBBINS3
G1 3
G\/-SemiLattRelStr
mc#1#2#3; \langle #1,#2,#3 \rangle
G2 3
G/\-SemiLattRelStr
mc#1#2#3; \langle #1,#2,#3 \rangle
G3 4
GLattRelStr
mc#1#2#3#4; \langle #1,#2,#3,#4 \rangle
G4 5
GOrthoLattRelStr
mc#1#2#3#4#5; \langle #1,#2,#3,#4,#5 \rangle
J1 1
G\/-SemiLattRelStr
hol#1; $\sqcup$-relational semilattice structure of #1
J2 1
G/\-SemiLattRelStr
hol#1; $\sqcap$-relational semilattice structure of #1
J3 1
GLattRelStr
hol#1; relational lattice structure of #1
J4 1
GOrthoLattRelStr
hol#1; relational ortholattice structure of #1
L1 0
G\/-SemiLattRelStr
ha $\sqcup$-relational semilattice structure #0
$\sqcup$-relational semilattice structures #0
L2 0
G/\-SemiLattRelStr
ha $\sqcap$-relational semilattice structure #0
$\sqcap$-relational semilattice structures #0
L3 0
GLattRelStr
ha relational lattice structure #0
relational lattice structures #0
L4 0
GOrthoLattRelStr
ha relational ortholattice structure #0
relational ortholattice structures #0
M1 0
MOrtholattice
hn ortholattice #0
ortholattices #0
M2 1
MRelAugmentation
ha relational augmentation #0 of #1
relational augmentations #0 of #1
M3 1
MLatAugmentation
ha lattice augmentation #0 of #1
lattice augmentations #0 of #1
M4 1
MCLatAugmentation
ha complemented lattice augmentation #0 of #1
complemented lattice augmentations #0 of #1
O1 1 1
O|_|
moi; #1 \underline\sqcup #2
O2 1 1
O|^|
moi; #1 \overline\sqcap #2
O3 1 1
O"|^|"
moi; #1 \sqcap_{\leq} #2
O4 1 1
O"|_|"
moi; #1 \sqcup_{\leq} #2
O5 0 0
OTrivLattRelStr
mol; \mathop{\rm TrivLattRelStr}
O6 0 0
OTrivCLRelStr
mol; \mathop{\rm TrivCLRelStr}
V1 1
Vjoin-Associative
a quasi-join-associative
V2 1
Vmeet-Associative
a quasi-meet-associative
V3 1
Vmeet-Absorbing
a quasi-meet-absorbing
V4 1
Vwith_Top
x top
V5 1
Vnaturally_sup-generated
a naturally sup-generated
V6 1
Vnaturally_inf-generated
a naturally inf-generated
#ROBBINS4
M1 0
MOrthomodular_Lattice
hn orthomodular lattice #0
orthomodular lattices #0
O1 0 0
OB_6
mow@s; B_6
O2 0 0
OBenzene
mol; \mathop{\rm Benzene}
V1 1
Vorthomodular
n orthomodular
V2 1
VOrthomodular
s OM
#ROUGHS_1
M1 0
MApproximation_Space
hn approximation space #0
approximation spaces #0
M2 0
MTolerance_Space
ha tolerance space #0
tolerance spaces #0
M3 1
MRoughSet
ha rough set #0 of #1
rough sets #0 of #1
O1 0 1
OLAp
mol#1; \mathop{\rm LAp}(#1)
O2 0 1
OUAp
mol#1; \mathop{\rm UAp}(#1)
O3 0 1
OBndAp
mol#1; \mathop{\rm BndAp}(#1)
O4 0 2
OMemberFunc
mol#1#2; \mathop{\rm MemberFunc}(#1,#2)
O5 0 2
OFinSeqM
mol#1#2; \mathop{\rm FinSeqM}(#1,#2)
R1 1 1
R_c=
mn #1 \subseteq_{\ast} #2
#1 \not\subseteq_{\ast} #2
R2 1 1
Rc=^
mn #1 \subseteq^{\ast} #2
#1 \not\subseteq^{\ast} #2
R3 1 1
R_c=^
mn #1 \subseteq_{\ast}^{\ast} #2
#1 \not\subseteq_{\ast}^{\ast} #2
R4 1 1
R_=
mn #1 =_{\ast} #2
#1 \not=_{\ast} #2
R5 1 1
R=^
mn #1 =^{\ast} #2
#1 \not=^{\ast} #2
R6 1 1
R_=^
mn #1 =_{\ast}^{\ast} #2
#1 \not=_{\ast}^{\ast} #2
V1 1
Vwith_equivalence
x equivalence relation
V2 1
Vwith_tolerance
x tolerance relation
V3 1
Vrough
a rough
V4 1
Vexact
n exact
#RPR_1
M1 1
MEl_ev
hn elementary event #0 of #1
elementary events #0 of #1
M2 1
MEvent
hn event #0 of #1
events #0 of #1
O1 0 1
Oprob
mcl@s#1; {\rm P}(#1)
O1 0 2
Oprob
mcl@s/1r@m/2l@m#1; {\rm P}(#1/#2)
R1 2 0
Rare_independent
h #1 and #2 are independent
#1 and #2 are not independent
#RSSPACE
O1 0 0
Othe_set_of_RealSequences
hol; set of real sequences
O2 0 1
Oseq_id
mol#1; \mathop{\rm id_{\rm seq}}(#1)
O3 0 1
OR_id
mol#1; \mathop{\rm id_{\mathbb R}}(#1)
O4 0 0
Ol_add
mow; \mathop{\rm add_{\rm seq}}
O5 0 0
Ol_mult
mow; \mathop{\rm mult_{\rm seq}}
O6 0 0
OZeroseq
mow; \mathop{\rm Zeroseq}
O7 0 0
OLinear_Space_of_RealSequences
hol; linear space of real sequences
O8 0 2
OAdd_
mol#1#2; \mathop{\rm Add}(#1,#2)
O9 0 1
OMult_
mow#1; \cdot_{#1}
O9 0 2
OMult_
mol#1#2; \mathop{\rm Mult}(#1,#2)
O10 0 2
OZero_
mol#1#2; \mathop{\rm Zero}(#1,#2)
O11 0 0
Othe_set_of_l2RealSequences
hol; set of l2-real sequences
O12 0 0
Ol_scalar
mow; \mathop{\rm scalar_{\rm seq}}
O13 0 0
Ol2_Space
mow; \mathop{\rm l2\hbox{-}Space}
#RSSPACE2
M1 0
MRealHilbertSpace
ha real Hilbert space of #0
real Hilbert spaces of #0
#RSSPACE3
O1 0 0
Othe_set_of_l1RealSequences
hol; set of l1-real sequences
O2 0 0
Ol_norm
mow; \mathop{\rm norm_{\rm seq}}
O3 0 0
Ol1_Space
mow; \mathop{\rm l1\hbox{-}Space}
V1 1
VCCauchy
a CCauchy
V2 1
VCauchy_sequence_by_Norm
a Cauchy sequence by norm
#RSSPACE4
O1 0 0
Othe_set_of_BoundedRealSequences
hol; set of bounded real sequences
O2 0 0
Olinfty_norm
mow; \mathop{\rm linfty\hbox{-}norm}
O3 0 0
Olinfty_Space
mow; \mathop{\rm linfty\hbox{-}Space}
O4 0 1
OBoundedFunctions
mol; \mathop{\rm BoundedFunctions} #1
O4 0 2
OBoundedFunctions
mow#1#2; \mathop{\rm BdFuncs}(#1,#2)
O5 0 2
OR_VectorSpace_of_BoundedFunctions
hol; set of bounded real sequences from #1 into #2
O6 0 1
OBoundedFunctionsNorm
mol; \mathop{\rm BoundedFunctionsNorm} #1
O6 0 2
OBoundedFunctionsNorm
mow#1#2; \mathop{\rm BdFuncsNorm}(#1,#2)
O7 0 2
OR_NormSpace_of_BoundedFunctions
hol; real normed space of bounded functions from #1 into #2
#RUSUB_4
O1 0 1
OUp
mol#1; \mathop{\rm Up}(#1)
O1 0 3
OUp
mol#1#2#3; \mathop{\rm Up}(#1,#2,#3)
V1 1
VAffine
n affine
V2 1
VSubspace-like
a subspace-like
#RUSUB_5
O1 0 1
OOrt_Comp
mol#1; \mathop{\rm Ort\_Comp} #1
O2 0 1
OTopUnitSpace
mol#1; \mathop{\rm TopUnitSpace} #1
R1 1 1
Ris_parallel_to
i parallel to #2
not parallel to #2
#RVSUM_1
K1 2 L1 vRVSUM_1
K|(
L)|
mc#1#2; |( #1,#2 )|
O1 0 0
Osqrreal
mow; \mathop{{\rm sqr}_{\mathbb R}}
O2 0 1
Osqr
mok; \mathopen{^2}#1
O3 0 2
Omlt
moi@5; #1 \bullet #2
R1 2 0
Rare_orthogonal
h #1, #2 are orthogonal
#1, #2 are not orthogonal
V1 1
Vcomplex-yielding
a complex yielding
#RVSUM_2
O1 0 0
Osqrcomplex
mol; \mathop{\rm sqrcomplex}
#SCMBSORT
O1 0 1
Obubble-sort
mol#1; \mathop{\rm bubble\hbox{-}sort}(#1)
O2 0 0
OBubble-Sort-Algorithm
hol; bubble sort algorithm
O3 0 0
OSorting-Function
mol; \mathop{\rm Sorting\hbox{-}Function}
#SCMFSA6A
O1 0 1
ODirected
mol#1; \mathop{\rm Directed}(#1)
O1 0 2
ODirected
mol#1#2; \mathop{\rm Directed}(#1,#2)
O2 0 1
OMacro
mol#1; \mathop{\rm Macro}(#1)
O3 0 1
OInitialized
mol#1; \mathop{\rm Initialized}(#1)
#SCMFSA6B
O1 0 2
OIExec
mol#1#2; \mathop{\rm IExec}(#1,#2)
O1 0 3
OIExec
mol#1#2#3; \mathop{\rm IExec}(#1,#2,#3)
V1 1
Vparaclosed
a paraclosed
V2 1
Vparahalting
a parahalting
V3 1
Vkeeping_0
a keeping 0
#SCMFSA6C
O1 0 1
OInitialize
mol#1; \mathop{\rm Initialize}(#1)
#SCMFSA7B
R1 1 1
Rrefers
h #1 refers #2
#1 not refers #2
R2 1 1
Rdestroys
h #1 destroys #2
#1 not destroys #2
R3 1 1
Ris_halting_on
i halting on #2
not halting on #2
R3 1 2
Ris_halting_on
i halting on #2,#3
not halting on #2,#3
V1 1
Vgood
a good
#SCMFSA8A
O1 0 1
OGoto
mol#1; \mathop{\rm Goto}(#1)
O2 0 3
Opseudo-LifeSpan
mol#1#2,#; \mathop{\rm pseudo-LifeSpan}(#1,#2,#3)
R1 1 2
Ris_pseudo-closed_on
i pseudo-closed on #2,#3
not pseudo-closed on #2,#3
V1 1
Vpseudo-paraclosed
a pseudo-paraclosed
#SCMFSA8B
O1 0 3
Oif=0
mo/3l#1; {\bf if\ } #1=0 {\bf \ then\ } #2 {\bf \ else\ } #3
O1 0 4
Oif=0
mo/4l#1; {\bf if\ } #1=#2 {\bf \ then\ } #3 {\bf \ else\ } #4
O2 0 3
Oif>0
mo/3l#1; {\bf if\ } #1>0 {\bf \ then\ } #2 {\bf \ else\ } #3
O2 0 4
Oif>0
mo/4l#1; {\bf if\ } #1>#2 {\bf \ then\ } #3 {\bf \ else\ } #4
O3 0 3
Oif<0
mo/3l#1; {\bf if\ } #1<0 {\bf \ then\ } #2 {\bf \ else\ } #3
O3 0 4
Oif<0
mo/4l#1; {\bf if\ } #1<#2 {\bf \ then\ } #3 {\bf \ else\ } #4
#SCMFSA8C
O1 0 1
Oloop
mol#1; \mathop{\rm loop} #1
O2 0 2
OTimes
mol#1#2; \mathop{\rm Times}(#1,#2)
#SCMFSA9A
O1 0 4
OExitsAtWhile=0
mol#1#2#3,#4; \mathop{\it ExitsAtWhile{=}0}(#1,#2,#3,#4)
O2 0 4
OExitsAtWhile>0
mol#1#2#3,#4; \mathop{\it ExitsAtWhile{>}0}(#1,#2,#3,#4)
O3 0 2
OFusc_macro
mol#1#2; \mathop{\rm Fusc\_macro}(#1,#2)
R1 0 4
RProperBodyWhile=0
m {\rm ProperBodyWhile}{=}0(#1,#2,#3,#4)
{\rm not\ ProperBodyWhile}{=}0(#1,#2,#3,#4)
R2 0 4
RWithVariantWhile=0
m {\rm WithVariantWhile}{=}0(#1,#2,#3,#4)
{\rm not\ WithVariantWhile}{=}0(#1,#2,#3,#4)
R3 0 4
RProperBodyWhile>0
m {\rm ProperBodyWhile}{>}0(#1,#2,#3,#4)
{\rm not\ ProperBodyWhile}{>}0(#1,#2,#3,#4)
R4 0 4
RWithVariantWhile>0
m {\rm WithVariantWhile}{>}0(#1,#2,#3,#4)
{\rm not\ WithVariantWhile}{>}0(#1,#2,#3,#4)
V1 1
Von_data_only
n on data only
#SCMFSA_1
M1 0
MSCM+FSA-State
hn \SCMFSA-state #0
\SCMFSA-states #0
O1 0 0
OSCM+FSA-Data-Loc
mow; {\rm Data\hbox{-}Loc}_{{\rm SCM}_{\rm FSA}}
O2 0 0
OSCM+FSA-Data*-Loc
mow; {\rm Data^\ast\hbox{-}Loc}_{{\rm SCM}_{\rm FSA}}
O3 0 0
OSCM+FSA-Memory
mow; {\rm Memory}_{{\rm SCM}_{\rm FSA}}
O4 0 0
OSCM+FSA-Instr
mow; {\rm Instr}_{{\rm SCM}_{\rm FSA}}
O5 0 0
OSCM+FSA-OK
mow; {\rm OK}_{{\rm SCM}_{\rm FSA}}
O6 0 2
OSCM+FSA-Chg
mol@s#1#2; {\rm Chg}_{{\rm SCM}_{\rm FSA}}(#1,#2)
O6 0 3
OSCM+FSA-Chg
mol@s#1#2#3; {\rm Chg}_{{\rm SCM}_{\rm FSA}}(#1,#2,#3)
O7 1 0
Oint_addr1
mor; #1~{\rm int\hbox{-}addr}_1
O8 1 0
Oint_addr2
mor; #1~{\rm int\hbox{-}addr}_2
O9 1 0
Ocoll_addr1
mor; #1~{\rm coll\hbox{-}addr}_1
O10 1 0
Oint_addr3
mor; #1~{\rm int\hbox{-}addr}_3
O11 1 0
Ocoll_addr2
mor; #1~{\rm coll\hbox{-}addr}_2
O12 0 2
OSCM+FSA-Exec-Res
mol@s#1#2; {\rm Exec\hbox{-}Res}_{{\rm SCM}_{\rm FSA}}(#1,#2)
O13 0 0
OSCM+FSA-Exec
mow; {\rm Exec}_{{\rm SCM}_{\rm FSA}}
#SCMFSA_2
M1 0
MInt-Location
hn integer location #0
integer locations #0
M2 0
MFinSeq-Location
ha finite sequence location #0
finite sequence locations #0
O1 0 0
OSCM+FSA
mc; {\bf SCM}_{\rm FSA}
O2 0 0
OInt-Locations
mol; \mathop{\rm Int\hbox{-}Locations}
O3 0 0
OFinSeq-Locations
mol; \mathop{\rm FinSeq\hbox{-}Locations}
O4 0 1
Ointloc
mol#1; \mathop{\rm intloc}(#1)
O6 0 1
Ofsloc
mol#1; \mathop{\rm fsloc}(#1)
O7 1 1
O:=len
moi@0; #1{:=}{\rm len} #2
O8 1 1
O:=<0,...,0>
moi@0#2; #1{:=}\langle\underbrace{0,\dots,0}_{#2}\rangle
#SCMFSA_7
O1 0 1
OLoad
mol#1; \mathop{\rm Load}(#1)
O2 0 2
OaSeq
mol#1#2; \mathop{\rm aSeq}(#1,#2)
#SCMFSA_9
O1 0 2
Owhile=0
mo/2l#1; {\bf while\ } #1=0 {\bf \ do\ } #2
O2 0 2
Owhile>0
mo/2l#1; {\bf while\ } #1>0 {\bf \ do\ } #2
O2 0 3
Owhile>0
mol#1#2#3; {\rm while}>0(#1,#2,#3)
O3 0 2
Owhile<0
mo/2l#1; {\bf while\ } #1<0 {\bf \ do\ } #2
O3 0 3
Owhile<0
mol#1#2#3; {\rm while}<0(#1,#2,#3)
O4 0 4
OStepWhile=0
mol#1#2#3#4; \mathop{\it StepWhile{=}0}(#1,#2,#3,#4)
O5 0 4
OStepWhile>0
mol#1#2#3#4; \mathop{\it StepWhile{>}0}(#1,#2,#3,#4)
#SCMISORT
O1 0 1
Oinsert-sort
mol#1; \mathop{\rm insert\hbox{-}sort} #1
O1 0 2
Oinsert-sort
mol#1#2; \mathop{\rm insert\hbox{-}sort}(#1,#2)
O2 0 0
OInsert-Sort-Algorithm
mol; \mathop{\rm Insert\hbox{-}Sort\hbox{-}Algorithm}
#SCMNORM
M1 1
MpreProgram
ha Program #0 of #1
Programs #0 of #1
M2 1
MAutonomy
ha autonomy #0 of #1
autonomys #0 of #1
O2 0 3
OComput
mol#1#2#3; \mathop{\rm Comput}(#1,#2,#3)
O3 0 2
OIncrIC
mol#1#2; \mathop{\rm IncrIC}(#1,#2)
O4 0 1
ONPP
mol; \mathop{\rm NPP} #1
V1 1
Vprogram-free
a program free
#SCMPDS_1
M1 0
MSCMPDS-State
hn SCMPDS-State #0
SCMPDS-States #0
O1 0 0
OSCMPDS-Instr
mol; \mathop{\rm SCMPDS\hbox{-}Instr}
O2 0 0
OSCMPDS-OK
mol; \mathop{\rm SCMPDS\hbox{-}OK}
O3 0 3
OAddress_Add
mol#1#2#3; \mathop{\rm Address\_Add}(#1,#2,#3)
O4 1 0
Oconst_INT
mor#1; #1 \mathop{\rm const\_INT}
O5 1 0
OP21address
mor#1; #1 \mathop{\rm P21address}
O6 1 0
OP22const
mor#1; #1 \mathop{\rm P22const}
O7 1 0
OP31address
mor#1; #1 \mathop{\rm P31address}
O8 1 0
OP32const
mor#1; #1 \mathop{\rm P32const}
O9 1 0
OP33const
mor#1; #1 \mathop{\rm P33const}
O10 1 0
OP41address
mor#1; #1 \mathop{\rm P41address}
O11 1 0
OP42address
mor#1; #1 \mathop{\rm P42address}
O12 1 0
OP43const
mor#1; #1 \mathop{\rm P43const}
O13 1 0
OP44const
mor#1; #1 \mathop{\rm P44const}
O14 0 2
OPopInstrLoc
mol#1#2; \mathop{\rm PopInstrLoc}(#1,#2)
O15 0 0
ORetSP
mol; \mathop{\rm RetSP}
O16 0 0
ORetIC
mol; \mathop{\rm RetIC}
O17 0 0
OSCMPDS-Exec
mol; \mathop{\rm SCMPDS\hbox{-}Exec}
#SCMPDS_2
M1 0
MInt_position
hn Int position #0
Int positions #0
O1 0 0
OSCMPDS
mol; \mathop{\rm SCMPDS}
O2 0 2
ODataLoc
mol#1#2; \mathop{\rm DataLoc}(#1,#2)
O3 0 1
Oreturn
mol#1; \mathop{\rm return} #1
O4 0 2
OsaveIC
mol#1#2; \mathop{\rm saveIC}(#1,#2)
O5 2 1
O<>0_goto
moi#1#2#3; (#1,#2)<>0\_{\rm goto\:} #3
O6 2 1
O<=0_goto
moi#1#2#3; (#1,#2)<=0\_{\rm goto\:} #3
O7 2 1
O>=0_goto
moi#1#2#3; (#1,#2)>=0\_{\rm goto\:} #3
O8 0 2
OICplusConst
mol#1#2; \mathop{\rm ICplusConst}(#1,#2)
#SCMPDS_4
O1 0 1
Ostop
mol#1; \mathop{\rm stop} #1
R1 1 1
Rvalid_at
h #1 valid at #2
#1 not valid at #2
V1 1
Vshiftable
a shiftable
#SCMPDS_5
V1 1
VNo-StopCode
a No-StopCode
#SCMPDS_6
O1 0 3
Oif<>0
mo/3l#1; {\bf if\ } #1\neq 0 {\bf \ then\ } #2 {\bf \ else\ } #3
O2 0 3
Oif<=0
mo/3l#1; {\bf if\ } #1\leq 0 {\bf \ then\ } #2 {\bf \ else\ } #3
O3 0 3
Oif>=0
mo/3l#1; {\bf if\ } #1\geq 0 {\bf \ then\ } #2 {\bf \ else\ } #3
#SCMPDS_7
O1 0 4
Ofor-down
mol#1#2#3#4; \mathop{\rm for\hbox{-}down}(#1,#2,#3,#4)
#SCMPDS_8
O1 0 1
ODstate
mol#1; \mathop{\rm Dstate} #1
#SCMP_GCD
O1 0 1
Ointpos
mol#1; \mathop{\rm intpos} #1
O2 0 0
OGBP
mol; \mathop{\rm GBP}
O3 0 0
OSBP
mol; \mathop{\rm SBP}
O4 0 0
OGCD-Algorithm
mol; \mathop{\rm GCD\hbox{-}Algorithm}
#SCMRING1
O1 1 0
Oconst_address
mor#1; #1 \mathop{\rm const\_address}
O2 1 0
Oconst_value
mor#1; #1 \mathop{\rm const\_value}
#SCM_1
M1 2
MState-consisting
ha state #0 with instruction counter on #1, located from #2
states #0 with instruction counter on #1, located from #2
#SCM_COMP
M1 0
Mbin-term
ha binary term #0
binary terms #0
O1 0 0
OSCM-AE
mow; {\rm AE}_{\rm SCM}
O2 1 2
O-Meaning_on
mor(1)#2#3; #1(#2,#3)
O3 0 2
OSelfwork
mol#1#2; \mathop{\rm Selfwork}(#1,#2)
O4 0 0
OSCM-Compile
mow; {\rm Compile}_{\rm SCM}
O4 0 2
OSCM-Compile
mol#1#2; \mathop{\rm Compile}(#1,#2)
O5 0 1
Od".
