:: CIRCCMB3 semantic presentation

REAL is V140() V141() V142() V146() V149() V150() V152() set
NAT is non empty non trivial V17() V18() V19() non finite V95() V96() V140() V141() V142() V143() V144() V145() V146() V147() V149() Element of bool REAL
bool REAL is set
NAT is non empty non trivial V17() V18() V19() non finite V95() V96() V140() V141() V142() V143() V144() V145() V146() V147() V149() set
bool NAT is set
bool NAT is set
{} is non pair empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() Function-yielding V34() finite finite-yielding V39() FinSequence-like FinSubsequence-like FinSequence-membered V47() V92() V95() non with_pair ext-real V140() V141() V142() V143() V144() V145() V146() V149() V150() V151() V152() V153() set
the non pair empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() Function-yielding V34() finite finite-yielding V39() FinSequence-like FinSubsequence-like FinSequence-membered V47() V92() V95() non with_pair ext-real V140() V141() V142() V143() V144() V145() V146() V149() V150() V151() V152() V153() set is non pair empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() Function-yielding V34() finite finite-yielding V39() FinSequence-like FinSubsequence-like FinSequence-membered V47() V92() V95() non with_pair ext-real V140() V141() V142() V143() V144() V145() V146() V149() V150() V151() V152() V153() set
1 is non pair non empty V17() V18() V19() V23() V47() ext-real positive V140() V141() V142() V143() V144() V145() V147() V149() V153() Element of NAT
{{},1} is non empty finite V95() non with_pair V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() set
K298() is set
bool K298() is set
K299() is Element of bool K298()
K339() is non empty V108() L10()
the carrier of K339() is non empty set
K302( the carrier of K339()) is non empty M21( the carrier of K339())
K338(K339()) is Element of bool K302( the carrier of K339())
bool K302( the carrier of K339()) is set
[:K338(K339()),NAT:] is Relation-like set
bool [:K338(K339()),NAT:] is set
[:NAT,K338(K339()):] is Relation-like set
bool [:NAT,K338(K339()):] is set
K420() is set
2 is non pair non empty V17() V18() V19() V23() V47() ext-real positive V140() V141() V142() V143() V144() V145() V147() V149() V153() Element of NAT
2 -tuples_on K420() is functional FinSequence-membered FinSequenceSet of K420()
[:(2 -tuples_on K420()),K420():] is Relation-like set
bool [:(2 -tuples_on K420()),K420():] is set
3 is non pair non empty V17() V18() V19() V23() V47() ext-real positive V140() V141() V142() V143() V144() V145() V147() V149() V153() Element of NAT
3 -tuples_on K420() is functional FinSequence-membered FinSequenceSet of K420()
[:(3 -tuples_on K420()),K420():] is Relation-like set
bool [:(3 -tuples_on K420()),K420():] is set
K441() is Relation-like 2 -tuples_on K420() -defined K420() -valued Function-like V30(2 -tuples_on K420(),K420()) Element of bool [:(2 -tuples_on K420()),K420():]
0 is non pair empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() Function-yielding V34() finite finite-yielding V39() FinSequence-like FinSubsequence-like FinSequence-membered V47() V92() V95() non with_pair ext-real V140() V141() V142() V143() V144() V145() V146() V149() V150() V151() V152() V153() Element of NAT
4 is non pair non empty V17() V18() V19() V23() V47() ext-real positive V140() V141() V142() V143() V144() V145() V147() V149() V153() Element of NAT
5 is non pair non empty V17() V18() V19() V23() V47() ext-real positive V140() V141() V142() V143() V144() V145() V147() V149() V153() Element of NAT
Seg 1 is non empty finite V42(1) V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
Seg 4 is non empty finite V42(4) V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
{1,2,3,4} is finite V95() set
Seg 5 is non empty finite V42(5) V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
{1,2,3,4,5} is finite V95() set
proj1 {} is non pair empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() Function-yielding V34() finite finite-yielding V39() FinSequence-like FinSubsequence-like FinSequence-membered V47() V92() V95() non with_pair ext-real V140() V141() V142() V143() V144() V145() V146() V149() V150() V151() V152() V153() set
proj2 {} is non pair empty trivial Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() Function-yielding V34() finite finite-yielding V39() FinSequence-like FinSubsequence-like FinSequence-membered V47() V92() V95() non with_pair ext-real V140() V141() V142() V143() V144() V145() V146() V149() V150() V151() V152() V153() set
X is non empty non void V79() Circuit-like ManySortedSign
the carrier of X is non empty set
InputVertices X is Element of bool the carrier of X
bool the carrier of X is set
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
the carrier' of X is non empty set
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
the carrier of X \ K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
S is non-empty finite-yielding MSAlgebra over X
the Sorts of S is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of S) is non empty functional V93() V94() set
x1 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
x2 is set
x1 . x2 is set
x3 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,x3) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
(Following (x1,x3)) . x2 is set
x3 + 1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,(x3 + 1)) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
(Following (x1,(x3 + 1))) . x2 is set
Following (Following (x1,x3)) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
(Following (Following (x1,x3))) . x2 is set
Following (x1,0) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
(Following (x1,0)) . x2 is set
X is non empty non void V79() Circuit-like ManySortedSign
the carrier of X is non empty set
S is non-empty finite-yielding MSAlgebra over X
the Sorts of S is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of S) is non empty functional V93() V94() set
X is non empty non void V79() Circuit-like ManySortedSign
X is non empty non void V79() Circuit-like ManySortedSign
S is non-empty finite-yielding MSAlgebra over X
the carrier of X is non empty set
the Sorts of S is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of S) is non empty functional V93() V94() set
x1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
x2 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
Following (x2,x1) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
X is non empty non void V79() Circuit-like ManySortedSign
the carrier of X is non empty set
S is non-empty finite-yielding MSAlgebra over X
the Sorts of S is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of S) is non empty functional V93() V94() set
x1 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
x2 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,x2) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
x2 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
x3 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
f is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,f) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
f is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,f) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
a is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,a) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
a is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,a) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
X is non empty non void V79() Circuit-like ManySortedSign
the carrier of X is non empty set
S is non-empty finite-yielding MSAlgebra over X
the Sorts of S is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of S) is non empty functional V93() V94() set
x1 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
x2 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,x2) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
x2 is non pair V17() V18() V19() V23() V47() ext-real V153() set
Following (x1,x2) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
x3 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,x3) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
f is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,f) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
x2 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,x2) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
x3 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,x3) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
X is non empty non void V79() Circuit-like ManySortedSign
the carrier of X is non empty set
S is non-empty finite-yielding MSAlgebra over X
the Sorts of S is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of S) is non empty functional V93() V94() set
x1 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
(X,S,x1) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
(X,S,x1) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,(X,S,x1)) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
X is non empty non void V79() Circuit-like ManySortedSign
the carrier of X is non empty set
S is non-empty finite-yielding MSAlgebra over X
the Sorts of S is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of S) is non empty functional V93() V94() set
x1 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
(X,S,x1) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
x2 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,x2) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
X is non empty non void V79() Circuit-like ManySortedSign
the carrier of X is non empty set
S is non-empty finite-yielding MSAlgebra over X
the Sorts of S is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of S) is non empty functional V93() V94() set
x1 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
(X,S,x1) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
x2 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,x2) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
X is non empty non void V79() Circuit-like ManySortedSign
the carrier of X is non empty set
S is non-empty finite-yielding MSAlgebra over X
the Sorts of S is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of S) is non empty functional V93() V94() set
x1 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
(X,S,x1) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
(X,S,x1) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
x2 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,x2) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
Following (x1,(X,S,x1)) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
X is non empty non void V79() Circuit-like ManySortedSign
the carrier of X is non empty set
InputVertices X is Element of bool the carrier of X
bool the carrier of X is set
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
the carrier' of X is non empty set
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
the carrier of X \ K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
S is non-empty finite-yielding MSAlgebra over X
the Sorts of S is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of S) is non empty functional V93() V94() set
x1 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
(X,S,x1) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
(X,S,x1) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (x1,(X,S,x1)) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
x2 is set
(X,S,x1) . x2 is set
x1 . x2 is set
X is non empty non void V79() Circuit-like ManySortedSign
InputVertices X is Element of bool the carrier of X
the carrier of X is non empty set
bool the carrier of X is set
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
the carrier' of X is non empty set
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
the carrier of X \ K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
S is non empty non void V79() Circuit-like ManySortedSign
InnerVertices S is Element of bool the carrier of S
the carrier of S is non empty set
bool the carrier of S is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K488( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
InputVertices S is Element of bool the carrier of S
the carrier of S \ K488( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
InnerVertices X is Element of bool the carrier of X
X +* S is non empty non void V79() strict ManySortedSign
x1 is non empty non void V79() Circuit-like ManySortedSign
the carrier of x1 is non empty set
x2 is non-empty finite-yielding MSAlgebra over X
the Sorts of x2 is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of x2) is non empty functional V93() V94() set
x3 is non-empty finite-yielding MSAlgebra over S
x2 +* x3 is strict non-empty MSAlgebra over X +* S
the Sorts of x3 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
K246( the Sorts of x3) is non empty functional V93() V94() set
f is non-empty finite-yielding MSAlgebra over x1
the Sorts of f is non empty Relation-like non-empty non empty-yielding the carrier of x1 -defined Function-like total set
K246( the Sorts of f) is non empty functional V93() V94() set
a is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
a | the carrier of X is Relation-like the carrier of X -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
a | the carrier of S is Relation-like the carrier of S -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
b is non empty Relation-like the carrier of X -defined Function-like the Sorts of x2 -compatible total Element of K246( the Sorts of x2)
c is non empty Relation-like the carrier of S -defined Function-like the Sorts of x3 -compatible total Element of K246( the Sorts of x3)
g is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (b,g) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x2 -compatible total Element of K246( the Sorts of x2)
k is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (c,k) is non empty Relation-like the carrier of S -defined Function-like the Sorts of x3 -compatible total Element of K246( the Sorts of x3)
max (g,k) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (a,(max (g,k))) is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
X is non empty non void V79() Circuit-like ManySortedSign
InputVertices X is Element of bool the carrier of X
the carrier of X is non empty set
bool the carrier of X is set
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
the carrier' of X is non empty set
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
the carrier of X \ K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
S is non empty non void V79() Circuit-like ManySortedSign
InnerVertices S is Element of bool the carrier of S
the carrier of S is non empty set
bool the carrier of S is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K488( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
InputVertices S is Element of bool the carrier of S
the carrier of S \ K488( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
InnerVertices X is Element of bool the carrier of X
X +* S is non empty non void V79() strict ManySortedSign
x1 is non empty non void V79() Circuit-like ManySortedSign
the carrier of x1 is non empty set
x2 is non-empty finite-yielding MSAlgebra over X
the Sorts of x2 is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of x2) is non empty functional V93() V94() set
x3 is non-empty finite-yielding MSAlgebra over S
x2 +* x3 is strict non-empty MSAlgebra over X +* S
the Sorts of x3 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
K246( the Sorts of x3) is non empty functional V93() V94() set
f is non-empty finite-yielding MSAlgebra over x1
the Sorts of f is non empty Relation-like non-empty non empty-yielding the carrier of x1 -defined Function-like total set
K246( the Sorts of f) is non empty functional V93() V94() set
a is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
a | the carrier of X is Relation-like the carrier of X -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
a | the carrier of S is Relation-like the carrier of S -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
(x1,f,a) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
b is non empty Relation-like the carrier of X -defined Function-like the Sorts of x2 -compatible total Element of K246( the Sorts of x2)
(X,x2,b) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
g is non empty Relation-like the carrier of S -defined Function-like the Sorts of x3 -compatible total Element of K246( the Sorts of x3)
(S,x3,g) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
max ((X,x2,b),(S,x3,g)) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (b,(X,x2,b)) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x2 -compatible total Element of K246( the Sorts of x2)
a1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (g,a1) is non empty Relation-like the carrier of S -defined Function-like the Sorts of x3 -compatible total Element of K246( the Sorts of x3)
Following (a,a1) is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
Following (b,a1) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x2 -compatible total Element of K246( the Sorts of x2)
Following (a,a1) is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
Following (g,(S,x3,g)) is non empty Relation-like the carrier of S -defined Function-like the Sorts of x3 -compatible total Element of K246( the Sorts of x3)
Following (a,(max ((X,x2,b),(S,x3,g)))) is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
X is non empty non void V79() Circuit-like ManySortedSign
InputVertices X is Element of bool the carrier of X
the carrier of X is non empty set
bool the carrier of X is set
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
the carrier' of X is non empty set
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
the carrier of X \ K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
S is non empty non void V79() Circuit-like ManySortedSign
InnerVertices S is Element of bool the carrier of S
the carrier of S is non empty set
bool the carrier of S is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K488( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