mol#1; {\bf d}^{-1}(#1)
O6 0 1
Omax_Data-Loc_in
mol#1; \mathop{\rm max}_{\rm DL}(#1)
#SCM_HALT
R1 1 2
Ris_closed_onInit
h #1 is closed onInit #2,#3
#1 is not closed onInit #2,#3
R2 1 2
Ris_halting_onInit
h #1 is halting onInit #2,#3
#1 is not halting onInit #2,#3
V1 1
VInitClosed
n InitClosed
V2 1
VInitHalting
n InitHalting
V3 1
VkeepInt0_1
a keepInt0 1
#SCPINVAR
O1 0 3
Owhile<>0
mol#1#2#3; {\rm while}<>0(#1,#2,#3)
#SCPISORT
R1 1 2
Ris_FinSequence_on
h #1 is FinSequence on #2,#3
#1 is not FinSequence on #2,#3
#SCPQSORT
O1 0 0
OPartition
mol; \mathop{\rm Partition}
O2 0 2
OQuickSort
mol#1#2; \mathop{\rm QuickSort}(#1,#2)
#SEMI_AF1
M1 0
MSemi_Affine_Space
ha semi affine space #0
semi affine spaces #0
O1 0 1
Osum
mol#1; \mathop{\rm sum} #1
O1 0 2
Osum
mol#1#2; \mathop{\rm sum}(#1,#2)
O1 0 3
Osum
mcl@s/3k#1#2#3; \mathop{\rm sum}_{#3}(#1,#2)
O1 0 5
Osum
mol#1#2#3#4#5; \mathop{\rm sum}(#1,#2,#3,#4,#5)
O2 0 2
Oopposite
mcl@s/2k#1#2; \mathop{\rm opposite}_{#2}(#1)
R1 0 5
Rtrap
h #1, #2, #3, #4 form a trapezium with vertex #5
#1, #2, #3, #4 do not form a trapezium with vertex #5
R2 0 2
Rqtrap
h there are trapeziums through #2 with vertex #1
there is no trapezium through #2 with vertex #1
V1 1
VSemi_Affine_Space-like
a semi affine space-like
#SEQFUNC
M1 2
MFunctional_Sequence
ha sequence #0 of partial functions from #1 into #2
sequences #0 of partial functions from #1 into #2
R1 1 1
Rcommon_on_dom
i common for elements of #2
not common for elements of #2
R2 1 1
Ris_point_conv_on
i point-convergent on #2
not point-convergent on #2
R3 1 1
Ris_unif_conv_on
i uniform-convergent on #2
not uniform-convergent on #2
#SEQM_3
V1 1
Vmonotone
a monotone
#SEQ_1
M1 0
MReal_Sequence
ha sequence #0 of real numbers
sequences #0 of real numbers
M1 1
MReal_Sequence
ha sequence #0 in ${\cal E}^{#1}_{\rm T}$
sequences #0 in ${\cal E}^{#1}_{\rm T}$
#SEQ_2
V1 1
Vconvergent
a convergent
#SEQ_4
O1 0 1
Oupper_bound
mol@s; \mathop{\rm sup} #1
O2 0 1
Olower_bound
mol@s; \mathop{\rm inf} #1
O2 0 2
Olower_bound
hol#1#2; lower bound (#1,#2)
#SERIES_1
O1 0 1
OPartial_Sums
mow; (\sum_{\alpha=0}^{\kappa}#1(\alpha))_{\kappa\in\mathbb N}
V1 1
Vsummable
a summable
V2 1
Vabsolutely_summable
n absolutely summable
#SERIES_3
O1 0 1
OPartial_Product
hol; partial product of #1
#SETFAM_1
M1 1
MSubset-Family
ha family #0 of subsets of #1
families #0 of subsets of #1
M2 1
MCover
ha cover #0 of #1
covers #0 of #1
O1 0 1
Omeet
mol@s; \bigcap #1
O1 1 1
Omeet
moi@m; #1 \cap #2
O2 0 2
OUNION
moi@a; #1 \Cup #2
O3 0 2
OINTERSECTION
moi@m; #1 \Cap #2
O4 0 2
ODIFFERENCE
moi@a; #1 \setminus\!\!\setminus #2
O5 0 1
OCOMPLEMENT
moq; #1 \mathclose{^{\rm c}}
O6 0 1
OIntersect
mol#1; \mathop{\rm Intersect}(#1)
O6 0 2
OIntersect
mol#1#2; \mathop{\rm Intersect}(#1,#2)
R1 1 1
Ris_finer_than
i finer than #2
not finer than #2
R2 1 1
Ris_coarser_than
i coarser than #2
not coarser than #2
V1 1
Vwith_non-empty_elements
x non empty elements
V2 1
Vempty-membered
n empty-membered
V3 1
Vwith_non-empty_element
x a non-empty element
V4 1
Vwith_proper_subsets
x proper subsets
#SETLIM_1
O1 0 1
Oinferior_setsequence
hol; inferior setsequence #1
O2 0 1
Osuperior_setsequence
hol; superior setsequence #1
#SETLIM_2
O1 1 1
O(/\)
moi; #1 \cap #2
O2 1 1
O(\/)
moi; #1 \cup #2
O3 1 1
O(\)
moi; #1 \setminus #2
O4 1 1
O(\+\)
moi; #1 \diffsym #2
#SETWISEO
K1 1 L1 vSETWISEO
K{.
L.}
mow#1; \lbrace #1 \rbrace_f
K1 2 L1 vSETWISEO
K{.
L.}
mow#1#2; \lbrace #1, #2 \rbrace_f
K1 3 L1 vSETWISEO
K{.
L.}
mow#1#2#3; \lbrace #1, #2, #3 \rbrace_f
O1 0 1
O{}.
mow/1k#1; \emptyset_{#1}
O2 1 1
O$$
moi@m; #1 \circledast #2
O2 1 2
O$$
moi(1,3)@a/2k#2; #1\hbox{-}\sum_{#2} #3
O3 0 1
OFinUnion
mow/1k#1; \mathop{\rm FinUnion}_{#1}
O3 0 2
OFinUnion
mcl@s#1#2; \mathop{\rm FinUnion}(#1,#2)
O4 0 1
Osingleton
mow/1k#1; \mathop{\rm singleton}_{#1}
V1 1
Vhaving_a_unity
a unital
#SETWOP_2
O1 0 1
OfinSeg
mol@s; \mathop{\rm Seg}_f #1
#SFMASTR1
O1 0 1
ORWNotIn-seq
mol#1; \mathop{\rm RWNotIn\hbox{-}seq} #1
O2 1 1
O-thRWNotIn
moi/1q/2l#1#2; #1^{\rm th}{\rm\hbox{-}RWNotIn}(#2)
O3 1 1
O-stRWNotIn
moi/1q/2l#1#2; 1^{\rm st}\mathop{\rm\hbox{-}RWNotIn}(#2)
O4 1 1
O-ndRWNotIn
moi/1q/2l#1#2; 2^{\rm nd}{\rm\hbox{-}RWNotIn}(#2)
O5 1 1
O-rdRWNotIn
moi/1q/2l#1#2; 3^{\rm rd}\mathop{\rm\hbox{-}RWNotIn}(#2)
O6 1 1
O-thNotUsed
moi/1q/2l#1#2; #1^{\rm th}{\rm\hbox{-}NotUsed}(#2)
O7 1 1
O-stNotUsed
moi/1q/2l#1#2; 1^{\rm st}{\rm\hbox{-}NotUsed}(#2)
O8 1 1
O-ndNotUsed
moi/1q/2l#1#2; 2^{\rm nd}{\rm\hbox{-}NotUsed}(#2)
O9 1 1
O-rdNotUsed
moi/1q/2l#1#2; 3^{\rm rd}{\rm\hbox{-}NotUsed}(#2)
O10 0 2
OFib_macro
mol#1#2; \mathop{\rm Fib\_macro}(#1,#2)
#SFMASTR2
O1 0 2
Otimes
mol#1#2; \mathop{\rm times}(#1,#2)
O1 1 1
Otimes
moi; #1 \mathop{\rm times} #2
O2 0 4
OStepTimes
mol#1#2#3#4; \mathop{\rm StepTimes}(#1,#2,#3,#4)
O3 0 1
Otriv-times
mol#1; \mathop{\rm triv\hbox{-}times}(#1)
O4 0 1
OFib-macro
mol#1; \mathop{\rm Fib\hbox{-}macro} #1
O4 0 2
OFib-macro
mol#1#2; \mathop{\rm Fib\hbox{-}macro}(#1,#2)
O5 0 2
Otimes*
mol#1#2; times(#1,#2)
R1 0 4
RProperTimesBody
h ProperTimesBody #1,#2,#3,#4
not ProperTimesBody #1,#2,#3,#4
#SFMASTR3
O1 0 6
OStepForUp
mol#1#2#3#4#5#6; \mathop{\rm StepForUp}(#1,#2,#3,#4,#5,#6)
O2 0 4
Ofor-up
mol#1#2#3#4; \mathop{\rm for\hbox{-}up}(#1,#2,#3,#4)
O3 0 4
OFinSeqMin
mol#1#2#3#4; \mathop{\rm FinSeqMin}(#1,#2,#3,#4)
O4 0 1
OSelection-sort
mol#1; \mathop{\rm Selection\hbox{-}sort} #1
R1 0 6
RProperForUpBody
h ProperForUpBody #1,#2,#3,#4,#5,#6
not ProperForUpBody #1,#2,#3,#4,#5,#6
#SF_MASTR
O1 0 1
OUsedIntLoc
mol#1; \mathop{\rm UsedIntLoc}(#1)
O2 0 1
OUsedInt*Loc
mol#1; \mathop{\rm UsedInt}^\ast{\rm Loc}(#1)
O3 0 1
OFirstNotIn
mol#1; \mathop{\rm FirstNotIn}(#1)
O4 0 1
OFirstNotUsed
mol#1; \mathop{\rm FirstNotUsed}(#1)
O5 0 1
OFirst*NotIn
mol#1; \mathop{\rm First}^\ast{\rm NotIn}(#1)
O6 0 1
OFirst*NotUsed
mol#1; \mathop{\rm First}^\ast{\rm NotUsed}(#1)
V1 1
Vread-only
a read-only
V2 1
Vread-write
a read-write
#SGRAPH1
G1 2
GSimpleGraphStruct
mc#1#2; \langle #1,#2\rangle
J1 1
GSimpleGraphStruct
hol#1; simple graph struct of #1
L1 0
GSimpleGraphStruct
ha simple graph structure #0
simple graph structures #0
M1 1
MSimpleGraph
ha simple graph #0 of #1
simple graphs #0 of #1
M2 1
MSubGraph
ha subgraph #0 of #1
subgraphs #0 of #1
O1 0 2
Onat_interval
mow#1#2; [#1,#2]_{\mathbb N}
O2 0 1
OTWOELEMENTSETS
mcl@s#1; \mathop{\rm TwoElementSets}(#1)
O3 0 1
OSIMPLEGRAPHS
mcl@s#1; \mathop{\rm SimpleGraphs}(#1)
O4 0 1
Odegree
mcl@s#1; \mathop{\rm degree}(#1)
O4 0 2
Odegree
mcl@s#1#2; \mathop{\rm degree}(#1,#2)
O5 0 2
OPATHS
mcl@s#1#2; \mathop{\rm Paths}(#1,#2)
O6 0 1
OK_
mow#1; \mathop{\rm K}_{#1}
O6 0 2
OK_
mow#1#2; \mathop{\rm K}_{#1,#2}
O7 0 0
OTriangleGraph
mc; \mathop{\rm TriangleGraph}
R1 1 1
Ris_isomorphic_to
i isomorphic to #2
not isomorphic to #2
R2 1 1
Ris_SetOfSimpleGraphs_of
i a set of simple graphs of #2
not a set of simple graphs of #2
R3 1 2
Ris_path_of
i a path of #2 and #3
not a path of #2 and #3
R4 1 1
Ris_cycle_of
i a cycle of #2
not a cycle of #2
U1 1
USEdges
hopl#1; SEdges of #1
SEdges
#SHEFFER1
G1 2
GShefferStr
mc#1#2; \langle #1,#2 \rangle
G2 4
GShefferLattStr
mc#1#2#3#4; \langle #1,#2,#3,#4 \rangle
G3 5
GShefferOrthoLattStr
mc#1#2#3#4#5; \langle #1,#2,#3,#4,#5 \rangle
J1 1
GShefferStr
hol#1; Sheffer structure of #1
J2 1
GShefferLattStr
hol#1; Sheffer lattice structure of #1
J3 1
GShefferOrthoLattStr
hol#1; Sheffer ortholattice structure of #1
L1 0
GShefferStr
ha Sheffer structure #0
Sheffer structures #0
L2 0
GShefferLattStr
ha Sheffer lattice structure #0
Sheffer lattice structures #0
L3 0
GShefferOrthoLattStr
ha Sheffer ortholattice structure #0
Sheffer ortholattice structures #0
O1 0 1
OTop'
mow#1; \top'_{#1}
O2 0 1
OBot'
mow#1; \bot'_{#1}
O3 1 0
O`#
moq; #1 \mathclose{^{\rm c'}}
O4 0 0
OTrivShefferOrthoLattStr
mol; \mathop{\rm TrivShefferOrthoLattStr}
R1 1 1
Ris_a_complement'_of
i a complement' of #2
not a complement' of #2
U1 1
Ustroke
hosl#1; Sheffer stroke of #1
Sheffer stroke
V1 1
Vupper-bounded'
n upper-bounded'
V2 1
Vlower-bounded'
a lower-bounded'
V3 1
Vdistributive'
a distributive'
V4 1
Vcomplemented'
a complemented'
V5 1
Vmeet-idempotent
a meet-idempotent
V6 1
Vproperly_defined
a properly defined
V7 1
Vsatisfying_Sheffer_1
s $({\rm Sheffer}_1)$
V8 1
Vsatisfying_Sheffer_2
s $({\rm Sheffer}_2)$
V9 1
Vsatisfying_Sheffer_3
s $({\rm Sheffer}_3)$
#SHEFFER2
V1 1
Vsatisfying_Sh_1
s $({\rm Sh}_1)$
#SIMPLEX0
M1 0
MSimplicialComplexStr
ha simplicial complex structure #0
simplicial complex structures #0
M1 1
MSimplicialComplexStr
ha simplicial complex str #0 of #1
simplicial complex str(s) #0 of #1
M2 1
MSimplicialComplex
ha simplicial complex #0 of #1
simplicial complex(s) #0 of #1
M3 1
MSubSimplicialComplex
ha sub simplicial complex #0 of #1
sub simplicial complexes #0 of #1
M4 1
MSimplex
ha simplex #0 of #1
simplexes #0 of #1
M4 2
MSimplex
ha simplex #0 of #1,#2
simplexes #0 of #1,#2
O2 0 1
Osubset-closed_closure_of
hol; subset-closure of #1
O3 0 1
OComplex_of
hol; complex of #1
O5 0 2
OSkeleton_of
hol#1#2; skeleton of #1 and #2
O6 0 2
Othe_subsets_with_limited_card
hol#1#2; subsets of #2 with cardinality limited by #1
O6 0 3
Othe_subsets_with_limited_card
hol#1#2#3; subsets of #2 and #3 with cardinality limited by #1
O8 0 2
Osubdivision
mol#1#2; \mathop{\rm subdivision}(#1,#2)
O8 0 3
Osubdivision
mol#1#2#3; \mathop{\rm subdivision}(#1,#2,#3)
O9 0 1
OVertices
mol; \mathop{\rm Vertices} #1
V1 1
Vsimplex-like
a simplex-like
V3 1
Vwith_empty_element
x empty element