X +* S is non empty non void V79() strict ManySortedSign
x1 is non empty non void V79() Circuit-like ManySortedSign
the carrier of x1 is non empty set
x2 is non-empty finite-yielding MSAlgebra over X
the Sorts of x2 is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of x2) is non empty functional V93() V94() set
x3 is non-empty finite-yielding MSAlgebra over S
x2 +* x3 is strict non-empty MSAlgebra over X +* S
the Sorts of x3 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
K246( the Sorts of x3) is non empty functional V93() V94() set
f is non-empty finite-yielding MSAlgebra over x1
the Sorts of f is non empty Relation-like non-empty non empty-yielding the carrier of x1 -defined Function-like total set
K246( the Sorts of f) is non empty functional V93() V94() set
a is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
a | the carrier of X is Relation-like the carrier of X -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
b is non empty Relation-like the carrier of X -defined Function-like the Sorts of x2 -compatible total Element of K246( the Sorts of x2)
(X,x2,b) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (a,(X,x2,b)) is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
(Following (a,(X,x2,b))) | the carrier of S is Relation-like the carrier of S -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
Following (b,(X,x2,b)) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x2 -compatible total Element of K246( the Sorts of x2)
g is non empty Relation-like the carrier of S -defined Function-like the Sorts of x3 -compatible total Element of K246( the Sorts of x3)
(S,x3,g) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (g,(S,x3,g)) is non empty Relation-like the carrier of S -defined Function-like the Sorts of x3 -compatible total Element of K246( the Sorts of x3)
(X,x2,b) + (S,x3,g) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (a,((X,x2,b) + (S,x3,g))) is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
X is non empty non void V79() Circuit-like ManySortedSign
InputVertices X is Element of bool the carrier of X
the carrier of X is non empty set
bool the carrier of X is set
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
the carrier' of X is non empty set
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
the carrier of X \ K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
S is non empty non void V79() Circuit-like ManySortedSign
InnerVertices S is Element of bool the carrier of S
the carrier of S is non empty set
bool the carrier of S is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K488( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
X +* S is non empty non void V79() strict ManySortedSign
x1 is non empty non void V79() Circuit-like ManySortedSign
the carrier of x1 is non empty set
x2 is non-empty finite-yielding MSAlgebra over X
the Sorts of x2 is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of x2) is non empty functional V93() V94() set
x3 is non-empty finite-yielding MSAlgebra over S
x2 +* x3 is strict non-empty MSAlgebra over X +* S
the Sorts of x3 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
K246( the Sorts of x3) is non empty functional V93() V94() set
f is non-empty finite-yielding MSAlgebra over x1
the Sorts of f is non empty Relation-like non-empty non empty-yielding the carrier of x1 -defined Function-like total set
K246( the Sorts of f) is non empty functional V93() V94() set
a is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
a | the carrier of X is Relation-like the carrier of X -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
(x1,f,a) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
b is non empty Relation-like the carrier of X -defined Function-like the Sorts of x2 -compatible total Element of K246( the Sorts of x2)
(X,x2,b) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (a,(X,x2,b)) is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
(Following (a,(X,x2,b))) | the carrier of S is Relation-like the carrier of S -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
g is non empty Relation-like the carrier of S -defined Function-like the Sorts of x3 -compatible total Element of K246( the Sorts of x3)
(S,x3,g) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
(X,x2,b) + (S,x3,g) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (b,(X,x2,b)) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x2 -compatible total Element of K246( the Sorts of x2)
a1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
x is non pair V17() V18() V19() V23() V47() ext-real V153() set
(X,x2,b) + x is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
k is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (g,k) is non empty Relation-like the carrier of S -defined Function-like the Sorts of x3 -compatible total Element of K246( the Sorts of x3)
(Following (a,(X,x2,b))) | the carrier of X is Relation-like the carrier of X -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
Following ((Following (a,(X,x2,b))),k) is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
(Following ((Following (a,(X,x2,b))),k)) | the carrier of S is Relation-like the carrier of S -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
Following (a,a1) is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
(Following (a,a1)) | the carrier of S is Relation-like the carrier of S -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
Following (b,a1) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x2 -compatible total Element of K246( the Sorts of x2)
Following (a,a1) is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
(Following (a,a1)) | the carrier of X is Relation-like the carrier of X -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
Following (g,(S,x3,g)) is non empty Relation-like the carrier of S -defined Function-like the Sorts of x3 -compatible total Element of K246( the Sorts of x3)
Following (a,((X,x2,b) + (S,x3,g))) is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
X is non empty non void V79() Circuit-like ManySortedSign
InputVertices X is Element of bool the carrier of X
the carrier of X is non empty set
bool the carrier of X is set
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
the carrier' of X is non empty set
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
the carrier of X \ K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
S is non empty non void V79() Circuit-like ManySortedSign
InnerVertices S is Element of bool the carrier of S
the carrier of S is non empty set
bool the carrier of S is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K488( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
x1 is non empty non void V79() Circuit-like ManySortedSign
X +* S is non empty non void V79() strict ManySortedSign
the carrier of x1 is non empty set
x2 is non-empty finite-yielding MSAlgebra over X
the Sorts of x2 is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of x2) is non empty functional V93() V94() set
x3 is non-empty finite-yielding MSAlgebra over S
x2 +* x3 is strict non-empty MSAlgebra over X +* S
the Sorts of x3 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
K246( the Sorts of x3) is non empty functional V93() V94() set
f is non-empty finite-yielding MSAlgebra over x1
the Sorts of f is non empty Relation-like non-empty non empty-yielding the carrier of x1 -defined Function-like total set
K246( the Sorts of f) is non empty functional V93() V94() set
a is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
a | the carrier of X is Relation-like the carrier of X -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
(x1,f,a) is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
(x1,f,a) | the carrier of X is Relation-like the carrier of X -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
b is non empty Relation-like the carrier of X -defined Function-like the Sorts of x2 -compatible total Element of K246( the Sorts of x2)
(X,x2,b) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (a,(X,x2,b)) is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
(Following (a,(X,x2,b))) | the carrier of S is Relation-like the carrier of S -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
(X,x2,b) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x2 -compatible total Element of K246( the Sorts of x2)
c is non empty Relation-like the carrier of S -defined Function-like the Sorts of x3 -compatible total Element of K246( the Sorts of x3)
(x1,f,a) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
(S,x3,c) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
(X,x2,b) + (S,x3,c) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (a,(x1,f,a)) is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of f -compatible total Element of K246( the Sorts of f)
(Following (a,(x1,f,a))) | the carrier of X is Relation-like the carrier of X -defined the carrier of x1 -defined Function-like the Sorts of f -compatible set
Following (b,(x1,f,a)) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x2 -compatible total Element of K246( the Sorts of x2)