V4 1
Vvertex-like
a vertex-like
V5 1
Vfinite-vertices
a finite-vertices
V6 1
Vlocally-finite
a locally-finite
#SIMPLEX1
M1 1
MSubdivisionStr
ha subdivision str #0 of #1
subdivision str(s) #0 of #1
M2 1
MSubdivision
ha subdivision #0 of #1
subdivision(s) #0 of #1
O1 0 1
OBCS
mol; \mathop{\rm BCS} #1
O1 0 2
OBCS
mol#1#2; \mathop{\rm BCS}(#1,#2)
V1 1
Vsimplex-join-closed
a simplex-join-closed
#SINCOS10
O1 0 0
Oarcsec1
hol; 1st part of arcsec
O1 0 1
Oarcsec1
mol; \mathop{{\rm arcsec}_1} #1
O2 0 0
Oarcsec2
hol; 2nd part of arcsec
O2 0 1
Oarcsec2
mol; \mathop{{\rm arcsec}_2} #1
O3 0 0
Oarccosec1
hol; 1st part of arccosec
O3 0 1
Oarccosec1
mol; \mathop{{\rm arccosec}_1} #1
O4 0 0
Oarccosec2
hol; 2nd part of arccosec
O4 0 1
Oarccosec2
mol; \mathop{{\rm arccosec}_2} #1
#SIN_COS
O1 0 2
OCHK
mol#1#2; \mathop{\rm CHK}(#1,#2)
O3 0 0
OProd_real_n
mol; \mathop{\rm Prod\_real\_n}
O5 1 0
OExpSeq
mor#1; #1 \mathop{\rm ExpSeq}
O6 1 0
OrExpSeq
mol#1; #1 \mathop{\rm ExpSeq_{\mathbb R}}
O7 0 1
OCoef
mol#1; \mathop{\rm Coef} #1
O8 0 1
OCoef_e
mol#1; \mathop{\rm Coef\_e} #1
O9 0 3
OExpan
mol#1#2#3; \mathop{\rm Expan}(#1,#2,#3)
O10 0 3
OExpan_e
mol#1#2#3; \mathop{\rm Expan\_e}(#1,#2,#3)
O11 0 3
OAlfa
mol#1#2#3; \mathop{\rm Alfa}(#1,#2,#3)
O12 0 3
OConj
mol#1#2#3; \mathop{\rm Conj}(#1,#2,#3)
O13 0 0
Osin
hosl@1; function sin
O13 0 1
Osin
mol; \mathop{\rm sin} #1
O14 0 0
Ocos
hosl@1; function cos
O14 0 1
Ocos
mol; \mathop{\rm cos} #1
O15 1 0
OP_sin
mor#1; #1 \mathop{\rm P\_sin}
O16 1 0
OP_cos
mor#1; #1 \mathop{\rm P\_cos}
O17 0 0
Oexp_R
hosl@1; function exp
O17 0 1
Oexp_R
mol; \mathop{\rm exp} #1
O18 1 0
OP_dt
mor#1; #1 \mathop{\rm P\_dt}
O19 1 0
OP_t
mor#1; #1 \mathop{\rm P\_t}
O20 0 0
Otan
hosl@1; function tan
O20 0 1
Otan
mol; \tan #1
O21 0 0
Ocot
hosl@1; function cot
O21 0 1
Ocot
mol; \cot #1
O22 0 0
OPI
mc; \pi
#SIN_COS2
O1 0 0
Osinh
hosl@1; function sinh
O1 0 1
Osinh
mol; \sinh #1
O2 0 0
Ocosh
hosl@1; function cosh
O2 0 1
Ocosh
mol; \cosh #1
O3 0 0
Otanh
hosl@1; function tanh
O3 0 1
Otanh
mol; \tanh #1
#SIN_COS3
O1 0 0
Osin_C
mc; \mathop{{\rm sin}_{\mathbb C}}
O2 0 0
Ocos_C
mc; \mathop{{\rm cos}_{\mathbb C}}
O3 0 0
Osinh_C
mc; \mathop{{\rm sinh}_{\mathbb C}}
O4 0 0
Ocosh_C
mc; \mathop{{\rm cosh}_{\mathbb C}}
#SIN_COS4
O1 0 0
Ocosec
mol; \mathop{\rm cosec}
O1 0 1
Ocosec
mol; \mathop{\rm cosec} #1
O2 0 0
Osec
mol; \mathop{\rm sec}
O2 0 1
Osec
mol; \sec #1
#SIN_COS5
O1 0 1
Ocoth
mol; \coth #1
O2 0 1
Osech
mol; \mathop{\rm sech} #1
O3 0 1
Ocosech
mol; \mathop{\rm cosech} #1
#SIN_COS6
O1 0 0
Oarcsin
hosl@1; function arcsin
O1 0 1
Oarcsin
mol; \mathop{\rm arcsin} #1
O2 0 0
Oarccos
hosl@1; function arccos
O2 0 1
Oarccos
mol; \mathop{\rm arccos} #1
#SIN_COS7
O1 0 1
Osinh"
mol; \sinh' #1
O2 0 1
Ocosh1"
mol; \cosh_1' #1
O3 0 1
Ocosh2"
mol; \cosh_2' #1
O4 0 1
Otanh"
mol; \tanh' #1
O5 0 1
Ocoth"
mol; \coth' #1
O6 0 1
Osech1"
mol; \mathop{\rm sech}_1' #1
O7 0 1
Osech2"
mol; \mathop{\rm sech}_2' #1
O8 0 1
Ocsch"
mol; \mathop{\rm csch}' #1
#SIN_COS9
O1 0 0
Oarctan
hol; function arctan
O1 0 1
Oarctan
mol; \mathop{\rm arctan} #1
O2 0 0
Oarccot
hol; function arccot
O2 0 1
Oarccot
mol; \mathop{\rm arccot} #1
#SPPOL_1
R1 1 1
Ris_extremal_in
i extremal in #2
not extremal in #2
R2 2 1
Rare_generators_of
h #1 and #2 are generators of #3
#1 and #2 are not generators of #3
V1 1
Vhorizontal
a horizontal
V2 1
Vvertical
a vertical
V3 1
Valternating
n alternating
#SPPOL_2
M1 0
MS-Sequence_in_R2
hn S-sequence #0 in ${\mathbb R}^2$
S-sequences #0 in ${\mathbb R}^2$
M2 0
MSpecial_polygon_in_R2
ha special polygon #0 in ${\mathbb R}^2$
special polygons #0 in ${\mathbb R}^2$
R1 2 1
Rsplit
h #1 and #2 split #3
#1 and #2 do not split #3
V1 1
Vspecial_polygonal
a special polygonal
#SPRECT_1
O1 0 1
OSpStSeq
mol#1; \mathop{\rm SpStSeq} #1
V1 1
Vrectangular
a rectangular
#SPRECT_2
R1 1 1
Ris_in_the_area_of
i in the area of #2
not in the area of #2
R2 1 1
Ris_a_h.c._for
i a h.c. for #2
not a h.c. for #2
R3 1 1
Ris_a_v.c._for
i a v.c. for #2
not a v.c. for #2
V1 1
Vclockwise_oriented
a clockwise oriented
#SQUARE_1
O1 1 0
O^2
moq; #1^{\bf 2}
O2 0 1
Osqrt
mc{w}@9#1; \sqrt{#1}
#STIRL2_1
O1 1 1
Oblock
moi; #1 \mathop{\rm block} #2
V1 1
V"increasing
n increasing
#STRUCT_0
G1 1
G1-sorted
mc#1; \langle #1\rangle
G2 2
GZeroStr
mc#1#2; \langle #1, #2\rangle
G3 2
GOneStr
mc#1#2; \langle #1,\,#2\rangle
G4 3
GZeroOneStr
mc#1#2#3; \langle #1,\,#2,\,#3\rangle
G5 2
G2-sorted
mc#1#2; \langle #1,#2 \rangle
J1 1
G1-sorted
hol#1; 1-sorted structure of #1
J2 1
GZeroStr
hol#1; zero structure of #1
J3 1
GOneStr
hol#1; one structure of #1
J4 1
GZeroOneStr
hol#1; zero-one structure of #1
J5 1
G2-sorted
hol#1; 2-sorted of #1
L1 0
G1-sorted
ha 1-sorted structure #0
1-sorted structures #0
L2 0
GZeroStr
ha zero structure #0
zero structures #0
L3 0
GOneStr
ha one structure #0
one structures #0
L4 0
GZeroOneStr
ha zero-one structure #0
zero-one structures #0
L5 0
G2-sorted
ha 2-sorted #0
2-sorted #0
O1 0 1
ONonZero
mol; \mathop{\rm NonZero} #1
U1 1
Ucarrier
hosl#1; carrier of #1
carrier
U2 1
UZeroF
hosl#1; zero of #1
zero
U3 1
UOneF
hosl#1; one of #1
one
U4 1
Ucarrier'
hosl#1; carrier' of #1
carrier'
V1 1
Vdegenerated
a degenerated
V2 1
Vvoid
a void
#SUBLEMMA
M1 1
MVal_Sub
ha value substitution #0 of #1
value substitutions #0 of #1
O1 0 2
OVal_S
mol#1#2; \mathop{\rm ValS}(#1,#2)
O2 0 2
OCQCSub_&
mol#1#2; \mathop{\rm CQCSubAnd}(#1,#2)
O3 0 2
OCQCSub_All
mol#1#2; \mathop{\rm CQCSubAll}(#1,#2)
O4 0 1
OCQCSub_the_scope_of
mol#1; \mathop{\rm CQCSubScope}(#1)
O5 0 2
OCQCQuant
mol#1#2; \mathop{\rm CQCQuant}(#1,#2)
O6 0 4
ONEx_Val
mol#1#2#3#4; \mathop{\rm NExVal}(#1,#2,#3,#4)
O7 0 1
ORSub1
mol; \mathop{\rm RSub1} #1
O8 0 2
ORSub2
mol#1#2; \mathop{\rm RSub2}(#1,#2)
V1 1
VCQC-WFF-like
a CQC-WFF-like
#SUBSET_1
M1 1
MElement
hn element #0 of #1
elements #0 of #1
M1 2
MElement
hn element #0 of #1,#2
elements #0 of #1,#2
M2 1
MSubset
ha subset #0 of #1
subsets #0 of #1
M2 2
MSubset
ha subset #0 of #1 reachable by #2
subsets #0 of #1 reachable by #2
O1 0 1
O[#]
mow/1k#1; \Omega_{#1}
O1 0 2
O[#]
mol@s/2k#2; \Omega_{#2}(#1)
O1 1 1
O[#]
moi@m; #1 \cdot #2
O2 1 0
O`
moq; #1 \mathclose{^{\rm c}}
O2 1 1
O`
moi; #1 ` #2
O3 0 1
Ochoose
mol#1; \mathop{\rm choose}(#1)
O3 1 1
Ochoose
mc#1#2; {{#1} \choose {#2}}
V1 1
Vproper
a proper
#SUBSTLAT
O1 0 2
OSubstitutionSet
mol#1#2; \mathop{\rm SubstitutionSet}(#1,#2)
O2 0 2
OSubstLatt
mol#1#2; \mathop{\rm SubstLatt}(#1,#2)
#SUBSTUT1
M1 0
MCQC_Substitution
ha CQC-substitution #0
CQC-substitutions #0
M2 1
Msecond_Q_comp
ha second q.-component #0 of #1
second q.-components #0 of #1
O1 0 0
OvSUB
mcl; \mathop{\rm vSUB}
O2 0 2
OCQC_Subst
mol#1#2; \mathop{\rm CQC\hbox{-}Subst}(#1,#2)
O3 0 3
ORestrictSub
mol#1#2#3; \mathop{\rm RestrictSub}(#1,#2,#3)
O4 0 1
OBound_Vars
mol#1; \mathop{\rm BoundVars}(#1)
O5 0 1
ODom_Bound_Vars
mol#1; \mathop{\rm DomBoundVars}(#1)
O6 0 1
OSub_Var
mol@2#1; \mathop{\rm Sub\hbox{-}Var}(#1)
O7 0 2
ONSub
mol#1#2; \mathop{\rm NSub}(#1,#2)
O8 0 2
OupVar
mol#1#2; \mathop{\rm upVar}(#1,#2)
O9 0 3
OExpandSub
mol#1#2#3; \mathop{\rm ExpandSub}(#1,#2,#3)
O10 0 0
OQSub
mcl; \mathop{\rm QSub}
O11 0 0
OQC-Sub-WFF
mcl; \mathop{\rm QC\hbox{-}Sub\hbox{-}WFF}
O12 0 3
OSub_P
mol#1#2#3; \mathop{\rm SubP}(#1,#2,#3)
O13 0 1
OSub_not
mol#1; \mathop{\rm SubNot}(#1)
O14 0 2
OSub_&
mol#1#2; \mathop{\rm SubAnd}(#1,#2)
O15 0 2
OSub_All
mol#1#2; \mathop{\rm SubAll}(#1,#2)
O16 0 1
OSub_the_arguments_of
mol#1; \mathop{\rm SubArguments}(#1)
O17 0 1
OSub_the_argument_of
mol#1; \mathop{\rm SubArgument}(#1)
O18 0 1
OSub_the_left_argument_of
mol#1; \mathop{\rm SubLeftArgument}(#1)
O19 0 1
OSub_the_right_argument_of
mol#1; \mathop{\rm SubRightArgument}(#1)
O20 0 1
OSub_the_bound_of
mol#1; \mathop{\rm SubBound}(#1)
O21 0 1
OSub_the_scope_of
mol#1; \mathop{\rm SubScope}(#1)
O22 0 1
OS_Bound
mol#1; \mathop{\rm S\hbox{-}Bound}(#1)
O23 0 2
OQuant
mol#1#2; \mathop{\rm Quant}(#1,#2)
O24 0 1
OCQC_Sub
mol#1; \mathop{\rm CQCSub}(#1)
O25 0 0
OCQC-Sub-WFF
mcl; \mathop{\rm CQC\hbox{-}Sub\hbox{-}WFF}
R1 2 1
RPQSub
my #3 = \mathop{\rm PQSub}(#1,#2)
#3 \neq\mathop{\rm PQSub}(#1,#2)
V1 1
VQC-Sub-closed
a QC-Sub-closed
V2 1
VSub_VERUM
a sub-verum
V3 1
Vquantifiable
a quantifiable
V4 1
VSub_atomic
a sub-atomic
V5 1
VSub_negative
a sub-negative
V6 1
VSub_conjunctive
a sub-conjunctive
V7 1
VSub_universal
a sub-universal
#SUBSTUT2
M1 2
MPATH
ha path #0 from #1 to #2
paths #0 from #1 to #2
O1 0 2
OSbst
mol#1#2; \mathop{\rm Sbst}(#1,#2)
O2 0 0
OCFQ
mcl; \mathop{\rm CFQ}
O3 0 3
OQScope
mol#1#2#3; \mathop{\rm QScope}(#1,#2,#3)
O4 0 3
OQsc
mol#1#2#3; \mathop{\rm Qsc}(#1,#2,#3)
#SUPINF_1
M1 0
MR_eal
hn extended real number #0
extended real numbers #0
M2 1
Mbool_DOMAIN
ha non empty set #0 of non empty subsets of #1
non empty sets #0 of non empty subsets of #1
O1 0 1
OSetMajorant
mc#1; \overline{#1}
O2 0 1
OSetMinorant
mc#1; \underline{#1}
O3 0 1
OSUP
mol@s; \mathop{\rm sup}_{\overline{\mathbb R}} #1
O4 0 1
OINF
mol@s; \mathop{\rm inf}_{\overline{\mathbb R}} #1
#SUPINF_2
M1 0
MDenum_Set_of_R_EAL
ha denumerable set #0 of larged real
denumerable sets #0 of larged real
M2 0
MPos_Denum_Set_of_R_EAL
ha denumerable set #0 of positive larged real
denumerable sets #0 of positive larged real
M3 1
MNum
ha numeration #0 of #1
numerations #0 of #1
M4 1
MSet_of_Series
ha set #0 of series of #1
sets #0 of series of #1
O1 0 0
O0.
mow; 0_{\overline{\mathbb R}}
O1 0 1
O0.
mow/1k#1; 0_{#1}
O1 0 2
O0.
moq{w}/2r@m#1; {0^{#2\times #2}_{#1}}
O1 0 3
O0.
moq{w}#1; {0^{#2\times #3}_{#1}}
O2 0 1
OSer
mol@s; \mathop{\rm Ser} #1
O2 0 2
OSer
mc#1#2; \mathop{\rm Ser}(#1,#2)
O3 0 1
OSUM
mol@s; \mathop{\overline{\sum}} #1
O3 0 2
OSUM
mol(2)@s#1; \sum_{#1}#2
R1 1 1
Ris_sumable
i #2 summable
not #2 summable
V1 1
Vnonnegative
a non-negative
#SYMSP_1
G1 5
GSymStr
mc#1#2#3#4#5; \langle #1,#2,#3,#4,#5 \rangle
J1 1
GSymStr
hol#1; simplectic structure of #1
L1 1
GSymStr
ha simplectic structure #0 over #1
simplectic structures #0 over #1
M1 1
MSymSp
ha simplectic space #0 over #1
simplectic spaces #0 over #1
O1 0 3
OProJ
mcl@s#1#2#3; {\rm J}(#1,#2,#3)
O2 0 4
OPProJ
mci(3,4)@m/1k#1#2; #3 \cdot_{#1,#2} #4
R1 1 1
R_|_
m #1 \perp #2
#1 \not\perp #2
R1 2 1
R_|_
m #1,#2 \perp #3
#1,#2 \not\perp #3
R1 2 2
R_|_
m #1,#2 \perp #3,#4
#1,#2 \not\perp #3,#4
V1 1
VSymSp-like
a simplectic space-like
#SYSREL
O1 0 1
OCL
mol@s#1; \mathop{\rm CL}(#1)
#TARSKI
O1 0 1
Ounion
mol@s; \bigcup #1
O1 0 2
Ounion
mol@s/2k#2; \bigcup_{#2}#1
O1 1 1
Ounion
moi@a; #1 \cup #2
R1 1 1
Rc=
m #1 \subseteq #2
#1 \not\subseteq #2
R2 2 0
Rare_equipotent
m #1 \approx #2
#1 \not\approx #2
#TAXONOM1
M1 1
MClassification
ha classification #0 of #1
classifications #0 of #1
M2 1
MStrong_Classification
ha strong classification #0 of #1
strong classifications #0 of #1
O1 0 2
Olow_toler
mol#1#2; \mathop{\rm T_l}(#1,#2)
O2 0 1
Ofam_class
mol#1; \mathop{\rm FamClass} #1
O3 0 2
Odist_toler
mol#1#2; \mathop{\rm T_m}(#1,#2)
O4 0 1
Ofam_class_metr
mol#1; \mathop{\rm MetricFamClass} #1
R1 2 1
Rare_in_tolerance_wrt
h #1,#2 are in tolerance w.r.t. #3
#1,#2 are not in tolerance w.r.t. #3
#TAXONOM2
M1 1
MHierarchy
ha hierarchy #0 of #1
hierarchies #0 of #1
V1 1
Vwith_superior
x superior elements
V2 1
Vwith_comparable_down
x comparable down elements
V3 1
Vhierarchic
a hierarchic
V4 1
Vmutually-disjoint
a mutually-disjoint
V5 1
Vwith_max's
x maximum elements
#TAYLOR_1
O1 0 1
Olog_
mow#1; \mathop{\rm log}_{#1}
O2 0 0
Oln
hosl@1; function ln
O3 0 4
OTaylor
mol#1#2#3#4; \mathop{\rm Taylor}(#1,#2,#3,#4)
#TAYLOR_2
O1 0 3
OMaclaurin
mol#1#2#3; \mathop{\rm Maclaurin}(#1,#2,#3)
#TBSP_1
V1 1
Vtotally_bounded
a totally bounded
#TDGROUP
M1 0
MTwo_Divisible_Group
ha 2-divisible group #0
2-divisible groups #0
M2 0
MUniquely_Two_Divisible_Group
ha uniquely 2-divisible group #0
uniquely 2-divisible groups #0
M3 0
MAffVect
ha space #0 of free vectors
spaces #0 of free vectors
O1 0 1
OCONGRD
mow/1k#1; \mathop{\rm Congr}_{#1}
O2 0 1
OAV
mol@s#1; \mathop{\rm Vectors}(#1)
R1 1 1
R==>
m #1\Rightarrow #2
#1\nRightarrow #2
R1 2 2
R==>
m #1,#2\Rightarrow #3,#4
#1,#2\nRightarrow #3,#4
V1 1
VTwo_Divisible
a 2-divisible
V2 1
VAffVect-like
a space of free vectors-like
#TDLAT_1
O1 0 1
ODomains_of
hol; domains of #1
O2 0 1
ODomains_Union
hol; domains union of #1
O3 0 1
OD-Union
mol@s#1; {\rm D\hbox{-}Union}(#1)
O4 0 1
ODomains_Meet
hol; domains meet of #1
O5 0 1
OD-Meet
mol@s#1; {\rm D\hbox{-}Meet}(#1)
O6 0 1
ODomains_Lattice
hol; lattice of domains of #1
O7 0 1
OClosed_Domains_of
hol; closed domains of #1
O8 0 1
OClosed_Domains_Union
hol; closed domains union of #1
O9 0 1
OCLD-Union
mol@s#1; {\rm CLD\hbox{-}Union}(#1)
O10 0 1
OClosed_Domains_Meet
hol; closed domains meet of #1
O11 0 1
OCLD-Meet
mol@s#1; {\rm CLD\hbox{-}Meet}(#1)
O12 0 1
OClosed_Domains_Lattice
hol; lattice of closed domains of #1
O13 0 1
OOpen_Domains_of
hol; open domains of #1
O14 0 1
OOpen_Domains_Union
hol; open domains union of #1
O15 0 1
OOPD-Union
mol@s#1; {\rm OPD\hbox{-}Union}(#1)
O16 0 1
OOpen_Domains_Meet
hol; open domains meet of #1
O17 0 1
OOPD-Meet
mol@s#1; {\rm OPD\hbox{-}Meet}(#1)
O18 0 1
OOpen_Domains_Lattice
hol; lattice of open domains of #1
#TDLAT_2
V1 1
Vdomains-family
a domains-family
V2 1
Vclosed-domains-family
a closed-domains-family
V3 1
Vopen-domains-family
n open-domains-family
#TDLAT_3
V1 1
Vanti-discrete
n anti-discrete
V2 1
Valmost_discrete
n almost discrete
V3 1
Vextremally_disconnected
n extremally disconnected
V4 1
Vhereditarily_extremally_disconnected
a hereditarily extremally disconnected
#TERMORD
O1 0 2
OHT
mol#1#2; \mathop{\rm HT}(#1,#2)
O2 0 2
OHM
mol#1#2; \mathop{\rm HM}(#1,#2)
O3 0 2
ORed
mol#1#2; \mathop{\rm Red}(#1,#2)
#TEX_1
O1 0 1
Ocobool
mor{qrw}@s#1; 2^{#1}_\ast
O2 0 1
OADTS
mol@s#1; \mathop{\rm ADTS}(#1)
O3 0 2
OSTS
mol@s#1#2; \mathop{\rm STS}(#1,#2)
#TEX_2
O1 0 1
OSspace
mol#1; \mathop{\rm Sspace}(#1)
V1 1
Vmaximal_discrete
a maximal discrete
#TEX_4
O1 0 1
OMaxADSF
mol#1; \mathop{\rm MaxADSF}(#1)
O2 0 1
OMaxADSet
mol#1; \mathop{\rm MaxADSet}(#1)
O3 0 1
OMaxADSspace
mol#1; \mathop{\rm MaxADSspace}(#1)
V1 1
Vanti-discrete-set-family
n anti-discrete-set-family
V2 1
Vmaximal_anti-discrete
a maximal anti-discrete
#TIETZE
R1 2 1
Ris_absolutely_bounded_by
i absolutely bounded by #3 in #2
not absolutely bounded by #3 in #2
#TMAP_1
O1 1 1
O-extension_of_the_topology_of
hoi; #1-extension of the topology of #2
O2 1 1
Omodified_with_respect_to
hoi; #1 modified w.r.t. #2
O3 0 2
Omodid
mow#1#2; \mathord{\rm modid}_{#1,#2}
R1 1 1
Ris_continuous_at
i continuous at #2
not continuous at #2
R2 1 1
Ris_not_continuous_at
i not continuous at #2
continuous at #2
#TOLER_1
M1 1
MTolSet
ha set #0 of mutually elements w.r.t. #1
sets #0 of mutually elements w.r.t. #1
M2 1
MTolClass
ha tolerance class #0 of #1
tolerance classes #0 of #1
O1 0 1
OTotal
mow/1k#1; \nabla_{#1}
O2 0 2
Oneighbourhood
mol@s; \mathop{\rm neighbourhood}(#1,#2)
O3 0 1
OTolSets
mol@s; \mathop{\rm TolSets} #1
O4 0 1
OTolClasses
mol@s; \mathop{\rm TolClasses} #1
V1 1
VTolClass-like
a tolerance class-like
#TOPALG_1
O1 0 2
OPaths
mol#1#2; \mathop{\rm Paths}(#1,#2)
O2 0 1
OLoops
mol#1; \mathop{\rm Loops}(#1)
O3 0 2
OFundamentalGroup
mol#1#2; \mathop{\rm FundamentalGroup}(#1,#2)
O4 0 2
Opi_1
mol#1#2; \mathop{\pi_1}(#1,#2)
O5 0 1
Opi_1-iso
mol#1; \mathop{\pi_1\hbox{-}{\rm iso}}(#1)
O6 0 2
ORealHomotopy
mol#1#2; \mathop{\rm RealHomotopy}(#1,#2)
#TOPALG_2
O1 0 2
OConvexHomotopy
mol#1#2; \mathop{\rm ConvexHomotopy}(#1,#2)
O2 0 2
OR1Homotopy
mol#1#2; \mathop{\rm R1Homotopy}(#1,#2)
#TOPALG_3
O1 0 2
OFundGrIso
mol#1#2; \mathop{\rm FundGrIso}(#1,#2)
#TOPALG_4
O1 0 2
OGr2Iso
mol#1#2; \mathop{\rm Gr2Iso}(#1,#2)
O2 0 2
OFGPrIso
mol#1#2; \mathop{\rm FGPrIso}(#1,#2)
#TOPALG_5
O1 0 1
OExtendInt
mol; \mathop{\rm ExtendInt} #1
O2 0 2
OPrj1
mol#1#2; \mathop{\rm Prj1}(#1,#2)
O3 0 2
OPrj2
mol#1#2; \mathop{\rm Prj2}(#1,#2)
O4 0 1
OcLoop
mol; \mathop{\rm cLoop} #1
O5 0 0
OCiso
mol; \mathop{\rm Ciso}
#TOPDIM_1
O1 0 1
OSeq_of_ind
hol; sequence of ind of #1
O2 0 1
Oind
mol; \mathop{\rm ind} #1
V1 1
Vwith_finite_small_inductive_dimension
x finite small inductive dimension
V2 1
Vfinite-ind
a finite-ind
#TOPGEN_1
O1 0 1
ODer
mol; \mathop{\rm Der} #1
O2 0 1
Odensity
mol; \mathop{\rm density} #1
R1 1 1
Ris_an_accumulation_point_of
i an accumulation point of #2
!not an accumulation point of #2
R2 1 1
Ris_isolated_in
i isolated in #2
!not isolated in #2
V1 1
Vdense-in-itself
a dense-in-itself
V2 1
Vperfect
a perfect
V3 1
Vscattered
a scattered
V4 1
Vseparable
a separable
#TOPGEN_2
M1 1
MNeighborhood_System
ha neighborhood system #0 of #1
neighborhood system(s) #0 of #1
O1 0 1
OChi
mol; \mathop{\rm Chi} #1
O1 0 2
OChi
mol#1#2; \mathop{\rm Chi}(#1,#2)
O2 0 2
ODiscrWithInfin
mol#1#2; \mathop{\rm DiscrWithInfin}(#1,#2)
V1 1
Vfinite-weight
a finite-weight
V2 1
Vinfinite-weight
n infinite-weight
#TOPGEN_3
O1 0 0
OSorgenfrey-line
Hcl@8; Sorgenfrey line
O2 0 0
Ocontinuum
mol; \mathfrak c
O3 1 1
O-powers
moi#2; #1{\rm\hbox{-}powers}(#2)
O4 0 1
OClFinTop
mcl#1; \mathop{\rm ClFinTop}(#1)
O5 1 1
O-PointClTop
moi#2; #1{\rm\hbox{-}PointClTop}(#2)
O6 1 1
O-DiscreteTop
moi#2; #1{\rm\hbox{-}DiscreteTop}(#2)
R1 1 1
Ris_local_minimum_of
iy local minimum of #2
not local minimum of #2
V1 1
Vpoint-filtered
a point-filtered
#TOPGEN_4
O1 0 1
OTotFam
mol; \mathop{\rm TotFam} #1
O2 0 1
OBorelSets
mol; \mathop{\rm BorelSets} #1
R1 1 1
Ris_a_condensation_point_of
i a condensation point of #2
!not a condensation point of #2
V1 1
Vall-open-containing
n all-open-containing
V2 1
Vall-closed-containing
n all-closed-containing
V3 1
Vclosed_for_countable_unions
a closed for countable unions
V4 1
Vclosed_for_countable_meets
a closed for countable meets
V5 1
VF_sigma
a $F_{\sigma}$
V6 1
VG_delta
a $G_{\delta}$
V7 1
VT_1/2
a $T_{1/2}$
V8 1
VBorel
a Borel
#TOPGEN_5
O1 0 0
Oy=0-line
mcl; (y=0){\rm\hbox{-}line}
O2 0 0
Oy>=0-plane
mcl; (y\geq 0){\rm\hbox{-}plane}
O3 0 0
ONiemytzki-plane
Hcsl@8; Niemytzki plane
V1 1
VTychonoff
a Tychonoff
#TOPGRP_1
G1 3
GTopGrStr
mc#1#2#3; \langle #1,#2,#3 \rangle
J1 1
GTopGrStr
hosl#1; topological group structure of #1
L1 0
GTopGrStr
ha topological group structure #0
topological group structures #0
M1 1
MHomeomorphism
ha homeomorphism #0 of #1
homeomorphisms #0 of #1
M1 2
MHomeomorphism
ha homeomorphism #0 of #1,#2
homeomorphisms #0 of #1,#2
M2 0
MTopGroup
ha semi topological group #0
semi topological groups #0
M3 0
MTopologicalGroup
ha topological group #0
topological groups #0
O1 0 1
OHomeoGroup
hosl#1; group of homeomorphisms of #1
V1 1
VUnContinuous
n inverse-continuous
V2 1
VBinContinuous
a continuous
#TOPMETR
O1 0 2
OClosed-Interval-MSpace
mow#1#2; \lbrack #1,\,#2\rbrack_{\rm M}
O2 0 0
OR^1
moq; {\mathbb R}^{\bf 1}
O2 0 1
OR^1
mol; R^1 #1
O3 0 2
OClosed-Interval-TSpace
mow#1#2; \lbrack #1,\,#2\rbrack_{\rm T}
V1 1
Vbeing_ball-family
b ball-family
#TOPREAL1
O1 0 0
OR^2-unit_square
mow; \square_{{\cal E}^2}
O2 0 1
OL~
mol@s#1; \widetilde{\cal L}(#1)
O3 0 1
Onorth_halfline
mol#1; \mathop{\rm NorthHalfline} #1
O4 0 1
Oeast_halfline
mol#1; \mathop{\rm EastHalfline} #1
O5 0 1
Osouth_halfline
mol#1; \mathop{\rm SouthHalfline} #1
O6 0 1
Owest_halfline
mol#1; \mathop{\rm WestHalfline} #1
R1 1 2
Ris_an_arc_of
i an arc from #2 to #3
not an arc from #2 to #3
V1 1
Vspecial
a special
V2 1
Vunfolded
n unfolded
V3 1
Vs.n.c.
a s.n.c.