S is non empty finite V95() set
x1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
x1 -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
[:(x1 -tuples_on S),S:] is Relation-like set
bool [:(x1 -tuples_on S),S:] is set
x2 is Relation-like NAT -defined Function-like finite V42(x1) FinSequence-like FinSubsequence-like V95() set
x3 is Relation-like x1 -tuples_on S -defined S -valued Function-like V30(x1 -tuples_on S,S) Element of bool [:(x1 -tuples_on S),S:]
1GateCircStr (x2,x3) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den ManySortedSign
the carrier of (1GateCircStr (x2,x3)) is non empty set
1GateCircuit (x2,x3) is strict non-empty finite-yielding gate`2=den MSAlgebra over 1GateCircStr (x2,x3)
the Sorts of (1GateCircuit (x2,x3)) is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (x2,x3)) -defined Function-like total set
K246( the Sorts of (1GateCircuit (x2,x3))) is non empty functional V93() V94() set
f is non empty Relation-like the carrier of (1GateCircStr (x2,x3)) -defined Function-like the Sorts of (1GateCircuit (x2,x3)) -compatible total Element of K246( the Sorts of (1GateCircuit (x2,x3)))
x2 * f is Relation-like NAT -defined Function-like finite V95() set
proj2 (x2 * f) is finite V95() set
c is set
proj2 f is non empty set
k is set
g is non empty set
proj1 f is non empty set
x is set
f . x is set
a1 is non empty Relation-like non-empty non empty-yielding g -defined Function-like total set
proj1 a1 is non empty set
k is Element of the carrier of (1GateCircStr (x2,x3))
f . k is set
the Sorts of (1GateCircuit (x2,x3)) . k is non empty set
proj2 x2 is finite V95() set
proj1 f is non empty set
c is set
[x2,x3] is pair non empty set
{x2,x3} is non empty functional finite V95() set
{x2} is non empty functional finite V39() V93() V95() set
{{x2,x3},{x2}} is non empty finite V39() V95() set
{[x2,x3]} is non empty Relation-like Function-like finite V95() set
(proj2 x2) \/ {[x2,x3]} is non empty finite V95() set
c is Relation-like NAT -defined S -valued Function-like finite FinSequence-like FinSubsequence-like V95() FinSequence of S
len c is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
len x2 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
X is set
S is set
x1 is set
x2 is set
<*X,S,x1,x2*> is non empty Relation-like NAT -defined Function-like finite V42(4) FinSequence-like FinSubsequence-like V95() set
proj2 <*X,S,x1,x2*> is non empty finite V95() set
{X,S,x1,x2} is finite V95() set
dom <*X,S,x1,x2*> is non empty finite V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
x3 is set
<*X,S,x1,x2*> . 1 is set
<*X,S,x1,x2*> . 2 is set
<*X,S,x1,x2*> . 3 is set
<*X,S,x1,x2*> . 4 is set
f is set
<*X,S,x1,x2*> . f is set
X is set
S is set
x1 is set
x2 is set
x3 is set
<*X,S,x1,x2,x3*> is non empty Relation-like NAT -defined Function-like finite V42(5) FinSequence-like FinSubsequence-like V95() set
proj2 <*X,S,x1,x2,x3*> is non empty finite V95() set
{X,S,x1,x2,x3} is finite V95() set
dom <*X,S,x1,x2,x3*> is non empty finite V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
f is set
<*X,S,x1,x2,x3*> . 1 is set
<*X,S,x1,x2,x3*> . 2 is set
<*X,S,x1,x2,x3*> . 3 is set
<*X,S,x1,x2,x3*> . 4 is set
<*X,S,x1,x2,x3*> . 5 is set
a is set
<*X,S,x1,x2,x3*> . a is set
X is non empty V79() ManySortedSign
S is set
X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V95() set
1GateCircStr (X,S) is non empty non void V79() strict Circuit-like unsplit gate`1=arity ManySortedSign
the carrier of (1GateCircStr (X,S)) is non empty set
proj2 X is finite V95() set
[X,S] is pair non empty set
{X,S} is non empty finite V95() set
{X} is non empty functional finite V39() V93() V95() set
{{X,S},{X}} is non empty finite V39() V95() set
{[X,S]} is non empty Relation-like Function-like finite V95() set
(proj2 X) \/ {[X,S]} is non empty finite V95() set
X is ManySortedSign
x1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
S is non empty finite V95() set
x1 -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
[:(x1 -tuples_on S),S:] is Relation-like set
bool [:(x1 -tuples_on S),S:] is set
x3 is Relation-like x1 -tuples_on S -defined S -valued Function-like V30(x1 -tuples_on S,S) Element of bool [:(x1 -tuples_on S),S:]
x2 is Relation-like NAT -defined Function-like finite V42(x1) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (x2,x3) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den ManySortedSign
X is non empty V79() ManySortedSign
x1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
S is non empty finite V95() set
x1 -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
[:(x1 -tuples_on S),S:] is Relation-like set
bool [:(x1 -tuples_on S),S:] is set
x3 is Relation-like x1 -tuples_on S -defined S -valued Function-like V30(x1 -tuples_on S,S) Element of bool [:(x1 -tuples_on S),S:]
x2 is Relation-like NAT -defined Function-like finite V42(x1) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (x2,x3) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den ManySortedSign
S is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
X is non empty finite V95() set
S -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
[:(S -tuples_on X),X:] is Relation-like set
bool [:(S -tuples_on X),X:] is set
x2 is Relation-like S -tuples_on X -defined X -valued Function-like V30(S -tuples_on X,X) Element of bool [:(S -tuples_on X),X:]
x1 is Relation-like NAT -defined Function-like finite V42(S) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (x1,x2) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den ManySortedSign
the non empty finite V95() set is non empty finite V95() set
the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
the Relation-like NAT -defined Function-like finite V42( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT ) FinSequence-like FinSubsequence-like V95() set is Relation-like NAT -defined Function-like finite V42( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT ) FinSequence-like FinSubsequence-like V95() set
the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set is non empty functional FinSequence-membered FinSequenceSet of the non empty finite V95() set
[:( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set ), the non empty finite V95() set :] is Relation-like set
bool [:( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set ), the non empty finite V95() set :] is set
the Relation-like the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set -defined the non empty finite V95() set -valued Function-like V30( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set , the non empty finite V95() set ) Element of bool [:( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set ), the non empty finite V95() set :] is Relation-like the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set -defined the non empty finite V95() set -valued Function-like V30( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set , the non empty finite V95() set ) Element of bool [:( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set ), the non empty finite V95() set :]
1GateCircStr ( the Relation-like NAT -defined Function-like finite V42( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT ) FinSequence-like FinSubsequence-like V95() set , the Relation-like the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set -defined the non empty finite V95() set -valued Function-like V30( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set , the non empty finite V95() set ) Element of bool [:( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set ), the non empty finite V95() set :]) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
X is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
S is finite-yielding MSAlgebra over X
x2 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
x1 is non empty finite V95() set
x2 -tuples_on x1 is non empty functional FinSequence-membered FinSequenceSet of x1
[:(x2 -tuples_on x1),x1:] is Relation-like set
bool [:(x2 -tuples_on x1),x1:] is set
f is Relation-like x2 -tuples_on x1 -defined x1 -valued Function-like V30(x2 -tuples_on x1,x1) Element of bool [:(x2 -tuples_on x1),x1:]
x3 is Relation-like NAT -defined Function-like finite V42(x2) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (x3,f) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
1GateCircuit (x3,f) is strict non-empty finite-yielding gate`2=den MSAlgebra over 1GateCircStr (x3,f)
S is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
X is non empty finite V95() set
S -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
[:(S -tuples_on X),X:] is Relation-like set
bool [:(S -tuples_on X),X:] is set
x2 is Relation-like S -tuples_on X -defined X -valued Function-like V30(S -tuples_on X,X) Element of bool [:(S -tuples_on X),X:]
x1 is Relation-like NAT -defined Function-like finite V42(S) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (x1,x2) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
1GateCircuit (x1,x2) is strict non-empty finite-yielding gate`2=den MSAlgebra over 1GateCircStr (x1,x2)
X is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