V4 1
Vbeing_S-Seq
b special sequence
V5 1
Vbeing_S-P_arc
b special polygonal arc
#TOPREAL2
M1 0
MSimple_closed_curve
ha simple closed curve
simple closed curves
V1 1
Vbeing_simple_closed_curve
s conditions of simple closed curve
#TOPREAL4
R1 1 2
Ris_S-P_arc_joining
i a special polygonal arc joining #2 and #3
not a special polygonal arc joining #2 and #3
V1 1
Vbeing_special_polygon
b special polygon
V2 1
Vbeing_Region
b region
#TOPREAL7
O1 0 2
Omax-Prod2
mol#1#2; \mathop{\rm max\hbox{-}Prod2}(#1,#2)
#TOPREALA
O1 0 4
OTrectangle
mol#1#2#3#4; \mathop{\rm Trectangle}(#1,#2,#3,#4)
O2 0 0
OR2Homeomorphism
mcl; \mathop{\rm R2Homeo}
#TOPREALB
O1 0 2
OIntIntervals
mol#1#2; \mathop{\rm IntIntervals}(#1,#2)
O2 0 2
OTcircle
mol#1#2; \mathop{\rm Tcircle}(#1,#2)
O3 0 1
OTunit_circle
mol; \mathop{\rm TopUnitCircle} #1
O4 0 0
Oc[10]
mol; c[10]
O5 0 0
Oc[-10]
mol; c[-10]
O6 0 1
OTopen_unit_circle
mol; \mathop{\rm TopOpenUnitCircle} #1
O7 0 0
OCircleMap
mcl; \mathop{\rm CircleMap}
O7 0 1
OCircleMap
mol; \mathop{\rm CircleMap} #1
O8 0 0
OCircle2IntervalR
mcl; \mathop{\rm Circle2IntervalR}
O9 0 0
OCircle2IntervalL
mcl; \mathop{\rm Circle2IntervalL}
#TOPREALC
O1 0 1
OTIMES
mow; \bigotimes_{#1}
O2 0 2
OPROJ
mol#1#2; \mathop{\rm PROJ}(#1,#2)
#TOPS_1
O1 0 1
OInt
mol@s; \mathop{\rm Int} #1
O2 0 1
OFr
mol@s; \mathop{\rm Fr} #1
V1 1
Vdense
a dense
V2 1
Vboundary
a boundary
V3 1
Vnowhere_dense
a nowhere dense
V4 1
Vcondensed
a condensed
V5 1
Vclosed_condensed
a closed condensed
V6 1
Vopen_condensed
n open condensed
#TOPS_2
V1 1
Vbeing_homeomorphism
b homeomorphism
#TOPS_3
V1 1
Veverywhere_dense
n everywhere dense
#TRANSGEO
M1 0
MCongrSpace
ha congruence space #0
congruence spaces #0
R1 1 1
Ris_FormalIz_of
i a formal isometry of #2
not a formal isometry of #2
R2 1 1
Ris_automorphism_of
i an automorphism of #2
not an automorphism of #2
R3 1 1
Ris_DIL_of
i a dilatation of #2
not a dilatation of #2
V1 1
VCongrSpace-like
a congruence space-like
V2 1
Vpositive_dilatation
a positive dilatation
V3 1
Vnegative_dilatation
a negative dilatation
V4 1
Vdilatation
a dilatation
V5 1
Vtranslation
a translation
V6 1
Vcollineation
a collineation
#TREAL_1
O1 0 2
OL[01]
mol@s#1#2; {\rm L}_{01}(#1,#2)
O1 0 4
OL[01]
mol@s#1#2#3#4; {\rm L}_{01}(#1,#2,#3,#4)
O2 0 4
OP[01]
mol@s#1#2#3#4; {\rm P}_{01}(#1,#2,#3,#4)
#TREES_1
M1 0
MTree
ha tree #0
trees #0
M2 1
MLeaf
ha leaf #0 of #1
leaves #0 of #1
M3 1
MSubtree
ha subtree #0 of #1
subtrees #0 of #1
M4 0
MAntiChain_of_Prefixes
hn antichain #0 of prefixes
antichains #0 of prefixes
M4 1
MAntiChain_of_Prefixes
hn antichain #0 of prefixes of #1
antichains #0 of prefixes of #1
O1 0 1
OProperPrefixes
mol@s#1; \mathop{{\rm Seg}_\preceq}(#1)
O2 0 1
Oelementary_tree
hol; elementary tree of #1
O3 0 1
OLeaves
mol@s#1; \mathop{\rm Leaves}(#1)
O4 1 2
Owith-replacement
moi#2#3; #1 \mathop{\rm with\hbox{-}replacement}(#2,#3)
O5 0 1
Oheight
mol@s; \mathop{\rm height} #1
O6 0 1
Owidth
mol@s; \mathop{\rm width} #1
R1 1 1
Ris_a_prefix_of
m #1 \preceq #2
#1 \npreceq #2
R2 1 1
Ris_a_proper_prefix_of
m #1 \prec #2
#1 \nprec #2
V1 1
VTree-like
a tree-like
V2 1
VAntiChain_of_Prefixes-like
n antichain of prefixes-like
#TREES_2
M1 0
MChain
ha chain #0
chains #0
M1 1
MChain
ha chain #0 of #1
chains #0 of #1
M1 2
MChain
ha #1-chain #0 of #2
#1-chains #0 of #2
M2 1
MLevel
ha level #0 of #1
levels #0 of #1
M3 1
MBranch
ha branch #0 of #1
branches #0 of #1
M4 0
MDecoratedTree
ha decorated tree #0
decorated trees #0
M4 1
MDecoratedTree
ha tree #0 decorated with elements of #1
trees #0 decorated with elements of #1
M4 2
MDecoratedTree
ha tree #0 decorated with elements of #1 and #2
trees #0 decorated with elements of #1 and #2
O1 1 1
O-level
moi#2; #1{\rm\hbox{-}level}(#2)
O2 0 1
Obranchdeg
hol; branch degree of #1
V1 1
Vfinite-order
a finite-order
V2 1
VBranch-like
a branch-like
V3 1
VDecoratedTree-like
a decorated tree-like
#TREES_3
M1 1
MDTree-set
ha set #0 of trees decorated with elements of #1
sets #0 of trees decorated with elements of #1
M1 2
MDTree-set
ha set #0 of trees decorated with elements of #1 and #2
sets #0 of trees decorated with elements of #1 and #2
M2 1
MT-Substitution
ha substitution #0 of structure of #1
substitutions #0 of structure of #1
O1 0 0
OTrees
mo; {\rm Trees}
O1 0 1
OTrees
mol@s#1; {\rm Trees}(#1)
O2 0 0
OFinTrees
mo; {\rm FinTrees}
O2 0 1
OFinTrees
mol@s#1; {\rm FinTrees}(#1)
O3 0 1
Oroots
hopl; roots of #1
V1 1
Vconstituted-Trees
a constituted of trees
V2 1
Vconstituted-FinTrees
a constituted of finite trees
V3 1
Vconstituted-DTrees
a constituted of decorated trees
V4 1
VTree-yielding
a tree yielding
V5 1
VFinTree-yielding
a finite tree yielding
V6 1
VDTree-yielding
a decorated tree yielding
#TREES_4
M1 1
MNode
ha node #0 of #1
nodes #0 of #1
O1 0 1
Oroot-tree
hosl; root tree of #1
O2 1 1
O-flat_tree
hosl(2)#1; flat tree of #1 and #2
O3 1 1
O-tree
moi#2; #1{\rm\hbox{-}tree}(#2)
O3 1 2
O-tree
moi#2#3; #1{\rm\hbox{-}tree}(#2,#3)
#TREES_9
O1 0 1
OSubtrees
mol#1; \mathop{\rm Subtrees}(#1)
O2 0 1
OFixedSubtrees
mol#1; \mathop{\rm FixedSubtrees}(#1)
O3 1 1
O-Subtrees
moi#2; #1\mathop{\rm \hbox{-}Subtrees}(#2)
O4 1 1
O-ImmediateSubtrees
moi#2; #1\mathop{\rm \hbox{-}ImmediateSubtrees}(#2)
V1 1
Vroot
a root
V2 1
Vfinite-branching
a finite-branching
#TREES_A
O1 0 1
Otree
mct#1; \mathop{\overbrace{#1}}
O1 0 2
Otree
mct#1#2; \mathop{\overbrace{#1,#2}}
O1 0 3
Otree
mct#1#2#3; \mathop{\overbrace{#1,#2,#3}}
#TRIANG_1
G1 2
GTriangStr
mc#1#2; \langle #1,#2 \rangle
J1 1
GTriangStr
hol#1; triangulation structure of #1
L1 0
GTriangStr
ha triangulation structure #0
triangulation structures #0
M1 1
Mtriangulation
ha triangulation #0 of #1
triangulation #0 of #1
M2 2
MSymplex
ha symplex #0 of #1 and #2
symplexes #0 of #1,#2
M3 1
MFace
ha face #0 of #1
faces #0 of #1
O1 0 1
Osymplexes
mol#1; \mathop{\rm symplexes}(#1)
O2 0 1
OFuncsSeq
mol#1; \mathop{\rm FuncsSeq}(#1)
O3 0 0
ONatEmbSeq
mol; \mathop{\rm NatEmbSeq}
O4 0 2
Oface
mol#1#2; \mathop{\rm face}(#1,#2)
O5 0 1
OTriang
mol#1; \mathop{\rm Triang}(#1)
U1 1
USkeletonSeq
hosl#1; skeleton sequence of #1
skeleton sequence
U2 1
UFacesAssign
hosl#1; faces assignment of #1
faces assignment
V1 1
Vlower_non-empty
a lower non-empty
#TSEP_1
R1 2 0
Rare_not_separated
hn #1 and #2 are not separated
#1 and #2 are separated
R2 2 0
Rare_weakly_separated
h #1 and #2 are weakly separated
#1 and #2 are not weakly separated
R3 2 0
Rare_not_weakly_separated
hn #1 and #2 are not weakly separated
#1 and #2 are weakly separated
#TSEP_2
R1 2 0
Rconstitute_a_decomposition
h #1 and #2 constitute a decomposition
#1 and #2 do not constitute a decomposition
R2 2 0
Rdo_not_constitute_a_decomposition
hn #1 and #2 do not constitute a decomposition
#1 and #2 constitute a decomposition
#TSP_1
M1 0
MKolmogorov_space
ha Kolmogorov space #0
Kolmogorov spaces #0
M2 0
Mnon-Kolmogorov_space
ha non-Kolmogorov space #0
non-Kolmogorov spaces #0
M3 1
MKolmogorov_subspace
ha Kolmogorov subspace #0 of #1
Kolmogorov subspaces #0 of #1
M4 1
Mnon-Kolmogorov_subspace
ha non-Kolmogorov subspace #0 of #1
non-Kolmogorov subspaces #0 of #1
#TSP_2
M1 1
Mmaximal_Kolmogorov_subspace
ha maximal Kolmogorov subspace #0 of #1
maximal Kolmogorov subspaces #0 of #1
O1 0 2
OStone-retraction
Hosl(2)#1#2; Stone-retraction of #1 onto #2
V1 1
Vmaximal_T_0
a maximal {\Tzero}
#TURING_1
G1 5
GTuringStr
mc#1#2#3#4#5; \langle #1,#2,#3,#4,#5 \rangle
J1 1
GTuringStr
hol#1; Turing machine structure of #1
L1 0
GTuringStr
ha Turing machine structure #0
Turing machine structures #0
M1 1
MTape
ha tape #0 of #1
tapes #0 of #1
M2 1
MAll-State
ha State #0 of #1
States #0 of #1
M3 1
MTran-Source
ha transition-source #0 of #1
transition-sources #0 of #1
M4 1
MTran-Goal
ha transition-target #0 of #1
transition-targets #0 of #1
O1 0 1
OSegM
mol#1; \mathop{\rm Seg}_M #1
O2 0 2
OPrefix
mol#1#2; \mathop{\rm Prefix}(#1,#2)
O3 0 3
OTape-Chg
mol#1#2#3; \mathop{\rm Tape\hbox{-}Chg}(#1,#2,#3)
O4 0 1
Ooffset
mol#1; \mathop{\rm offset}(#1)
O5 0 1
OHead
mol#1; \mathop{\rm Head}(#1)
O6 0 1
OTRAN
mor; #1 \mathop{\rm\hbox{-}target}
O7 0 0
OSum_Tran
mc; \mathop{\rm SumTran}
O8 0 0
OSumTuring
mc; \mathop{\rm SumTuring}
O9 0 0
OSucc_Tran
mc; \mathop{\rm SuccTran}
O10 0 0
OSuccTuring
mc; \mathop{\rm SuccTuring}
O11 0 0
OZero_Tran
mc; \mathop{\rm ZeroTran}
O12 0 0
OZeroTuring
mc; \mathop{\rm ZeroTuring}
O13 0 0
OU3(n)Tran
mor; n \mathop{\rm\hbox{-}proj3Tran}
O14 0 0
OU3(n)Turing
mor; n \mathop{\rm\hbox{-}proj3Turing}
O15 0 2
OUnionSt
mol#1#2; \mathop{\rm SeqStates}(#1,#2)
O16 0 3
OFirstTuringTran
mol#1#2#3; \mathop{\rm 1^{st}SeqTran}(#1,#2,#3)
O17 0 3
OSecondTuringTran
mol#1#2#3; \mathop{\rm 2^{nd}SeqTran}(#1,#2,#3)
O18 0 1
OFirstTuringState
mol#1; \mathop{\rm 1^{st}SeqState} #1
O19 0 1
OSecondTuringState
mol#1; \mathop{\rm 2^{nd}SeqState} #1
O20 0 1
OFirstTuringSymbol
mol#1; \mathop{\rm 1^{st}SeqSymbol} #1
O21 0 1
OSecondTuringSymbol
mol#1; \mathop{\rm 2^{nd}SeqSymbol} #1
O22 0 3
OUniontran
mol#1#2#3; \mathop{\rm SeqTran}(#1,#2,#3)
O23 0 2
OUnionTran
mol#1#2; \mathop{\rm SeqTran}(#1,#2)
O24 1 1
O';'
moi; #1{\bf;\ }#2
R1 1 2
Ris_1_between
i 1 between #2,#3
not 1 between #2,#3
R2 1 1
RstoreData
h #1 stores data #2
#1 does not store data #2
R3 1 1
Rcomputes
h #1 computes #2
#1 does not compute #2
R3 2 1
Rcomputes
h #1,#2 computes #2
#1,#2 does not compute #2
U1 1
USymbols
hopl#1; symbols of #1
symbols
U2 1
UAcceptS
honl#1; accepting state of #1
accepting state
V1 1
VAccept-Halt
n accepting
#TWOSCOMP
O1 0 0
Oand2
mow; \mathop{\rm and}_2
O2 0 0
Oand2a
mor{qrw}@9; \mathop{\rm and}_{2a}
O3 0 0
Oand2b
mor{qrw}@9; \mathop{\rm and}_{2b}
O4 0 0
Onand2
mow; \mathop{\rm nand}_2
O5 0 0
Onand2a
mor{qrw}@9; \mathop{\rm nand}_{2a}
O6 0 0
Onand2b
mor{qrw}@9; \mathop{\rm nand}_{2b}
O7 0 0
Oor2
mow; \mathop{\rm or}_2
O8 0 0
Oor2a
mor{qrw}@9; \mathop{\rm or}_{2a}
O9 0 0
Oor2b
mor{qrw}@9; \mathop{\rm or}_{2b}
O10 0 0
Onor2
mow; \mathop{\rm nor}_2
O11 0 0
Onor2a
mor{qrw}@9; \mathop{\rm nor}_{2a}
O12 0 0
Onor2b
mor{qrw}@9; \mathop{\rm nor}_{2b}
O13 0 0
Oxor2
mow; \mathop{\rm xor}_2
O14 0 0
Oxor2a
mor{qrw}@9; \mathop{\rm xor}_{2a}
O15 0 0
Oxor2b
mor{qrw}@9; \mathop{\rm xor}_{2b}
O16 0 0
Oand3
mow; \mathop{\rm and}_3
O17 0 0
Oand3a
mor{qrw}@9; \mathop{\rm and}_{3a}
O18 0 0
Oand3b
mor{qrw}@9; \mathop{\rm and}_{3b}
O19 0 0
Oand3c
mor{qrw}@9; \mathop{\rm and}_{3c}
O20 0 0
Onand3
mow; \mathop{\rm nand}_3
O21 0 0
Onand3a
mor{qrw}@9; \mathop{\rm nand}_{3a}
O22 0 0
Onand3b
mor{qrw}@9; \mathop{\rm nand}_{3b}
O23 0 0
Onand3c
mor{qrw}@9; \mathop{\rm nand}_{3c}
O24 0 0
Oor3a
mor{qrw}@9; \mathop{\rm or}_{3a}
O25 0 0
Oor3b
mor{qrw}@9; \mathop{\rm or}_{3b}
O26 0 0
Oor3c
mor{qrw}@9; \mathop{\rm or}_{3c}
O27 0 0
Onor3
mow; \mathop{\rm nor}_3
O28 0 0
Onor3a
mor{qrw}@9; \mathop{\rm nor}_{3a}
O29 0 0
Onor3b
mor{qrw}@9; \mathop{\rm nor}_{3b}
O30 0 0
Onor3c
mor{qrw}@9; \mathop{\rm nor}_{3c}
O31 0 0
Oxor3
mow; \mathop{\rm xor}_3
O32 0 2
OCompStr
mol#1#2; \mathop{\rm CompStr}(#1,#2)
O33 0 2
OCompCirc
mol#1#2; \mathop{\rm CompCirc}(#1,#2)
O34 0 2
OCompOutput
mol#1#2; \mathop{\rm CompOutput}(#1,#2)
O35 0 2
OIncrementStr
mol#1#2; \mathop{\rm IncrementStr}(#1,#2)
O36 0 2
OIncrementCirc
mol#1#2; \mathop{\rm IncrementCirc}(#1,#2)
O37 0 2
OIncrementOutput
mol#1#2; \mathop{\rm IncrementOutput}(#1,#2)
O38 0 2
OBitCompStr
mol#1#2; \mathop{\rm BitCompStr}(#1,#2)
O39 0 2
OBitCompCirc
mol#1#2; \mathop{\rm BitCompCirc}(#1,#2)
#T_0TOPSP
M1 0
MT_0-TopSpace
ha \Tzero-space #0
\Tzero-spaces #0
O1 0 1
OIndiscernibility
mol#1; \mathop{\rm Indiscernibility}(#1)
O2 0 1
OIndiscernible
mow; #1_{/\mathop{\rm Indiscernibility} #1}
O3 0 1
OT_0-reflex
mol#1; \mathop{\rm {\it T}_0\hbox{-}reflex}(#1)
O4 0 1
OT_0-canonical_map
mol#1; \mathop{\rm {\it T}_0\hbox{-}map}(#1)
R1 2 0
Rare_homeomorphic
h #1 and #2 are homeomorphic
#1 and #2 are not homeomorphic
#T_1TOPSP
O1 0 1
OClosed_Partitions
mol#1; \mathop{\rm ClosedPartitions} #1
O2 0 1
OT_1-reflex
mol#1; \mathop{T_1\hbox{-}\rm reflex} #1
O3 0 1
OT_1-reflect
mol#1; \mathop{T_1\hbox{-}\rm reflect} #1
#UNIALG_1
G1 2
GUAStr
mc#1#2; \langle #1,\allowbreak #2\rangle
J1 1
GUAStr
hol#1; universal algebra structure of #1
L1 0
GUAStr
ha universal algebra structure #0
universal algebra structures #0
M1 1
MPFuncFinSequence
ha finite sequence #0 of operational functions of #1
finite sequences #0 of operational functions of #1
M2 0
MUniversal_Algebra
ha universal algebra #0
universal algebras #0
O1 0 1
Oarity
mol@s; \mathop{\rm arity} #1
O2 0 1
Osignature
mol@s; \mathop{\rm signature} #1
U1 1
Ucharact
hosl#1; characteristic of #1
characteristic
V1 1
Vhomogeneous
a homogeneous
#UNIALG_2
M1 1
MPFuncsDomHQN
ha set #0 of universal functions on #1
sets #0 of universal functions on #1
M2 1
Moperation
hn operation #0 of #1
operation #0 of #1
M3 1
MSubAlgebra
ha subalgebra #0 of #1
subalgebras #0 of #1
O1 0 1
OOperations
mol#1; \mathop{\rm Operations}(#1)
O2 0 2
OOpers
mol#1#2; \mathop{\rm Opers}(#1,#2)
O3 0 1
OUniAlgSetClosed
mc#1; \langle #1, {\rm Ops}\rangle
O4 0 1
OConstants
mol#1; \mathop{\rm Constants}(#1)
O4 0 2
OConstants
mol#1#2; \mathop{\rm Constants}(#1,#2)
O5 0 1
OGenUnivAlg
mol#1; \mathop{\rm Gen}^{\rm UA}(#1)
O6 0 1
OSub
mol#1; \mathop{\rm Sub}(#1)
O7 0 1
OUniAlg_join
mow#1; \bigsqcup_{#1}
O8 0 1
OUniAlg_meet
mow#1; \bigsqcap_{#1}
O9 0 1
OUnSubAlLattice
hol#1; lattice of subalgebras of #1
R1 1 1
Ris_closed_on
i closed on #2
not closed on #2
R1 1 2
Ris_closed_on
i closed on #2,#3
not closed on #2,#3
V1 1
Vopers_closed
n operations closed
V2 1
Vwith_const_op
x constants
#UNIALG_3
M1 1
MSubAlgebra-Family
ha family #0 of subalgebras of #1
families #0 of subalgebras of #1
#UNIROOTS
O1 0 1
OMultGroup
mol#1; \mathop{\rm MultGroup}(#1)
O2 1 0
O-roots_of_1
mol#1; #1\mathop{\rm\hbox{-}roots\_of\_1}
O3 1 0
O-th_roots_of_1
mol#1; #1\mathop{\rm\hbox{-}th\_roots\_of\_1}
O4 0 2
Ounital_poly
mol#1#2; \mathop{\rm unital\_poly}(#1,#2)
O5 0 1
Ocyclotomic_poly
mol#1; \mathop{\rm cyclotomic\_poly}(#1)
#UPROOTS
M1 1
MRbag
ha real bag #0 over #1
real bags #0 over #1
O1 0 1
OcanFS
mol#1; \mathop{\rm CFS}(#1)
O2 2 0
O-bag
mol#1#2; (#1,#2)\mathop{\rm\hbox{-}bag}
O3 0 2
Opoly_shift
mol#1#2; \mathop{\rm poly\_shift}(#1,#2)
O4 0 2
Opoly_quotient
mol#1#2; \mathop{\rm poly\_quotient}(#1,#2)
O5 0 2
Omultiplicity
mol#1#2; \mathop{\rm multiplicity}(#1,#2)
O6 0 1
OBRoots
mol#1; \mathop{\rm BRoots}(#1)
O7 0 2
Ofpoly_mult_root
mol#1#2; \mathop{\rm fpoly\_mult\_root}(#1,#2)
O8 0 1
Opoly_with_roots
mol#1; \mathop{\rm poly\_with\_roots}(#1)
#URYSOHN1
M1 2
MNbhd
ha neighbourhood #0 of #1 in #2
neighbourhoods #0 of #1 in #2
M2 2
MBetween
ha between(?) #0 of #1 and #2
between(?)(s) #0 of #1 and #2
O1 0 1
Odyadic
mol#1; \mathop{\rm dyadic}(#1)
O2 0 0
ODYADIC
mol; \mathop{\rm DYADIC}
O3 0 1
Odyad
mol#1; \mathop{\rm dyad}(#1)
O4 0 1
Oaxis
mol#1; \mathop{\rm axis}#1
#URYSOHN3
M1 3
MDrizzle
ha drizzle #0 of #1,#2,#3
drizzles #0 of #1,#2,#3
M2 2
MRain
ha rain #0 of #1,#2
rains #0 of #1,#2
O1 0 1
Oinf_number_dyadic
mol#1; \mathop{\rm InfDyadic} #1
O2 0 1
OTempest
mol#1; \mathop{\rm Tempest} #1
O3 0 2
ORainbow
mol#1#2; \mathop{\rm Rainbow}(#1,#2)
O4 0 1
OThunder
mol#1; \mathop{\rm Thunder} #1
#VALUAT_1
M1 1
Minterpretation
hn interpretation #0 of #1
interpretations #0 of #1
O1 0 1
OValuations_in
mcl@s#1; \mathop{\hbox{\bfit V}}(#1)
O2 0 2
OFOR_ALL
mol(2)@s/1k/2m#1; \bigwedge_{#1}#2
O3 0 2
OValid
mcl@s#1#2; \mathop{\rm Valid}(#1,#2)
#VALUED_0
M1 1
Msubsequence
ha subsequence #0 of #1
subsequence #0 of #1
V1 1
Vcomplex-valued
a complex-valued
V2 1
Vext-real-valued
n extended real-valued
V3 1
Vreal-valued
a real-valued
V4 1
Vrational-valued
a rational-valued
V5 1
Vinteger-valued
n integer-valued
V6 1
Vnatural-valued
a natural-valued
V7 1
Vnon-zero
a non-zero
V8 1
Vdecreasing
a decreasing
V9 1
Vnon-decreasing
a non-decreasing
V10 1
Vnon-increasing
a non-increasing
V11 1
Vzeroed
a zeroed
#VALUED_1
O1 0 1
O(#)
mol@s; \square #1
O1 0 2
O(#)
mow#2; #1_{[#1,#2]_{\rm T}}
O1 1 1
O(#)
moi@m; #1 \cdot #2
O1 2 0
O(#)
mow#1; #2_{[#1,#2]_{\rm T}}
O2 1 0
O/"
moq; #1 \mathclose{^{-1}}
O2 1 1
O/"
moi@m; #1/#2
O3 0 1
OShift
mol#1; \mathop{\rm Shift} #1
O3 0 2
OShift
mol#1#2; \mathop{\rm Shift}(#1,#2)
O3 0 3
OShift
mol#1#2#3; \mathop{\rm Shift}(#1,#2,#3)
O3 1 1
OShift
mol(2)#1; \mathop{\rm Shift}^{#1} #2
#VALUED_2
O1 0 1
ODOMS
mol#1; \mathop{\rm DOMS}(#1)
O2 0 1
OC_PFuncs
mol; \mathop{\rm{\mathbb C}\hbox{-}PFuncs} #1
O3 0 1
OC_Funcs
mol; \mathop{\rm{\mathbb C}\hbox{-}Funcs} #1
O4 0 1
OE_PFuncs
mol; \mathop{\rm\overline{\mathbb R}\hbox{-}PFuncs} #1
O5 0 1
OE_Funcs
mol; \mathop{\rm\overline{\mathbb R}\hbox{-}Funcs} #1
O6 0 1
OR_PFuncs
mol; \mathop{\rm{\mathbb R}\hbox{-}PFuncs} #1
O7 0 1
OR_Funcs
mol; \mathop{\rm{\mathbb R}\hbox{-}Funcs} #1
O8 0 1
OQ_PFuncs
mol; \mathop{\rm{\mathbb Q}\hbox{-}PFuncs} #1
O9 0 1
OQ_Funcs
mol; \mathop{\rm{\mathbb Q}\hbox{-}Funcs} #1
O10 0 1
OI_PFuncs
mol; \mathop{\rm{\mathbb Z}\hbox{-}PFuncs} #1
O11 0 1
OI_Funcs
mol; \mathop{\rm{\mathbb Z}\hbox{-}Funcs} #1
O12 0 1
ON_PFuncs
mol; \mathop{\rm{\mathbb N}\hbox{-}PFuncs} #1
O13 0 1
ON_Funcs
mol; \mathop{\rm{\mathbb N}\hbox{-}Funcs} #1
O14 1 1
O(/)
moi@m; #1 / #2
O15 0 1
O<->
mol@a; - #1
O15 1 1
O<->
moi@a; #1 - #2
O16 0 1
O(-)
mol; (-) #1
O16 1 0
O(-)
moi@m; #1\circ-
O16 1 1
O(-)
moi@4; #1 \ominus #2
O17 0 1
O</>
mol@m; {^1}/ #1
O17 1 1
O</>
moi@m; #1 / #2
O18 0 0
O[+]
mc; [+]
O18 1 1
O[+]
moi@a; #1 + #2
O19 0 0
O[-]
mc; [-]
O19 1 1
O[-]
moi@a; #1 - #2
O20 1 1
O[/]
moi@m; #1 / #2
O21 1 1
O<+>
moi@a; #1 + #2
O22 1 1
O<#>
moi@m; #1 \cdot #2
O23 1 1
O<++>
moi@a; #1 + #2
O24 1 1
O<-->
moi@a; #1 - #2
O25 1 1
O<##>
moi@m; #1 \cdot #2
O26 1 1
O<//>
moi@m; #1 / #2
V1 1
Vcomplex-functions-membered
a complex-functions-membered
V2 1
Vext-real-functions-membered
n extended-real-functions-membered
V3 1
Vreal-functions-membered
a real-functions-membered
V4 1
Vrational-functions-membered
a rational-functions-membered
V5 1
Vinteger-functions-membered
n integer-functions-membered
V6 1
Vnatural-functions-membered
a natural-functions-membered
V7 1
Vcomplex-functions-valued
a complex-functions-valued
V8 1
Vext-real-functions-valued
n extended-real-functions-valued
V9 1
Vreal-functions-valued
a real-functions-valued
V10 1
Vrational-functions-valued
a rational-functions-valued
V11 1
Vinteger-functions-valued
n integer-functions-valued
V12 1
Vnatural-functions-valued
a natural-functions-valued
#VECTMETR
G1 5
GRLSMetrStruct
mc#1#2#3#4#5; \langle #1,#2,#3,#4,#5 \rangle
J1 1
GRLSMetrStruct
hol#1; RLSMetrStruct of #1
L1 0
GRLSMetrStruct
ha RLSMetrStruct #0
RLSMetrStruct #0
M2 0
MRealLinearMetrSpace
ha RealLinearMetrSpace #0
RealLinearMetrSpace #0
O1 0 1
OISOM
mol; \mathop{\rm ISOM} #1
O2 0 1
ONorm
mol; \mathop{\rm Norm} #1
O3 0 1
ORLMSpace
mol; \mathop{\rm RLMSpace} #1
O4 0 1
OIsomGroup
mol; \mathop{\rm IsomGroup} #1
O5 0 1
OSubIsomGroupRel
mol; \mathop{\rm SubIsomGroupRel} #1
V1 1
Vinternal
n internal
V2 1
Visometric
n isometric
V3 1
Vtranslatible
a translatible
#VECTSP10
O1 0 1
OStructVectSp
mol#1; \mathop{\rm StructVectSp} (#1)
O2 0 1
OCosetSet
mol; \mathop{\rm CosetSet} #1
O2 0 2
OCosetSet
mol#1#2; \mathop{\rm CosetSet}(#1,#2)
O3 0 1
OaddCoset
mol; \mathop{\rm addCoset} #1
O3 0 2
OaddCoset
mol#1#2; \mathop{\rm addCoset}(#1,#2)
O4 0 1
OzeroCoset
mol; \mathop{\rm zeroCoset} #1
O4 0 2
OzeroCoset
mol#1#2; \mathop{\rm zeroCoset}(#1,#2)
O5 0 1
OlmultCoset
mol; \mathop{\rm lmultCoset} #1
O5 0 2
OlmultCoset
mol#1#2; \mathop{\rm lmultCoset}(#1,#2)
O6 0 2
OVectQuot
mo{kqmw}@m; {}^{#1}/_{#2}
O7 0 2
OcoeffFunctional
mol#1#2; \mathop{\rm coeffFunctional}(#1,#2)
O8 0 1
Oker
mol#1; \mathop{\rm ker} #1
O9 0 2
OQFunctional
mo{kqmw}@m; {}^{#1}/_{#2}
O10 0 1
OCQFunctional
mow; \mathop{\rm CQFunctional} #1
#VECTSP11
M1 1
Meigenvalue
hn eigenvalue #0 of #1
eigenvalues #0 of #1
M2 2
Meigenvector
hn eigenvector #0 of #1 and #2
eigenvectors #0 of #1 and #2
O1 0 1
OUnionKers
mol; \mathop{\rm UnionKers} #1
V1 1
Vwith_eigenvalues
x eigenvalues
#VECTSP_1
G1 4
GVectSpStr
mc#1#2#3#4; \langle #1,#2,#3,#4 \rangle
J1 1
GVectSpStr
hol#1; vector space structure of #1
L1 1
GVectSpStr
ha vector space structure #0 over #1
vector space structures #0 over #1
M1 0
MAddGroup
ha group #0
groups #0
M2 0
MAbGroup
hn Abelian group #0
Abelian groups #0
M3 0
MField
ha field #0
fields #0
M3 1
MField
ha field #0 of subsets of #1
fields #0 of subsets of #1
M4 1
MScalar
ha scalar #0 of #1
scalars #0 of #1
M5 1
MVector
ha vector #0 of #1
vectors #0 of #1
M6 1
MVectSp
ha vector space #0 over #1
vector spaces #0 over #1
O1 0 0
OG_Real
mow; {\mathbb R}_{\rm G}
O2 0 0
OF_Real
mow; {\mathbb R}_{\rm F}
O3 0 1
Ocomp
mol@s; \mathop{\rm comp} #1
U1 1
Ulmult
hosl#1; left multiplication of #1
left multiplication
V1 1
Vright-distributive
a right distributive
V2 1
Vleft-distributive
a left distributive
V3 1
Vright_unital
a right unital
V4 1
Vwell-unital
a well unital
V5 1
Vleft_unital
a left unital
V7 1
VFanoian
a Fanoian
#VECTSP_2
G1 4
GRightModStr
mc#1#2#3#4; \langle #1,#2,#3,#4 \rangle
G2 5
GBiModStr
mc#1#2#3#4#5; \langle #1,#2,#3,#4,#5 \rangle
J1 1
GRightModStr
hol#1; right module structure of #1
J2 1
GBiModStr
hol#1; bimodule structure of #1
L1 1
GRightModStr
ha right module structure #0 over #1
right module structures #0 over #1
L2 2
GBiModStr
ha bimodule structure #0 over #1,#2
bimodule structures #0 over #1,#2
M1 0
McomRing
ha commutative ring #0
commutative rings #0
M2 0
MdomRing
hn integral domain #0
integral domains #0
M3 0
MSkew-Field
ha skew field #0
skew fields #0
M4 1
MLeftMod
ha left module #0 over #1
left modules #0 over #1
M5 1
MRightMod
ha right module #0 over #1
right modules #0 over #1
M6 2
MBiMod
ha bimodule #0 over #1 and #2
bimodules #0 over #1 and #2
O1 0 1
OAbGr
mol@s#1; \mathop{\rm AbGr}(#1)
O2 0 1
OLeftModule
mol@s#1; \mathop{\rm LeftMod}(#1)
O3 0 1
ORightModule
mol@s#1; \mathop{\rm RightMod}(#1)
O4 0 2
OBiModule
mol@s#1#2; \mathop{\rm BiMod}(#1, #2)
U1 1
Urmult
hosl#1; right multiplication of #1
right multiplication
V1 1
VdomRing-like
n integral domain-like
V2 1
VRightMod-like
a right module-like
V3 1
VBiMod-like
a bimodule-like
#VECTSP_8
M1 1
MSubVS-Family
ha family #0 of subspaces of #1
families #0 of subspaces of #1
M2 2
MSemilattice-Homomorphism
ha lower homomorphism #0 between #1 and #2
lower homomorphisms #0 between #1 and #2
M3 2
Msup-Semilattice-Homomorphism
hn upper homomorphism #0 between #1 and #2
upper homomorphisms #0 between #1 and #2
O1 0 1
OFuncLatt
mol#1; \mathop{\rm FuncLatt}(#1)
#VFUNCT_1
R1 1 1
Ris_bounded_on
i bounded on #2
not bounded on #2
#WAYBEL10
M1 1
MSystem
ha system #0 of #1
systems #0 of #1
O1 0 1
OClOpers
mol#1; \mathop{\rm ClOpers}(#1)
O2 0 1
OClosureSystems
mol#1; \mathop{\rm ClosureSystems}(#1)
O3 0 1
OClImageMap
mol#1; \mathop{\rm ClImageMap}(#1)
O4 0 1
Oclosure_op
hosl#1; closure operation of #1
O5 0 1
ODsupClOpers
mol#1; \mathop{\rm ClOpers}^\ast(#1)
O6 0 1
OSubalgebras
mol#1; \mathop{\rm Subalgebras}(#1)
#WAYBEL11
O1 0 1
OScott-Convergence
hol#1; Scott convergence of #1
O2 0 1
ONet-Str
mol#1; \mathop{\rm NetStr}(#1)
O2 0 2
ONet-Str
mol#1#2; \mathop{\rm NetStr}(#1,#2)
R1 1 1
Ris_S-limit_of
i S-limit of #2
not S-limit of #2
V1 1
Vinaccessible_by_directed_joins
n inaccessible by directed joins
V2 1
Vclosed_under_directed_sups
a closed under directed sups
V3 1
Vproperty(S)
a property(S)
V4 1
Vdirectly_closed
a directly closed
V5 1
VScott
a Scott
#WAYBEL14
V1 1
Vjointly_Scott-continuous
a jointly Scott-continuous
#WAYBEL15
O1 0 1
OATOM
mol#1; \mathop{\rm ATOM}(#1)
V1 1
Vatom
n atom
#WAYBEL16
M1 2
MCLHomomorphism
ha CLHomomorphism #0 of #1,#2
CLHomomorphism #0 of #1,#2
O1 0 1
OIrr
mol#1; \mathop{\rm Irr} #1
R1 1 0
Ris_FG_set
i a free generator set
not a free generator set
V1 1
Vcompletely-irreducible
a completely-irreducible
#WAYBEL17
O1 2 0
O,...
moi@w#1#2; #1,#2,...