x1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
S is non empty finite V95() set
x1 -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
[:(x1 -tuples_on S),S:] is Relation-like set
bool [:(x1 -tuples_on S),S:] is set
x3 is Relation-like x1 -tuples_on S -defined S -valued Function-like V30(x1 -tuples_on S,S) Element of bool [:(x1 -tuples_on S),S:]
x2 is Relation-like NAT -defined Function-like finite V42(x1) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (x2,x3) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
1GateCircuit (x2,x3) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (x2,x3)) MSAlgebra over 1GateCircStr (x2,x3)
f is finite-yielding MSAlgebra over X
X is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
the carrier' of X is non empty set
union the carrier' of X is set
the carrier of X is non empty finite V95() set
x1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
S is non empty finite V95() set
x1 -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
[:(x1 -tuples_on S),S:] is Relation-like set
bool [:(x1 -tuples_on S),S:] is set
x3 is Relation-like x1 -tuples_on S -defined S -valued Function-like V30(x1 -tuples_on S,S) Element of bool [:(x1 -tuples_on S),S:]
x2 is Relation-like NAT -defined Function-like finite V42(x1) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (x2,x3) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
[x2,x3] is pair non empty set
{x2,x3} is non empty functional finite V95() set
{x2} is non empty functional finite V39() V93() V95() set
{{x2,x3},{x2}} is non empty finite V39() V95() set
{[x2,x3]} is non empty Relation-like Function-like finite V95() set
proj2 x2 is finite V95() set
(proj2 x2) \/ {[x2,x3]} is non empty finite V95() set
X is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
(X) is Element of the carrier of X
the carrier of X is non empty finite V95() set
the carrier' of X is non empty set
union the carrier' of X is set
x1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
S is non empty finite V95() set
x1 -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
[:(x1 -tuples_on S),S:] is Relation-like set
bool [:(x1 -tuples_on S),S:] is set
x3 is Relation-like x1 -tuples_on S -defined S -valued Function-like V30(x1 -tuples_on S,S) Element of bool [:(x1 -tuples_on S),S:]
x2 is Relation-like NAT -defined Function-like finite V42(x1) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (x2,x3) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
[x2,x3] is pair non empty set
{x2,x3} is non empty functional finite V95() set
{x2} is non empty functional finite V39() V93() V95() set
{{x2,x3},{x2}} is non empty finite V39() V95() set
{[x2,x3]} is non empty Relation-like Function-like finite V95() set
X is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
(X) is pair non empty Element of the carrier of X
the carrier of X is non empty finite V95() set
the carrier' of X is non empty set
union the carrier' of X is set
S is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V95() set
x1 is set
1GateCircStr (S,x1) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity ManySortedSign
[S,x1] is pair non empty set
{S,x1} is non empty finite V95() set
{S} is non empty functional finite V39() V93() V95() set
{{S,x1},{S}} is non empty finite V39() V95() set
{[S,x1]} is non empty Relation-like Function-like finite V95() set
union {[S,x1]} is set
X is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
InnerVertices X is finite V95() Element of bool the carrier of X
the carrier of X is non empty finite V95() set
bool the carrier of X is finite V39() V95() set
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
the carrier' of X is non empty set
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
K488( the carrier of X, the ResultSort of X) is finite V95() Element of bool the carrier of X
(X) is pair non empty Element of the carrier of X
union the carrier' of X is set
{(X)} is non empty Relation-like finite V95() set
x1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
S is non empty finite V95() set
x1 -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
[:(x1 -tuples_on S),S:] is Relation-like set
bool [:(x1 -tuples_on S),S:] is set
x3 is Relation-like x1 -tuples_on S -defined S -valued Function-like V30(x1 -tuples_on S,S) Element of bool [:(x1 -tuples_on S),S:]
x2 is Relation-like NAT -defined Function-like finite V42(x1) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (x2,x3) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
[x2,x3] is pair non empty set
{x2,x3} is non empty functional finite V95() set
{x2} is non empty functional finite V39() V93() V95() set
{{x2,x3},{x2}} is non empty finite V39() V95() set
X is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
S is strict non-empty finite-yielding (X) MSAlgebra over X
x1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
x2 is non empty finite V95() set
x1 -tuples_on x2 is non empty functional FinSequence-membered FinSequenceSet of x2
[:(x1 -tuples_on x2),x2:] is Relation-like set
bool [:(x1 -tuples_on x2),x2:] is set
x3 is Relation-like x1 -tuples_on x2 -defined x2 -valued Function-like V30(x1 -tuples_on x2,x2) Element of bool [:(x1 -tuples_on x2),x2:]
f is Relation-like NAT -defined Function-like finite V42(x1) FinSequence-like FinSubsequence-like V95() set
1GateCircuit (f,x3) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (f,x3)) MSAlgebra over 1GateCircStr (f,x3)
1GateCircStr (f,x3) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
b is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
a is non empty finite V95() set
b -tuples_on a is non empty functional FinSequence-membered FinSequenceSet of a
[:(b -tuples_on a),a:] is Relation-like set
bool [:(b -tuples_on a),a:] is set
g is Relation-like b -tuples_on a -defined a -valued Function-like V30(b -tuples_on a,a) Element of bool [:(b -tuples_on a),a:]
c is Relation-like NAT -defined Function-like finite V42(b) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (c,g) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
1GateCircuit (c,g) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (c,g)) MSAlgebra over 1GateCircStr (c,g)
[f,x3] is pair non empty set
{f,x3} is non empty functional finite V95() set
{f} is non empty functional finite V39() V93() V95() set
{{f,x3},{f}} is non empty finite V39() V95() set
{[f,x3]} is non empty Relation-like Function-like finite V95() set
the carrier' of (1GateCircStr (f,x3)) is non empty set
the Charact of (1GateCircuit (c,g)) is non empty Relation-like the carrier' of (1GateCircStr (c,g)) -defined Function-like total Function-yielding V34() ManySortedFunction of the Arity of (1GateCircStr (c,g)) * ( the Sorts of (1GateCircuit (c,g)) #), the ResultSort of (1GateCircStr (c,g)) * the Sorts of (1GateCircuit (c,g))
the carrier' of (1GateCircStr (c,g)) is non empty set
the Arity of (1GateCircStr (c,g)) is Relation-like the carrier' of (1GateCircStr (c,g)) -defined the carrier of (1GateCircStr (c,g)) * -valued Function-like V30( the carrier' of (1GateCircStr (c,g)), the carrier of (1GateCircStr (c,g)) * ) Function-yielding V34() Element of bool [: the carrier' of (1GateCircStr (c,g)),( the carrier of (1GateCircStr (c,g)) *):]
the carrier of (1GateCircStr (c,g)) is non empty finite V95() set
the carrier of (1GateCircStr (c,g)) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (1GateCircStr (c,g))
[: the carrier' of (1GateCircStr (c,g)),( the carrier of (1GateCircStr (c,g)) *):] is Relation-like set
bool [: the carrier' of (1GateCircStr (c,g)),( the carrier of (1GateCircStr (c,g)) *):] is set
the Sorts of (1GateCircuit (c,g)) is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (c,g)) -defined Function-like total set
the Sorts of (1GateCircuit (c,g)) # is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (c,g)) * -defined Function-like total set
the Arity of (1GateCircStr (c,g)) * ( the Sorts of (1GateCircuit (c,g)) #) is non empty Relation-like non-empty non empty-yielding the carrier' of (1GateCircStr (c,g)) -defined Function-like total set
the ResultSort of (1GateCircStr (c,g)) is Relation-like the carrier' of (1GateCircStr (c,g)) -defined the carrier of (1GateCircStr (c,g)) -valued Function-like V30( the carrier' of (1GateCircStr (c,g)), the carrier of (1GateCircStr (c,g))) Element of bool [: the carrier' of (1GateCircStr (c,g)), the carrier of (1GateCircStr (c,g)):]
[: the carrier' of (1GateCircStr (c,g)), the carrier of (1GateCircStr (c,g)):] is Relation-like set
bool [: the carrier' of (1GateCircStr (c,g)), the carrier of (1GateCircStr (c,g)):] is set
the ResultSort of (1GateCircStr (c,g)) * the Sorts of (1GateCircuit (c,g)) is non empty Relation-like non-empty non empty-yielding the carrier' of (1GateCircStr (c,g)) -defined Function-like total set
proj1 the Charact of (1GateCircuit (c,g)) is non empty set
[c,g] is pair non empty set
{c,g} is non empty functional finite V95() set
{c} is non empty functional finite V39() V93() V95() set
{{c,g},{c}} is non empty finite V39() V95() set