O2 0 2
OSCMaps
mol#1#2; \mathop{\rm SCMaps}(#1,#2)
#WAYBEL18
O1 0 1
Oproduct_prebasis
hosl#1; product prebasis for #1
O2 0 0
OSierpinski_Space
hosl; Sierpi{\'n}ski space
R1 1 1
Ris_Retract_of
i a topological retract of #2
not a topological retract of #2
V1 1
VTopSpace-yielding
a topological space yielding
#WAYBEL19
M1 0
MTopPoset
ha top-poset #0
top-posets #0
V1 1
VLawson
a Lawson
#WAYBEL20
O1 0 1
OEqRel
mol#1; \mathop{\rm EqRel}(#1)
O1 0 2
OEqRel
mol#1#2; \mathop{\rm EqRel}(#1,#2)
O1 0 3
OEqRel
mol#1#2#3; \mathop{\rm EqRel}(#1,#2,#3)
O2 0 1
Okernel_op
hol#1; kernel operation of #1
O3 0 1
Okernel_congruence
hol#1; kernel congruence of #1
V1 1
VCLCongruence
ax continuous lattice congruence
#WAYBEL21
M1 2
MSemilatticeHomomorphism
ha semilattice morphism #0 from #1 into #2
semilattice morphisms #0 from #1 into #2
M2 2
MEmbedding
hn embedding #0 of #1 into #2
embeddings #0 of #1 into #2
V1 1
Vlim_infs-preserving
a liminfs-preserving
#WAYBEL22
O1 0 1
OFixedUltraFilters
hosl#1; fixed ultrafilters of #1
O2 1 0
O-extension_to_hom
hosc#1; extension of #1 to homomorphism
R1 1 1
Ris_FreeGen_set_of
i a set of free generators of #2
not a set of free generators of #2
#WAYBEL23
M1 1
MCLbasis
ha CLbasis #0 of #1
CLbasis #0 of #1
O1 0 1
Oweight
mol#1; \mathop{\rm weight} #1
O2 0 1
OsupMap
mol#1; \mathop{\rm supMap} #1
O3 0 1
OidsMap
mol#1; \mathop{\rm idsMap} #1
O4 0 1
ObaseMap
mol#1; \mathop{\rm baseMap} #1
V1 1
Vinfs-closed
n infs-closed
V2 1
Vsups-closed
a sups-closed
V3 1
Vsecond-countable
a second-countable
V4 1
Vwith_bottom
x bottom
V5 1
Vwith_top
x top
#WAYBEL24
O1 0 2
OContMaps
moc#1#2; [#1\to #2]
#WAYBEL25
O1 0 1
OOmega
mol; \Omega #1
V1 1
Vmonotone-convergence
a monotone convergence
#WAYBEL26
O1 1 1
O-POS_prod
moi; #1 \mathop{\rm\hbox{-}prod}_{\rm POS} #2
O2 1 1
O-TOP_prod
moi; #1 \mathop{\rm\hbox{-}prod}_{\rm TOP} #2
O3 0 2
OoContMaps
moc#1#2; [#1\to #2]
O4 0 1
O*graph
mor#1; G_{#1}
O4 2 0
O*graph
mol#1#2; \Theta_{#2}(#1)
#WAYBEL27
O1 0 2
OUPS
mol#1#2; \mathop{\rm UPS}(#1,#2)
V1 1
Vuncurrying
n uncurrying
V2 1
Vcurrying
a currying
V3 1
Vcommuting
a commuting
#WAYBEL28
O1 0 1
Olim_inf-Convergence
hosl#1; lim inf convergence of #1
O2 0 1
Oxi
mol#1; \xi (#1)
V1 1
Vgreater_or_equal_to_id
a greater or equal to id
#WAYBEL29
O1 0 1
OSigma
mol#1; \Sigma #1
O2 0 2
OTheta
mol#1#2; \Theta (#1,#2)
#WAYBEL30
O1 1 0
O^0
mor#1; #1 ^0
V1 1
Vwith_small_semilattices
x small semilattices
V2 1
Vwith_compact_semilattices
x compact semilattices
V3 1
Vwith_open_semilattices
x open semilattices
#WAYBEL31
O1 0 1
OCLweight
mol#1; \mathop{\rm CLweight} #1
O2 0 2
OWay_Up
mol#1#2; \mathop{\rm Way\_Up}(#1,#2)
#WAYBEL32
O1 0 1
Oinf_net
mol#1; \mathop{\rm inf\_net} #1
V1 1
Vorder_consistent
n order consistent
#WAYBEL33
O1 0 1
OXi
mol#1; \Xi(#1)
V1 1
Vlim-inf
a lim-inf
#WAYBEL34
O1 0 1
OLowerAdj
hosl#1; lower adjoint of #1
O1 1 0
OLowerAdj
mow#1; \mathop{\rm LowerAdj}_{#1}
O2 0 1
OUpperAdj
hosl#1; upper adjoint of #1
O2 1 0
OUpperAdj
mow#1; \mathop{\rm UpperAdj}_{#1}
O3 1 0
O-INF_category
mow#1; {\it INF}_{#1}
O4 1 0
O-SUP_category
mow#1; {\it SUP}_{#1}
O5 1 0
O-INF(SC)_category
mor{rqw}#1; {\it INF}^\uparrow_{#1}
O6 1 0
O-SUP(SO)_category
mor{rqw}#1; {\it SUP}^0_{#1}
O7 1 0
O-CL_category
mow#1; {\it CL}_{#1}
O8 1 0
O-CL-opp_category
mor{rqw}#1; {\it CL}^{\rm op}_{#1}
V1 1
Vwaybelow-preserving
a waybelow-preserving
V2 1
Vrelatively_open
a relatively open
V3 1
Vcompact-preserving
a compact-preserving
V4 1
Vfinite-sups-preserving
a finite-sups-preserving
V5 1
Vbottom-preserving
a bottom-preserving
V6 1
Vfinite-sups-inheriting
a finite-sups-inheriting
V7 1
Vbottom-inheriting
a bottom-inheriting
#WAYBEL35
M1 1
Mstrict_chain
ha strict chain #0 of #1
strict chains #0 of #1
O1 1 0
O-LowerMap
mor; #1 \mathop{\rm -LowerMap}
O2 0 2
OStrict_Chains
mol#1#2; \mathop{\rm StrictChains}(#1,#2)
O3 0 3
OSetBelow
mol#1#2#3; \mathop{\rm SetBelow}(#1,#2,#3)
O4 0 2
OSupBelow
mol#1#2; \mathop{\rm SupBelow}(#1,#2)
R1 1 1
Ris_inductive_wrt
i inductive w.r.t. #2
not inductive w.r.t. #2
R2 1 1
Rsatisfies_SIC_on
h #1 satisfies SIC on #2
#1 does not satisfy SIC on #2
V1 1
Vextra-order
n extra-order
V2 1
Vsatisfying_SIC
s SIC
V3 1
Vsup-closed
a sup-closed
#WAYBEL_0
G1 3
GNetStr
mc#1#2#3; \langle #1,#2,#3 \rangle
J1 1
GNetStr
hol#1; net structure of #1
L1 1
GNetStr
ha net structure #0 over #1
net structures #0 over #1
M1 1
Mprenet
ha prenet #0 over #1
prenets #0 over #1
M2 1
Mnet
ha net #0 in #1
nets #0 in #1
M3 0
MSemilattice
ha semilattice #0
semilattices #0
M4 0
Msup-Semilattice
ha sup-semilattice #0
sup-semilattices #0
M5 0
MLATTICE
ha lattice #0
lattices #0
O1 0 2
Onetmap
mol#1#2; \mathop{\rm netmap}(#1,#2)
O2 0 1
Odownarrow
mol; \mathopen{\downarrow} #1
O3 0 1
Ouparrow
mol; \mathopen{\uparrow} #1
O4 0 1
OIds
mol#1; \mathop{\rm Ids}(#1)
O5 0 1
OFilt
mol#1; \mathop{\rm Filt}(#1)
O6 0 1
OIds_0
mol#1; \mathop{\rm Ids}_0(#1)
O7 0 1
OFilt_0
mol#1; \mathop{\rm Filt}_0(#1)
O8 0 1
Ofinsups
mol#1; \mathop{\rm finsups}(#1)
O9 0 1
Ofininfs
mol#1; \mathop{\rm fininfs}(#1)
R1 1 1
Ris_eventually_in
i eventually in #2
not eventually in #2
R2 1 1
Ris_often_in
i often in #2
not often in #2
R3 1 1
Rpreserves_inf_of
h #1 preserves inf of #2
#1 does not preserve inf of #2
R4 1 1
Rpreserves_sup_of
h #1 preserves sup of #2
#1 does not preserve sup of #2
U1 1
Umapping
hosl#1; mapping of #1
mapping
V1 1
Vdirected
a directed
V2 1
Vfiltered
a filtered
V3 1
Vfiltered-infs-inheriting
a filtered-infs-inheriting
V4 1
Vdirected-sups-inheriting
a directed-sups-inheriting
V5 1
Vantitone
n antitone
V6 1
Veventually-directed
n eventually-directed
V7 1
Veventually-filtered
n eventually-filtered
V8 1
Vlower
a lower
V9 1
Vupper
n upper
V10 1
Vinfs-preserving
n infs-preserving
V11 1
Vsups-preserving
a sups-preserving
V12 1
Vmeet-preserving
a meet-preserving
V13 1
Vjoin-preserving
a join-preserving
V14 1
Vfiltered-infs-preserving
a filtered-infs-preserving
V15 1
Vdirected-sups-preserving
a directed-sups-preserving
V16 1
Vup-complete
n up-complete
V17 1
V/\-complete
n inf-complete
#WAYBEL_1
M1 2
MConnection
ha connection #0 between #1 and #2
connections #0 between #1 and #2
O1 0 1
Ocorestr
moq; #1^\circ
O2 0 1
Oinclusion
mow; #1_\circ
R1 0 2
Rex_min_of
h min #1 exists in #2
min #1 does not exist in #2
R2 0 2
Rex_max_of
h max #1 exists in #2
max #1 does not exist in #2
R3 1 1
Rhas_the_min_in
h #1 has the minimum in #2
#1 has not the minimum in #2
R4 1 1
Rhas_the_max_in
h #1 has the maximum in #2
#1 has not the maximum in #2
R5 1 1
Ris_minimum_of
i a minimum of #2
not a minimum of #2
R6 1 1
Ris_maximum_of
i a maximum of #2
not a maximum of #2
V1 1
VGalois
a Galois
V2 1
Vupper_adjoint
n upper adjoint
V3 1
Vlower_adjoint
a lower adjoint
V4 1
Vprojection
a projection
V5 1
Vclosure
a closure
V6 1
Vkernel
a kernel
#WAYBEL_2
O1 0 1
OFinSups
mol#1; \mathop{\rm FinSups}(#1)
O2 0 1
Oinf_op
mow#1; \sqcap_{#1}
O3 0 1
Osup_op
mow#1; \sqcup_{#1}
V1 1
Vsatisfying_MC
s MC
V2 1
Vmeet-continuous
a meet-continuous
#WAYBEL_3
O1 0 1
Owaybelow
mol; \twoheaddownarrow #1
O2 0 1
Owayabove
mol; \twoheaduparrow #1
R1 1 1
Ris_way_below
i way below #2
not way below #2
R2 1 1
R<<
m #1 \ll #2
#1 \not\ll #2
R3 1 1
R>>
m #1 \gg #2
#1 \not\gg #2
V1 1
Visolated_from_below
n isolated from below
V2 1
Vsatisfying_axiom_of_approximation
s axiom of approximation
V3 1
Vnon-Empty
a nonempty
V4 1
Vreflexive-yielding
a reflexive-yielding
V5 1
Vlocally-compact
a locally-compact
#WAYBEL_4
O1 1 0
O-waybelow
mow#1; \mathop{\ll}_{#1}
O2 0 1
OIntRel
mow#1; \mathop{\leq}_{#1}
O3 0 1
OAux
mol#1; \mathop{\rm Aux}(#1)
O4 0 1
OAuxBottom
mol#1; \mathop{\rm AuxBottom}(#1)
O5 1 0
O-below
mol; \twoheaddownarrow #1
O5 1 1
O-below
mol#1; \twoheaddownarrow_{#1}#2
O6 1 1
O-above
mol#1; \twoheaduparrow_{#1}#2
O7 0 1
OMonSet
mol#1; \mathop{\rm MonSet}(#1)
O8 0 1
ORel2Map
mol#1; \mathop{\rm Rel2Map}(#1)
O9 0 1
OMap2Rel
mol#1; \mathop{\rm Map2Rel}(#1)
O10 0 1
ODownMap
mol#1; \mathop{\rm DownMap}(#1)
O11 0 1
OApp
mol#1; \mathop{\rm App}(#1)
R1 1 1
Ris_directed_wrt
i directed w.r.t. #2
not directed w.r.t. #2
R2 1 2
Ris_maximal_wrt
i maximal w.r.t. #2,#3
not maximal w.r.t. #2,#3
R3 1 2
Ris_minimal_wrt
i minimal w.r.t. #2,#3
not minimal w.r.t. #2,#3
V1 1
Vauxiliary(i)
n auxiliary(i)
V2 1
Vauxiliary(ii)
n auxiliary(ii)
V3 1
Vauxiliary(iii)
n auxiliary(iii)
V4 1
Vauxiliary(iv)
n auxiliary(iv)
V5 1
Vauxiliary
n auxiliary
V6 1
Vapproximating
n approximating
V7 1
Vsatisfying_SI
s strong interpolation property
V8 1
Vsatisfying_INT
s interpolation property
#WAYBEL_5
M1 2
MDoubleIndexedSet
ha set #0 of elements of #2 double indexed by #1
sets #0 of elements of #2 double indexed by #1
M2 1
MCLSubFrame
ha continuous subframe #0 of #1
continuous subframes #0 of #1
O1 0 2
O\//
mol(1)@s; \mathop{\underline\bigsqcup_{#2}} #1
O2 0 2
O/\\
mol(1)@s; \mathop{\overline{\bigsqcap}_{#2}} #1
O3 0 1
OSups
mol#1; \mathop{\rm Sups}(#1)
O4 0 1
OInfs
mol#1; \mathop{\rm Infs}(#1)
V1 1
Vcompletely-distributive
a completely-distributive
#WAYBEL_6
O1 0 1
OIRR
mol#1; \mathop{\rm IRR}(#1)
O2 0 1
OPRIME
mol#1; \mathop{\rm PRIME}(#1)
V1 1
VOpen
n open
V2 1
Vmeet-irreducible
a meet-irreducible
V3 1
Vjoin-irreducible
a join-irreducible
V4 1
Vorder-generating
n order-generating
V5 1
Vco-prime
a co-prime
#WAYBEL_7
R1 1 1
Ris_a_cluster_point_of
i a cluster point of #2
not a cluster point of #2
R1 1 2
Ris_a_cluster_point_of
i a cluster point of #2,#3
not a cluster point of #2,#3
R2 1 2
Ris_a_convergence_point_of
i a convergence point of #2,#3
not a convergence point of #2,#3
V1 1
Vpseudoprime
a pseudoprime
#WAYBEL_8
O1 0 1
OCompactSublatt
mol#1; \mathop{\rm CompactSublatt}(#1)
O2 0 1
Ocompactbelow
mol#1; \mathop{\rm compactbelow}(#1)
V1 1
Vsatisfying_axiom_K
s axiom K
V2 1
Valgebraic
n algebraic
V3 1
Varithmetic
n arithmetic
#WAYBEL_9
G1 3
GTopRelStr
mc#1#2#3; \langle #1,#2,#3 \rangle
J1 1
GTopRelStr
hol#1; FR-structure of #1
L1 0
GTopRelStr
ha FR-structure #0
FR-structures #0
M1 0
MTopLattice
ha top-lattice #0
top-lattices #0
O1 1 0
O+id
mc#1; \langle #1;{\rm id}\rangle
O2 1 0
Oopp+id
mc/1q; \langle #1^{\rm op};{\rm id}\rangle
#WEDDWITT
O1 0 1
OCentralizer
mol#1; \mathop{\rm Centralizer}(#1)
O2 1 0
O-con_map
mol#1; #1\mathop{\rm\hbox{-}con\_map}
O3 0 1
Oconjugate_Classes
mol#1; \mathop{\rm conjugate\_Classes}(#1)
O4 0 1
Ocentralizer
mol#1; \mathop{\rm centralizer}(#1)
O5 0 1
OVectSp_over_center
mol#1; \mathop{\rm VectSp\_over~Z}(#1)
#WEIERSTR
O1 0 1
Odist_max
mol#1; \mathop{\rm dist}_{\rm max}(#1)
O2 0 1
Odist_min
mol#1; \mathop{\rm dist}_{\rm min}(#1)
O2 0 2
Odist_min
mol#1#2; \mathop{\rm dist}_{\rm min}(#1,#2)
O3 0 2
Omin_dist_min
mol#1#2; \mathop{\rm dist}^{\rm min}_{\rm min}(#1,#2)
O4 0 2
Omax_dist_min
mol#1#2; \mathop{\rm dist}^{\rm max}_{\rm min}(#1,#2)
O5 0 2
Omin_dist_max
mol#1#2; \mathop{\rm dist}^{\rm min}_{\rm max}(#1,#2)
O6 0 2
Omax_dist_max
mol#1#2; \mathop{\rm dist}^{\rm max}_{\rm max}(#1,#2)
#WELLFND1
O1 0 1
Owell_founded-Part
mol#1; \mathop{\rm WF\hbox{-}Part}(#1)
R1 1 1
Ris_recursively_expressed_by
i recursively expressed by #2
not recursively expressed by #2
V1 1
Vdescending
a descending
#WELLORD1
O1 1 1
O-Seg
mor@s#2; #1 \mathclose{\rm\hbox{-}Seg}(#2)
O2 1 1
O|_2
moi@m; #1 \mathbin{\mid^2} #2
O3 0 2
Ocanonical_isomorphism_of
ho; canonical isomorphism between #1 and #2
R1 1 1
Ris_well_founded_in
i well founded in #2
not well founded in #2
R2 1 1
Rwell_orders
h #1 well orders #2
#1 does not well order #2
R3 1 2
Ris_isomorphism_of
i an isomorphism between #2 and #3
not isomorphism between #2 and #3
R4 2 0
Rare_isomorphic
h #1 and #2 are isomorphic
#1 and #2 are not isomorphic
V1 1
Vwell_founded
a well founded
V2 1
Vwell-ordering
a well-ordering
#WELLORD2
O1 0 1
ORelIncl
mow/1k#1; {^\subseteq}_{#1}
O2 0 1
Oorder_type_of
mct#1; \overline{#1}
R1 1 1
Ris_order_type_of
i an order type of #2
not an order type of #2
#XBOOLEAN
O1 0 0
OFALSE
mc; {\it false}
O2 0 0
OTRUE
mc; {\it true}
O3 0 1
O'not'
mol@s; \neg #1
O4 0 0
O'&'
mc; \&
O4 1 1
O'&'
moi@m; #1 \wedge #2
O5 0 0
O'or'
mc; \mathop{\rm or}
O5 1 1
O'or'
moi@a; #1 \vee #2
O6 1 0
O=>
moi; #1\Rightarrow\square
O6 1 1
O=>
mox@w; #1 \Rightarrow #2
O7 1 1
O<=>
mox@w; #1 \Leftrightarrow #2
O8 1 1
O'nand'
moi@a; #1 {\rm~'nand'~} #2
O9 1 1
O'nor'
moi@a; #1 {\rm~'nor'~} #2
O10 0 0
O'xor'
mc; \mathop{\rm xor}
O10 1 1
O'xor'
moi@a; #1 \oplus #2
O11 1 1
O'\'
moi; #1 \setminus #2
V1 1
Vboolean
a boolean
#XBOOLE_0
O1 0 0
O{}
mc; \emptyset
O1 0 1
O{}
mow/1k#1; \emptyset_{#1}
O1 0 2
O{}
mow#1#2; \emptyset_{#1,#2}
O2 1 1
O\/
moi@a; #1 \cup #2
O3 0 1
O/\
mol@s; \bigcap #1
O3 1 1
O/\
moi@m; #1 \cap #2
O4 1 1
O\
moi@a; #1 \setminus #2
O4 1 2
O\
moi#2#3; #1{\upharpoonright}^{#2}_{\neq #3}
O5 1 1
O\+\
moi@a; #1 \diffsym #2
R1 1 1
Rmisses
h #1 misses #2
#1 does not miss #2
R2 1 1
Rc<
m #1 \subset #2
#1 \not\subset #2
R3 2 0
Rare_c=-comparable
h #1 and #2 are $\subseteq$-comparable
#1 and #2 are not $\subseteq$-comparable
R4 1 1
Rmeets
h #1 meets #2
#1 does not meet #2
V1 1
Vempty
n empty
#XCMPLX_0
O1 0 0
O<i>
mo@7; i
V1 1
Vcomplex
a complex
V2 1
Vzero
a zero
#XREAL_0
V1 1
Vreal
a real
#XXREAL_0
O1 0 0
O+infty
mc; +\infty
O2 0 0
O-infty
mc; -\infty
O3 0 1
Omin
mol@s; \mathop{\rm min} #1
O3 0 2
Omin
mol@s#1#2; \mathop{\rm min}(#1, #2)
O3 0 3
Omin
mol#1#2#3; \mathop{\rm min}_{#3}(#1,#2)
O3 0 4
Omin
mol#1#2#3#4; \mathop{\rm min}(#1,#2,#3,#4)
O4 0 1
Omax
mol; \mathop{\rm max} #1
O4 0 2
Omax
mol@s#1#2; \mathop{\rm max}(#1, #2)
O4 0 3
Omax
mol#1#2#3; \mathop{\rm max}_{#3}(#1,#2)
O4 0 4
Omax
mol#1#2#3#4; \mathop{\rm max}(#1,#2,#3,#4)
O5 0 4
OIFGT
mc#1#2#3#4; (#1 > #2 \rightarrow #3, #4)
R1 1 1
R<=
m #1 \leq #2
#1 \not\leq #2
R1 1 2
R<=
m #1 \leq_{#3} #2
#1 \not\leq_{#3} #2
R2 1 1
R>=
m #1 \geq #2
#1 \not\geq #2
R3 1 1
R>
m #1 > #2
#1 \not> #2
V1 1
Vext-real
n extended real
V2 1
Vpositive
a positive
V3 1
Vnegative
a negative
#XXREAL_1
K1 2 L1 vXXREAL_1
K[.
L.]
mc#1#2; \lbrack #1,#2 \rbrack
K1 3 L1 vXXREAL_1
K[.
L.]
mc#1#2#3; \lbrack #1,\,#2,\,#3\rbrack
K1 4 L1 vXXREAL_1
K[.
L.]
mc#1#2; \lbrack #1,#2,#3,#4 \rbrack
K1 2 L2 vXXREAL_1
K[.
L.]
mc#1#2; \lbrack #1,#2 \rbrack
K2 2 L1 vXXREAL_1
K].
L.[
mc; \mathopen{\rbrack} #1,#2 \mathclose{\lbrack}
K2 2 L2 vXXREAL_1
K].
L.[
mc#1#2; \rbrack #1,#2 \lbrack
#XXREAL_2
M1 1
MUpperBound
ha upper bound #0 of #1
upper bounds #0 of #1
M2 1
MLowerBound
ha lower bound #0 of #1
lower bounds #0 of #1
V1 1
Vleft_end
a left-ended
V2 1
Vright_end
a right-ended
V3 1
Vbounded_below
a lower bounded
V4 1
Vbounded_above
n upper bounded
V5 1
Vbounded
a bounded
#YELLOW11
K1 2 L1 vYELLOW11
K[#
L#]
mc#1#2; [#1, #2]
O1 0 0
ON_5
mol; N_5
O2 0 0
OM_3
mol; M_3
#YELLOW13
M1 1
Mbasis
ha generalized basis #0 of #1
generalized bases #0 of #1
V1 1
Vtopological_semilattice
s conditions of topological semilattice
#YELLOW15
O1 0 2
OMergeSequence
mol#1#2; \mathop{\rm MergeSequence}(#1,#2)
O2 0 1
OComponents
mol; \mathop{\rm Components} #1
V1 1
Vin_general_position
n in general position
#YELLOW16
R1 1 2
Ris_a_retraction_of
h #1 is a retraction of #2 into #3
#1 is not a retraction of #2 into #3
R2 1 2
Ris_an_UPS_retraction_of
h #1 is a UPS retraction of #2 into #3
#1 is not a UPS retraction of #2 into #3
R3 1 1
Ris_an_UPS_retract_of
h #1 is a UPS retract of #2
#1 is not a UPS retract of #2
R4 1 2
Rinherits_sup_of
h #1 inherits sup of #2 from #3
#1 does not inherit sup of #2 from #3
R5 1 2
Rinherits_inf_of
h #1 inherits inf of #2 from #3
#1 does not inherit inf of #2 from #3
V1 1
VPoset-yielding
a poset-yielding
#YELLOW18
O1 0 2
Odualizing-func
hosl#1#2; dualizing functor from #1 into #2
O2 1 1
O-carrier_of
Hosi; #1-carrier of #2
O3 0 1
Othe_carrier_of
hosl#1; carrier of #1
O4 0 1
OConcretized
hosl#1; concretized #1
O5 0 1
OConcretization
hosl#1; concretization of #1
R1 2 0
Rare_opposite
h #1 and #2 are opposite
#1 and #2 are not opposite
R2 2 0
Rare_dual
h #1 and #2 are dual
#1 and #2 are not dual
V1 1
Vpara-functional
a para-functional
V2 1
Vset-id-inheriting
a set-id-inheriting
V3 1
Vconcrete
a concrete
#YELLOW19
O1 0 1
ONeighborhoodSystem
hosl#1; neighborhood system of #1
O2 0 1
Oa_filter
hosl#1; filter of #1
O3 0 1
Oa_net
hosl#1; net of #1
#YELLOW20
R1 2 0
Rhave_the_same_composition
h #1 and #2 have the same composition
#1 and #2 do not have the same composition
R2 2 1
Rare_isomorphic_under
h #1 and #2 are isomorphic under #3
#1 and #2 are not isomorphic under #3
R3 2 1
Rare_anti-isomorphic_under
h #1 and #2 are anti-isomorphic under #3
#1 and #2 are not anti-isomorphic under #3
#YELLOW21
O1 1 0
Oas_1-sorted
Hosr#1; #1 as 1-sorted
O2 0 1
OPOSETS
mol#1; \mathop{\rm POSETS}(#1)
O3 1 0
O-UPS_category
mow#1; {\it UPS}_{#1}
O4 1 0
O-CONT_category
mow#1; {\it CONT}_{#1}
O5 1 0
O-ALG_category
mow#1; {\it ALG}_{#1}
V1 1
Vcarrier-underlaid
a carrier-underlaid
V2 1
Vlattice-wise
a lattice-wise
V3 1
Vwith_complete_lattices
x complete lattices
V4 1
Vwith_all_isomorphisms
x all isomorphisms
#YELLOW_0
M1 1
MSubRelStr
ha relational substructure #0 of #1
relational substructures #0 of #1
O1 0 1
Osubrelstr
mol#1; \mathop{\rm sub}(#1)
R1 0 1
Rex_sup_of
h sup #1 exists
sup #1 does not exist
R1 0 2
Rex_sup_of
h sup #1 exists in #2
sup #1 does not exist in #2
R2 0 1
Rex_inf_of
h inf #1 exists
inf #1 does not exist
R2 0 2
Rex_inf_of
h inf #1 exists in #2
inf #1 does not exist in #2
V1 1
Vmeet-inheriting
a meet-inheriting
V2 1
Vjoin-inheriting
a join-inheriting
V3 1
Vinfs-inheriting
n infs-inheriting
V4 1
Vsups-inheriting
a sups-inheriting
#YELLOW_1
O1 0 1
OInclPoset
moc#1; \langle #1,\subseteq\rangle
O2 0 1
OBoolePoset
mor{qrw}#1; 2^{#1}_\subseteq
O3 0 2
OMonMaps
mol#1#2; \mathop{\rm MonMaps}(#1,#2)
V1 1
VRelStr-yielding
a relational structure yielding
#YELLOW_2
O1 0 1
OSupMap
mol#1; \mathop{\rm SupMap}(#1)
O2 0 1
OIdsMap
mol#1; \mathop{\rm IdsMap}(#1)
O3 0 2
O\\/
mol(1)@s; \bigsqcup_{#2} #1
O4 0 2
O//\
mol(1)@s; \bigsqcap_{#2} #1
O5 0 1
OSup
mol#1; \mathop{\rm Sup}(#1)
O6 0 1
OInf
mol#1; \mathop{\rm Inf}(#1)
#YELLOW_3
K1 2 L1 vYELLOW_3
K["
L"]
moi@s; #1\times #2
#YELLOW_6
M1 1
MSubNetStr
ha structure #0 of a subnet of #1
structures #0 of subnets of #1
M2 1
Msubnet
ha subnet #0 of #1
subnet #0 of #1
M3 2
Mnet_set
ha net set #0 of #1,#2
net sets #0 of #1,#2
M4 1
MConvergence-Class
ha convergence class #0 of #1
convergence classes #0 of #1
O1 0 1
Othe_universe_of
hol#1; universe of #1
O2 0 2
OConstantNet
mol#1#2; \mathop{\rm ConstantNet}(#1,#2)
O3 0 1
ONetUniv
mol#1; \mathop{\rm NetUniv}(#1)
O4 0 1
OIterated
mol#1; \mathop{\rm Iterated}(#1)
O5 0 1
OOpenNeighborhoods
hopl#1; open neighbourhoods of #1
O6 0 1
OConvergence
mol#1; \mathop{\rm Convergence}(#1)
O7 0 1
OConvergenceSpace
mol#1; \mathop{\rm ConvergenceSpace}(#1)
V1 1
Vyielding_non-empty_carriers
a yielding non-empty carriers
V2 1
V(CONSTANTS)
x (CONSTANTS) property
V3 1
V(SUBNETS)
x (SUBNETS) property
V4 1
V(DIVERGENCE)
x (DIVERGENCE) property
V5 1
V(ITERATED_LIMITS)
x (ITERATED LIMITS) property
V6 1
Vtopological
a topological
#YELLOW_7
O1 0 1
OComplMap
mow#1; \neg_{#1}
#YELLOW_8
O1 0 1
OCofinTop
mol#1; \mathop{\rm CofinTop} #1
R1 1 1
Ris_dense_point_of
i dense point of #2
not dense point of #2
V1 2
V-quasi_basis
a #1 -quasi basis
V2 1
VBaire
a Baire
V3 1
Virreducible
n irreducible
V4 1
Vsober
a sober
#YELLOW_9
M1 1
MTopAugmentation
ha topological augmentation #0 of #1
topological augmentations #0 of #1
M2 1
MTopExtension
ha topological extension #0 of #1
topological extension #0 of #1
M3 2
MRefinement
ha refinement #0 of #1 and #2
refinements #0 of #1 and #2
#YONEDA_1
K1 1 L1 vYONEDA_1
K<|
L,?>
mol@s#1; \mathop{\rm hom}^{\rm F}(#1,{-})
O1 0 1
OEnsHom
mol#1; \mathop{\rm EnsHom} #1
O2 0 1
OYoneda
mol#1; \mathop{\rm Yoneda} #1
#ZFMISC_1
K1 1 L1 vZFMISC_1
K[:
L:]
mol@s; \prod^\circ #1
K1 2 L1 vZFMISC_1
K[:
L:]
moi@m; #1\times\allowbreak #2
K1 3 L1 vZFMISC_1
K[:
L:]
moi; #1\times\allowbreak #2\times\allowbreak\ #3
K1 4 L1 vZFMISC_1
K[:
L:]
mc#1#2#3#4; \mizleftcart\,#1,\allowbreak\,#2,\allowbreak\,#3,\allowbreak\,#4\,\mizrightcart
K1 5 L1 vZFMISC_1
K[:
L:]
mc#1#2#3#4#5; \mizleftcart\,#1,\allowbreak\,#2,\allowbreak\,#3,\allowbreak\,#4,\allowbreak\,#5\,\mizrightcart
K1 6 L1 vZFMISC_1
K[:
L:]
mc#1#2#3#4#5#6; \mizleftcart\,#1,\allowbreak\,#2,\allowbreak\,#3,\allowbreak\,#4,\allowbreak\,#5\,\allowbreak\,#6\,\mizrightcart
K1 7 L1 vZFMISC_1
K[:
L:]
mc#1#2#3#4#5#6#7; \mizleftcart\,#1,\allowbreak\,#2,\allowbreak\,#3,\allowbreak\,#4,\allowbreak\,#5\,\allowbreak\,#6\,\allowbreak\,#7\,\mizrightcart
K1 8 L1 vZFMISC_1
K[:
L:]
mc#1#2#3#4#5#6#7#8; \mizleftcart\,#1,\allowbreak\,#2,\allowbreak\,#3,\allowbreak\,#4,\allowbreak\,#5\,\allowbreak\,#6\,\allowbreak\,#7\,\allowbreak\,#8\,\mizrightcart
K1 9 L1 vZFMISC_1
K[:
L:]
mc#1#2#3#4#5#6#7#8#9; \mizleftcart\,#1,\allowbreak\,#2,\allowbreak\,#3,\allowbreak\,#4,\allowbreak\,#5\,\allowbreak\,#6\,\allowbreak\,#7\,\allowbreak\,#8\,\allowbreak\,#9\,\mizrightcart
O1 0 1
Obool
moq@s/1m#1; 2^{#1}
R1 3 0
Rare_mutually_different
h #1, #2, #3 are mutually different
#1, #2, #3 are not mutually different
R1 4 0
Rare_mutually_different
h #1, #2, #3, #4 are mutually different
#1, #2, #3, #4 are not mutually different
R1 5 0
Rare_mutually_different
h #1,#2,#3,#4,#5 are mutually different
#1,#2,#3,#4,#5 are not mutually different
R1 6 0
Rare_mutually_different
h #1,#2,#3,#4,#5,#6 are mutually different
#1,#2,#3,#4,#5,#6 are not mutually different
R1 7 0
Rare_mutually_different
h #1,#2,#3,#4,#5,#6,#7 are mutually different
#1,#2,#3,#4,#5,#6,#7 are not mutually different
V1 1
Vtrivial
a trivial
#ZFMODEL1
O1 0 2
Odef_func'
mcr@s/1k#1#2; {\hbox{\cal f'}_{#1}} [#2]
O2 0 2
Odef_func
mcr@s/1k#1#2; {\hbox{\cal f}_{#1}} [#2]
R1 1 1
Ris_definable_in
i definable in #2
not definable in #2
R2 1 1
Ris_parametrically_definable_in
i parametrically definable in #2
not parametrically definable in #2
#ZFREFLE1
O1 0 0
OZF-axioms
mow; {\bf Ax}_{\rm ZF}
R1 1 1
R<==>
m #1 \equiv #2
#1 \not\equiv #2
R2 1 1
Ris_elementary_subsystem_of
m #1 \prec #2
#1 \nprec #2
#ZF_COLLA
O1 0 2
OCollapse
mow/2k#2; #1_{#2}
R1 1 2
Ris_epsilon-isomorphism_of
i an isomorphism between #2 and #3
not an isomorphism between #2 and #3
R2 2 0
Rare_epsilon-isomorphic
h #1 and #2 are isomorphic
#1 and #2 are not isomorphic
#ZF_FUND1
O1 0 0
Odecode
mc; \mathop{\rm decode}
O2 0 1
Ox".
mok/1w#1; {}^{#1}x
O3 0 1
Ocode
mcl@s#1; \mathop{\rm code}(#1)
O4 0 2
ODiagram
mcl@s/2k#1#2; \mathop{\rm D}_{#2}(#1)
V1 1
Vclosed_wrt_A1
a closed w.r.t. A1
V2 1
Vclosed_wrt_A2
a closed w.r.t. A2
V3 1
Vclosed_wrt_A3
a closed w.r.t. A3
V4 1
Vclosed_wrt_A4
a closed w.r.t. A4
V5 1
Vclosed_wrt_A5
a closed w.r.t. A5
V6 1
Vclosed_wrt_A6
a closed w.r.t. A6
V7 1
Vclosed_wrt_A7
a closed w.r.t. A7
V8 1
Vclosed_wrt_A1-A7
a closed w.r.t. A1-A7
#ZF_FUND2
O1 0 2
OSection
mcl(1)@s/2k#1#2; \mathop{\rm S}_{#2}(#1)
V1 1
Vpredicatively_closed
a predicatively closed
#ZF_LANG
M1 0
MVariable
ha variable #0
variables #0
M1 1
MVariable
ha variable #0 in #1
variables #0 in #1
M2 0
MZF-formula
ha ZF-formula #0
ZF-formulae #0
O1 0 0
OVAR
mc; \mathop{\rm VAR}
O2 0 1
Ox.
mow/1k; {\rm x}_{#1}
O3 1 1
O'='
moi@9; #1 \hbox{\scriptsize =} #2
O4 1 1
O'in'
moi@9; #1 \epsilon #2
O5 0 0
OWFF
mc; \mathop{\rm WFF}
O6 0 1
OVar1
mol@s#1; {\mathop{\rm Var}_1}(#1)
O7 0 1
OVar2
mol@s#1; {\mathop{\rm Var}_2}(#1)
O8 0 1
Othe_argument_of
mcl@s#1; \mathop{\rm Arg}(#1)
O9 0 1
Othe_left_argument_of
mcl@s#1; \mathop{\rm LeftArg}(#1)
O10 0 1
Othe_right_argument_of
mcl@s#1; \mathop{\rm RightArg}(#1)
O11 0 1
Obound_in
mcl@s#1; \mathop{\rm Bound}(#1)
O11 0 2
Obound_in
hol#2; bound in $#1(#2)$
O12 0 1
Othe_scope_of
mcl@s#1; \mathop{\rm Scope}(#1)
O12 0 2
Othe_scope_of
hol#2; scope of $#1(#2)$
O13 0 1
Othe_antecedent_of
mcl@s#1; \mathop{\rm Antecedent}(#1)
O14 0 1
Othe_consequent_of
mcl@s#1; \mathop{\rm Consequent}(#1)
O15 0 1
Othe_left_side_of
mcl@s#1; \mathop{\rm LeftSide}(#1)
O16 0 1
Othe_right_side_of
mcl@s#1; \mathop{\rm RightSide}(#1)
O17 0 1
OSubformulae
mol@s; \mathop{\rm Subformulae} #1
R1 1 1
Ris_immediate_constituent_of
i an immediate constituent of #2
not an immediate constituent of #2
R2 1 1
Ris_subformula_of
i a subformula of #2
not a subformula of #2
R3 1 1
Ris_proper_subformula_of
i a proper subformula of #2
not a proper subformula of #2
V1 1
VZF-formula-like
a ZF-formula-like
V2 1
Vbeing_equality
b equality
V3 1
Vbeing_membership
b membership
V4 1
Vconjunctive
a conjunctive
V5 1
Vatomic
n atomic
V6 1
Vdisjunctive
a disjunctive
V7 1
Vconditional
a conditional
V8 1
Vbiconditional
a biconditional
V9 1
Vexistential
n existential
#ZF_LANG1
O1 0 1
Ovariables_in
mol; \mathop{\rm Var}#1
O1 0 2
Ovariables_in
mol@s/2k#1#2; \mathop{\rm variables}_{#2}(#1)
O1 1 1
Ovariables_in
mol(2)#1; \mathop{\rm Var}_{#1}#2
O1 2 0
Ovariables_in
mor@3#1#2; \mathop{{\rm vars}^{#1}_{#2}}
#ZF_MODEL
O1 0 1
OFree
mol@s; \mathop{\rm Free} #1
O1 0 2
OFree
mol(2)#1#2; \mathop{\rm Free}_{#1}(#2)
O2 0 1
OVAL
mol@s; \mathop{\rm VAL} #1
O3 0 2
OSt
mcl(1)@s/2k#1#2; \mathop{\rm St}_{#2}(#1)
O4 0 0
Othe_axiom_of_extensionality
ho; axiom of extensionality
O5 0 0
Othe_axiom_of_pairs
ho; axiom of pairs
O6 0 0
Othe_axiom_of_unions
ho; axiom of unions
O7 0 0
Othe_axiom_of_infinity
ho; axiom of infinity
O8 0 0
Othe_axiom_of_power_sets
ho; axiom of power sets
O9 0 1
Othe_axiom_of_substitution_for
hol; axiom of substitution for #1
R1 0 1
R|=
my \vDash #1
\nvDash #1
R1 1 1
R|=
m #1 \models #2
#1 \not\models #2
R1 2 1
R|=
m #1 \models_{#2} #3
#1\not\models_{#2} #3
V1 1
Vbeing_a_model_of_ZF
b model of ZF
#ZF_REFLE
M1 1
MSubclass
ha subclass #0 of #1
subclasses #0 of #1
M2 1
MDOMAIN-Sequence
ha transfinite sequence #0 of non empty sets from #1
transfinite sequences #0 of non empty sets from #1
V1 1
VDOMAIN-yielding
a non empty set yielding
!