{[c,g]} is non empty Relation-like Function-like finite V95() set
X is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
S is non empty finite V95() set
X -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
[:(X -tuples_on S),S:] is Relation-like set
bool [:(X -tuples_on S),S:] is set
x1 is Relation-like X -tuples_on S -defined S -valued Function-like V30(X -tuples_on S,S) Element of bool [:(X -tuples_on S),S:]
x2 is Relation-like NAT -defined Function-like finite V42(X) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (x2,x1) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
the carrier of (1GateCircStr (x2,x1)) is non empty finite V95() set
1GateCircuit (x2,x1) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (x2,x1)) MSAlgebra over 1GateCircStr (x2,x1)
the Sorts of (1GateCircuit (x2,x1)) is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (x2,x1)) -defined Function-like total set
K246( the Sorts of (1GateCircuit (x2,x1))) is non empty functional V93() V94() set
((1GateCircStr (x2,x1))) is pair non empty Element of the carrier of (1GateCircStr (x2,x1))
the carrier' of (1GateCircStr (x2,x1)) is non empty set
union the carrier' of (1GateCircStr (x2,x1)) is set
x3 is non empty Relation-like the carrier of (1GateCircStr (x2,x1)) -defined Function-like the Sorts of (1GateCircuit (x2,x1)) -compatible total Element of K246( the Sorts of (1GateCircuit (x2,x1)))
Following x3 is non empty Relation-like the carrier of (1GateCircStr (x2,x1)) -defined Function-like the Sorts of (1GateCircuit (x2,x1)) -compatible total Element of K246( the Sorts of (1GateCircuit (x2,x1)))
(Following x3) . ((1GateCircStr (x2,x1))) is set
x2 * x3 is Relation-like NAT -defined Function-like finite V95() set
x1 . (x2 * x3) is set
[x2,x1] is pair non empty set
{x2,x1} is non empty functional finite V95() set
{x2} is non empty functional finite V39() V93() V95() set
{{x2,x1},{x2}} is non empty finite V39() V95() set
X is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
the carrier of X is non empty finite V95() set
S is strict non-empty finite-yielding (X) MSAlgebra over X
the Sorts of S is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of S) is non empty functional V93() V94() set
x1 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
Following x1 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
x3 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
x2 is non empty finite V95() set
x3 -tuples_on x2 is non empty functional FinSequence-membered FinSequenceSet of x2
[:(x3 -tuples_on x2),x2:] is Relation-like set
bool [:(x3 -tuples_on x2),x2:] is set
a is Relation-like x3 -tuples_on x2 -defined x2 -valued Function-like V30(x3 -tuples_on x2,x2) Element of bool [:(x3 -tuples_on x2),x2:]
f is Relation-like NAT -defined Function-like finite V42(x3) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (f,a) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
1GateCircuit (f,a) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (f,a)) MSAlgebra over 1GateCircStr (f,a)
X is non empty non void V79() Circuit-like ManySortedSign
S is non-empty finite-yielding MSAlgebra over X
x3 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
x2 is non empty finite V95() set
x3 -tuples_on x2 is non empty functional FinSequence-membered FinSequenceSet of x2
[:(x3 -tuples_on x2),x2:] is Relation-like set
bool [:(x3 -tuples_on x2),x2:] is set
a is Relation-like x3 -tuples_on x2 -defined x2 -valued Function-like V30(x3 -tuples_on x2,x2) Element of bool [:(x3 -tuples_on x2),x2:]
f is Relation-like NAT -defined Function-like finite V42(x3) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (f,a) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
1GateCircuit (f,a) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (f,a)) MSAlgebra over 1GateCircStr (f,a)
x1 is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
the carrier of X is non empty set
the Sorts of S is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of S) is non empty functional V93() V94() set
x3 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
Following (x3,1) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
the carrier of x1 is non empty finite V95() set
x2 is strict non-empty finite-yielding (x1) MSAlgebra over x1
the Sorts of x2 is non empty Relation-like non-empty non empty-yielding the carrier of x1 -defined Function-like total set
K246( the Sorts of x2) is non empty functional V93() V94() set
f is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of x2 -compatible total Element of K246( the Sorts of x2)
Following f is non empty Relation-like the carrier of x1 -defined Function-like the Sorts of x2 -compatible total Element of K246( the Sorts of x2)
X is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
the carrier of X is non empty finite V95() set
S is strict non-empty finite-yielding (X) (X) (X) MSAlgebra over X
the Sorts of S is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of S) is non empty functional V93() V94() set
x1 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
(X,S,x1) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
Following x1 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
Following (x1,1) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
X is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
the carrier of X is non empty finite V95() set
S is strict non-empty finite-yielding (X) (X) (X) MSAlgebra over X
the Sorts of S is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of S) is non empty functional V93() V94() set
x1 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
(X,S,x1) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following x1 is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
Following (x1,1) is non empty Relation-like the carrier of X -defined Function-like the Sorts of S -compatible total Element of K246( the Sorts of S)
F<sub>2</sub>() is non empty finite V95() set
F<sub>1</sub>() is set
{F<sub>1</sub>()} is non empty finite V95() set
1 -tuples_on F<sub>2</sub>() is non empty functional FinSequence-membered FinSequenceSet of F<sub>2</sub>()
[:(1 -tuples_on F<sub>2</sub>()),F<sub>2</sub>():] is Relation-like set
bool [:(1 -tuples_on F<sub>2</sub>()),F<sub>2</sub>():] is set
X is Relation-like 1 -tuples_on F<sub>2</sub>() -defined F<sub>2</sub>() -valued Function-like V30(1 -tuples_on F<sub>2</sub>(),F<sub>2</sub>()) Element of bool [:(1 -tuples_on F<sub>2</sub>()),F<sub>2</sub>():]
<*F<sub>1</sub>()*> is non empty Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (<*F<sub>1</sub>()*>,X) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
S is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
InputVertices S is finite V95() Element of bool the carrier of S
the carrier of S is non empty finite V95() set
bool the carrier of S is finite V39() V95() set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K488( the carrier of S, the ResultSort of S) is finite V95() Element of bool the carrier of S
the carrier of S \ K488( the carrier of S, the ResultSort of S) is finite V95() Element of bool the carrier of S
(S) is pair non empty Element of the carrier of S
union the carrier' of S is set
1GateCircuit (<*F<sub>1</sub>()*>,X) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (<*F₁()*>,X)) ( 1GateCircStr (<*F₁()*>,X)) ( 1GateCircStr (<*F₁()*>,X)) MSAlgebra over 1GateCircStr (<*F₁()*>,X)
x1 is strict non-empty finite-yielding (S) (S) (S) MSAlgebra over S
the Sorts of x1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
K246( the Sorts of x1) is non empty functional V93() V94() set
proj2 <*F₁()*> is non empty finite V95() set
x2 is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(S,x1,x2) is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(S,x1,x2) . (S) is set
x2 . F₁() is set
F₃((x2 . F₁())) is Element of F₂()
<*F₁()*> * x2 is Relation-like NAT -defined Function-like finite V95() set
dom <*F₁()*> is non empty finite V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
Following x2 is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(Following x2) . (S) is set
[<*F₁()*>,X] is pair non empty set
{<*F₁()*>,X} is non empty functional finite V95() set
{<*F₁()*>} is non empty functional finite V39() V93() V95() set
{{<*F₁()*>,X},{<*F₁()*>}} is non empty finite V39() V95() set
(Following x2) . [<*F₁()*>,X] is set
X . (<*F₁()*> * x2) is set
x3 is Relation-like NAT -defined F₂() -valued Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() Element of 1 -tuples_on F₂()
x3 . 1 is set
F₃((x3 . 1)) is Element of F₂()
<*F₁()*> . 1 is set
x2 . (<*F₁()*> . 1) is set
F₃((x2 . (<*F₁()*> . 1))) is Element of F₂()
F₃() is non empty finite V95() set
F₁() is set
F₂() is set
{F₁(),F₂()} is non empty finite V95() set
2 -tuples_on F₃() is non empty functional FinSequence-membered FinSequenceSet of F₃()
[:(2 -tuples_on F₃()),F₃():] is Relation-like set
bool [:(2 -tuples_on F₃()),F₃():] is set
X is Relation-like 2 -tuples_on F₃() -defined F₃() -valued Function-like V30(2 -tuples_on F₃(),F₃()) Element of bool [:(2 -tuples_on F₃()),F₃():]
<*F₁(),F₂()*> is non empty Relation-like NAT -defined Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (<*F₁(),F₂()*>,X) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
S is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
InputVertices S is finite V95() Element of bool the carrier of S
the carrier of S is non empty finite V95() set
bool the carrier of S is finite V39() V95() set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K488( the carrier of S, the ResultSort of S) is finite V95() Element of bool the carrier of S
the carrier of S \ K488( the carrier of S, the ResultSort of S) is finite V95() Element of bool the carrier of S
(S) is pair non empty Element of the carrier of S
union the carrier' of S is set
1GateCircuit (<*F₁(),F₂()*>,X) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>()*>,X)) ( 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>()*>,X)) ( 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>()*>,X)) MSAlgebra over 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>()*>,X)
x1 is strict non-empty finite-yielding (S) (S) (S) MSAlgebra over S
the Sorts of x1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
K246( the Sorts of x1) is non empty functional V93() V94() set
proj2 <*F<sub>1</sub>(),F<sub>2</sub>()*> is non empty finite V95() set
x2 is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(S,x1,x2) is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(S,x1,x2) . (S) is set
x2 . F<sub>1</sub>() is set
x2 . F<sub>2</sub>() is set
F<sub>4</sub>((x2 . F<sub>1</sub>()),(x2 . F<sub>2</sub>())) is Element of F<sub>3</sub>()
<*F<sub>1</sub>(),F<sub>2</sub>()*> * x2 is Relation-like NAT -defined Function-like finite V95() set
dom <*F<sub>1</sub>(),F<sub>2</sub>()*> is non empty finite V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
Seg 2 is non empty finite V42(2) V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
Following x2 is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
[<*F<sub>1</sub>(),F<sub>2</sub>()*>,X] is pair non empty set
{<*F<sub>1</sub>(),F<sub>2</sub>()*>,X} is non empty functional finite V95() set
{<*F<sub>1</sub>(),F<sub>2</sub>()*>} is non empty functional finite V39() V93() V95() set
{{<*F<sub>1</sub>(),F<sub>2</sub>()*>,X},{<*F<sub>1</sub>(),F<sub>2</sub>()*>}} is non empty finite V39() V95() set
(Following x2) . [<*F<sub>1</sub>(),F<sub>2</sub>()*>,X] is set
X . (<*F<sub>1</sub>(),F<sub>2</sub>()*> * x2) is set
x3 is Relation-like NAT -defined F<sub>3</sub>() -valued Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() Element of 2 -tuples_on F<sub>3</sub>()
x3 . 1 is set
x3 . 2 is set
F<sub>4</sub>((x3 . 1),(x3 . 2)) is Element of F<sub>3</sub>()
<*F<sub>1</sub>(),F<sub>2</sub>()*> . 1 is set
x2 . (<*F<sub>1</sub>(),F<sub>2</sub>()*> . 1) is set
F<sub>4</sub>((x2 . (<*F<sub>1</sub>(),F<sub>2</sub>()*> . 1)),(x3 . 2)) is Element of F<sub>3</sub>()
<*F<sub>1</sub>(),F<sub>2</sub>()*> . 2 is set
x2 . (<*F<sub>1</sub>(),F<sub>2</sub>()*> . 2) is set
F<sub>4</sub>((x2 . (<*F<sub>1</sub>(),F<sub>2</sub>()*> . 1)),(x2 . (<*F<sub>1</sub>(),F<sub>2</sub>()*> . 2))) is Element of F<sub>3</sub>()
F<sub>4</sub>((x2 . F<sub>1</sub>()),(x2 . (<*F<sub>1</sub>(),F<sub>2</sub>()*> . 2))) is Element of F<sub>3</sub>()
F<sub>4</sub>() is non empty finite V95() set
F<sub>1</sub>() is set
F<sub>2</sub>() is set
F<sub>3</sub>() is set
{F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>()} is finite V95() set
3 -tuples_on F<sub>4</sub>() is non empty functional FinSequence-membered FinSequenceSet of F<sub>4</sub>()
[:(3 -tuples_on F<sub>4</sub>()),F<sub>4</sub>():] is Relation-like set
bool [:(3 -tuples_on F<sub>4</sub>()),F<sub>4</sub>():] is set
X is Relation-like 3 -tuples_on F<sub>4</sub>() -defined F<sub>4</sub>() -valued Function-like V30(3 -tuples_on F<sub>4</sub>(),F<sub>4</sub>()) Element of bool [:(3 -tuples_on F<sub>4</sub>()),F<sub>4</sub>():]
<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>()*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>()*>,X) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
S is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
InputVertices S is finite V95() Element of bool the carrier of S
the carrier of S is non empty finite V95() set
bool the carrier of S is finite V39() V95() set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K488( the carrier of S, the ResultSort of S) is finite V95() Element of bool the carrier of S
the carrier of S \ K488( the carrier of S, the ResultSort of S) is finite V95() Element of bool the carrier of S
(S) is pair non empty Element of the carrier of S
union the carrier' of S is set
1GateCircuit (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>()*>,X) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (<*F₁(),F₂(),F₃()*>,X)) ( 1GateCircStr (<*F₁(),F₂(),F₃()*>,X)) ( 1GateCircStr (<*F₁(),F₂(),F₃()*>,X)) MSAlgebra over 1GateCircStr (<*F₁(),F₂(),F₃()*>,X)
x1 is strict non-empty finite-yielding (S) (S) (S) MSAlgebra over S
the Sorts of x1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
K246( the Sorts of x1) is non empty functional V93() V94() set
proj2 <*F₁(),F₂(),F₃()*> is non empty finite V95() set
x2 is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(S,x1,x2) is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(S,x1,x2) . (S) is set
x2 . F₁() is set
x2 . F₂() is set
x2 . F₃() is set
F₅((x2 . F₁()),(x2 . F₂()),(x2 . F₃())) is Element of F₄()
<*F₁(),F₂(),F₃()*> * x2 is Relation-like NAT -defined Function-like finite V95() set
dom <*F₁(),F₂(),F₃()*> is non empty finite V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
Seg 3 is non empty finite V42(3) V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
Following x2 is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
[<*F₁(),F₂(),F₃()*>,X] is pair non empty set
{<*F₁(),F₂(),F₃()*>,X} is non empty functional finite V95() set
{<*F₁(),F₂(),F₃()*>} is non empty functional finite V39() V93() V95() set
{{<*F₁(),F₂(),F₃()*>,X},{<*F₁(),F₂(),F₃()*>}} is non empty finite V39() V95() set
(Following x2) . [<*F₁(),F₂(),F₃()*>,X] is set
X . (<*F₁(),F₂(),F₃()*> * x2) is set
x3 is Relation-like NAT -defined F₄() -valued Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() Element of 3 -tuples_on F₄()
x3 . 1 is set
x3 . 2 is set
x3 . 3 is set
F₅((x3 . 1),(x3 . 2),(x3 . 3)) is Element of F₄()
<*F₁(),F₂(),F₃()*> . 1 is set
x2 . (<*F₁(),F₂(),F₃()*> . 1) is set
F₅((x2 . (<*F₁(),F₂(),F₃()*> . 1)),(x3 . 2),(x3 . 3)) is Element of F₄()
F₅((x2 . F₁()),(x3 . 2),(x3 . 3)) is Element of F₄()
<*F₁(),F₂(),F₃()*> . 2 is set
x2 . (<*F₁(),F₂(),F₃()*> . 2) is set
F₅((x2 . F₁()),(x2 . (<*F₁(),F₂(),F₃()*> . 2)),(x3 . 3)) is Element of F₄()
F₅((x2 . F₁()),(x2 . F₂()),(x3 . 3)) is Element of F₄()
<*F₁(),F₂(),F₃()*> . 3 is set
x2 . (<*F₁(),F₂(),F₃()*> . 3) is set
F₅((x2 . F₁()),(x2 . F₂()),(x2 . (<*F₁(),F₂(),F₃()*> . 3))) is Element of F₄()
F₅() is non empty finite V95() set
F₁() is set
F₂() is set
F₃() is set
F₄() is set
{F₁(),F₂(),F₃(),F₄()} is finite V95() set
4 -tuples_on F₅() is non empty functional FinSequence-membered FinSequenceSet of F₅()
[:(4 -tuples_on F₅()),F₅():] is Relation-like set
bool [:(4 -tuples_on F₅()),F₅():] is set
X is Relation-like 4 -tuples_on F₅() -defined F₅() -valued Function-like V30(4 -tuples_on F₅(),F₅()) Element of bool [:(4 -tuples_on F₅()),F₅():]
<*F₁(),F₂(),F₃(),F₄()*> is non empty Relation-like NAT -defined Function-like finite V42(4) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (<*F₁(),F₂(),F₃(),F₄()*>,X) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
S is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
InputVertices S is finite V95() Element of bool the carrier of S
the carrier of S is non empty finite V95() set
bool the carrier of S is finite V39() V95() set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K488( the carrier of S, the ResultSort of S) is finite V95() Element of bool the carrier of S
the carrier of S \ K488( the carrier of S, the ResultSort of S) is finite V95() Element of bool the carrier of S
(S) is pair non empty Element of the carrier of S
union the carrier' of S is set
1GateCircuit (<*F₁(),F₂(),F₃(),F₄()*>,X) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>,X)) ( 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>,X)) ( 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>,X)) MSAlgebra over 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>,X)
x1 is strict non-empty finite-yielding (S) (S) (S) MSAlgebra over S
the Sorts of x1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
K246( the Sorts of x1) is non empty functional V93() V94() set
proj2 <*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> is non empty finite V95() set
x2 is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(S,x1,x2) is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(S,x1,x2) . (S) is set
x2 . F<sub>1</sub>() is set
x2 . F<sub>2</sub>() is set
x2 . F<sub>3</sub>() is set
x2 . F<sub>4</sub>() is set
F<sub>6</sub>((x2 . F<sub>1</sub>()),(x2 . F<sub>2</sub>()),(x2 . F<sub>3</sub>()),(x2 . F<sub>4</sub>())) is Element of F<sub>5</sub>()
<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> * x2 is Relation-like NAT -defined Function-like finite V95() set
dom <*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> is non empty finite V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
Following x2 is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
[<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>,X] is pair non empty set
{<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>,X} is non empty functional finite V95() set
{<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>} is non empty functional finite V39() V93() V95() set
{{<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>,X},{<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>}} is non empty finite V39() V95() set
(Following x2) . [<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>,X] is set
X . (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> * x2) is set
x3 is Relation-like NAT -defined F<sub>5</sub>() -valued Function-like finite V42(4) FinSequence-like FinSubsequence-like V95() Element of 4 -tuples_on F<sub>5</sub>()
x3 . 1 is set
x3 . 2 is set
x3 . 3 is set
x3 . 4 is set
F<sub>6</sub>((x3 . 1),(x3 . 2),(x3 . 3),(x3 . 4)) is Element of F<sub>5</sub>()
<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> . 1 is set
x2 . (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> . 1) is set
F<sub>6</sub>((x2 . (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> . 1)),(x3 . 2),(x3 . 3),(x3 . 4)) is Element of F<sub>5</sub>()
F<sub>6</sub>((x2 . F<sub>1</sub>()),(x3 . 2),(x3 . 3),(x3 . 4)) is Element of F<sub>5</sub>()
<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> . 2 is set
x2 . (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> . 2) is set
F<sub>6</sub>((x2 . F<sub>1</sub>()),(x2 . (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> . 2)),(x3 . 3),(x3 . 4)) is Element of F<sub>5</sub>()
F<sub>6</sub>((x2 . F<sub>1</sub>()),(x2 . F<sub>2</sub>()),(x3 . 3),(x3 . 4)) is Element of F<sub>5</sub>()
<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> . 3 is set
x2 . (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> . 3) is set
F<sub>6</sub>((x2 . F<sub>1</sub>()),(x2 . F<sub>2</sub>()),(x2 . (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> . 3)),(x3 . 4)) is Element of F<sub>5</sub>()
F<sub>6</sub>((x2 . F<sub>1</sub>()),(x2 . F<sub>2</sub>()),(x2 . F<sub>3</sub>()),(x3 . 4)) is Element of F<sub>5</sub>()
<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> . 4 is set
x2 . (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> . 4) is set
F<sub>6</sub>((x2 . F<sub>1</sub>()),(x2 . F<sub>2</sub>()),(x2 . F<sub>3</sub>()),(x2 . (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*> . 4))) is Element of F<sub>5</sub>()
F<sub>6</sub>() is non empty finite V95() set
F<sub>1</sub>() is set
F<sub>2</sub>() is set
F<sub>3</sub>() is set
F<sub>4</sub>() is set
F<sub>5</sub>() is set
{F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>(),F<sub>5</sub>()} is finite V95() set
5 -tuples_on F<sub>6</sub>() is non empty functional FinSequence-membered FinSequenceSet of F<sub>6</sub>()
[:(5 -tuples_on F<sub>6</sub>()),F<sub>6</sub>():] is Relation-like set
bool [:(5 -tuples_on F<sub>6</sub>()),F<sub>6</sub>():] is set
X is Relation-like 5 -tuples_on F<sub>6</sub>() -defined F<sub>6</sub>() -valued Function-like V30(5 -tuples_on F<sub>6</sub>(),F<sub>6</sub>()) Element of bool [:(5 -tuples_on F<sub>6</sub>()),F<sub>6</sub>():]
<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>(),F<sub>5</sub>()*> is non empty Relation-like NAT -defined Function-like finite V42(5) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>(),F<sub>5</sub>()*>,X) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
S is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
InputVertices S is finite V95() Element of bool the carrier of S
the carrier of S is non empty finite V95() set
bool the carrier of S is finite V39() V95() set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K488( the carrier of S, the ResultSort of S) is finite V95() Element of bool the carrier of S
the carrier of S \ K488( the carrier of S, the ResultSort of S) is finite V95() Element of bool the carrier of S
(S) is pair non empty Element of the carrier of S
union the carrier' of S is set
1GateCircuit (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>(),F<sub>5</sub>()*>,X) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (<*F₁(),F₂(),F₃(),F₄(),F₅()*>,X)) ( 1GateCircStr (<*F₁(),F₂(),F₃(),F₄(),F₅()*>,X)) ( 1GateCircStr (<*F₁(),F₂(),F₃(),F₄(),F₅()*>,X)) MSAlgebra over 1GateCircStr (<*F₁(),F₂(),F₃(),F₄(),F₅()*>,X)
x1 is strict non-empty finite-yielding (S) (S) (S) MSAlgebra over S
the Sorts of x1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
K246( the Sorts of x1) is non empty functional V93() V94() set
proj2 <*F₁(),F₂(),F₃(),F₄(),F₅()*> is non empty finite V95() set
x2 is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(S,x1,x2) is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(S,x1,x2) . (S) is set
x2 . F₁() is set
x2 . F₂() is set
x2 . F₃() is set
x2 . F₄() is set
x2 . F₅() is set
F₇((x2 . F₁()),(x2 . F₂()),(x2 . F₃()),(x2 . F₄()),(x2 . F₅())) is Element of F₆()
<*F₁(),F₂(),F₃(),F₄(),F₅()*> * x2 is Relation-like NAT -defined Function-like finite V95() set
dom <*F₁(),F₂(),F₃(),F₄(),F₅()*> is non empty finite V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
Following x2 is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
[<*F₁(),F₂(),F₃(),F₄(),F₅()*>,X] is pair non empty set
{<*F₁(),F₂(),F₃(),F₄(),F₅()*>,X} is non empty functional finite V95() set
{<*F₁(),F₂(),F₃(),F₄(),F₅()*>} is non empty functional finite V39() V93() V95() set
{{<*F₁(),F₂(),F₃(),F₄(),F₅()*>,X},{<*F₁(),F₂(),F₃(),F₄(),F₅()*>}} is non empty finite V39() V95() set
(Following x2) . [<*F₁(),F₂(),F₃(),F₄(),F₅()*>,X] is set
X . (<*F₁(),F₂(),F₃(),F₄(),F₅()*> * x2) is set
x3 is Relation-like NAT -defined F₆() -valued Function-like finite V42(5) FinSequence-like FinSubsequence-like V95() Element of 5 -tuples_on F₆()
x3 . 1 is set
x3 . 2 is set
x3 . 3 is set
x3 . 4 is set
x3 . 5 is set
F₇((x3 . 1),(x3 . 2),(x3 . 3),(x3 . 4),(x3 . 5)) is Element of F₆()
<*F₁(),F₂(),F₃(),F₄(),F₅()*> . 1 is set
x2 . (<*F₁(),F₂(),F₃(),F₄(),F₅()*> . 1) is set
F₇((x2 . (<*F₁(),F₂(),F₃(),F₄(),F₅()*> . 1)),(x3 . 2),(x3 . 3),(x3 . 4),(x3 . 5)) is Element of F₆()
F₇((x2 . F₁()),(x3 . 2),(x3 . 3),(x3 . 4),(x3 . 5)) is Element of F₆()
<*F₁(),F₂(),F₃(),F₄(),F₅()*> . 2 is set
x2 . (<*F₁(),F₂(),F₃(),F₄(),F₅()*> . 2) is set
F₇((x2 . F₁()),(x2 . (<*F₁(),F₂(),F₃(),F₄(),F₅()*> . 2)),(x3 . 3),(x3 . 4),(x3 . 5)) is Element of F₆()
F₇((x2 . F₁()),(x2 . F₂()),(x3 . 3),(x3 . 4),(x3 . 5)) is Element of F₆()
<*F₁(),F₂(),F₃(),F₄(),F₅()*> . 3 is set
x2 . (<*F₁(),F₂(),F₃(),F₄(),F₅()*> . 3) is set
F₇((x2 . F₁()),(x2 . F₂()),(x2 . (<*F₁(),F₂(),F₃(),F₄(),F₅()*> . 3)),(x3 . 4),(x3 . 5)) is Element of F₆()
F₇((x2 . F₁()),(x2 . F₂()),(x2 . F₃()),(x3 . 4),(x3 . 5)) is Element of F₆()
<*F₁(),F₂(),F₃(),F₄(),F₅()*> . 4 is set
x2 . (<*F₁(),F₂(),F₃(),F₄(),F₅()*> . 4) is set
F₇((x2 . F₁()),(x2 . F₂()),(x2 . F₃()),(x2 . (<*F₁(),F₂(),F₃(),F₄(),F₅()*> . 4)),(x3 . 5)) is Element of F₆()
F₇((x2 . F₁()),(x2 . F₂()),(x2 . F₃()),(x2 . F₄()),(x3 . 5)) is Element of F₆()
<*F₁(),F₂(),F₃(),F₄(),F₅()*> . 5 is set
x2 . (<*F₁(),F₂(),F₃(),F₄(),F₅()*> . 5) is set
F₇((x2 . F₁()),(x2 . F₂()),(x2 . F₃()),(x2 . F₄()),(x2 . (<*F₁(),F₂(),F₃(),F₄(),F₅()*> . 5))) is Element of F₆()
X is non empty set
S is non empty set
x1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
x1 -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
x2 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
x2 -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
x3 is set
x1 |-> x3 is Relation-like NAT -defined Function-like finite V42(x1) FinSequence-like FinSubsequence-like V95() set
S * is non empty functional FinSequence-membered FinSequenceSet of S
{ b₁ where b₁ is Relation-like NAT -defined S -valued Function-like finite FinSequence-like FinSubsequence-like V95() Element of S * : len b₁ = x2 } is set
proj2 (x1 |-> x3) is finite V95() set
f is Relation-like NAT -defined S -valued Function-like finite FinSequence-like FinSubsequence-like V95() Element of S *
len f is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Seg x1 is finite V42(x1) V95() V140() V141() V142() V143() V144() V145() V149() V150() V151() Element of bool NAT
(Seg x1) --> x3 is Relation-like Seg x1 -defined Seg x1 -defined {x3} -valued Function-like constant total total V30( Seg x1,{x3}) finite FinSequence-like FinSubsequence-like V95() Element of bool [:(Seg x1),{x3}:]
{x3} is non empty finite V95() set
[:(Seg x1),{x3}:] is Relation-like finite V95() set
bool [:(Seg x1),{x3}:] is finite V39() V95() set
x3 is set
x2 |-> x3 is Relation-like NAT -defined Function-like finite V42(x2) FinSequence-like FinSubsequence-like V95() set
Seg x2 is finite V42(x2) V95() V140() V141() V142() V143() V144() V145() V149() V150() V151() Element of bool NAT
(Seg x2) --> x3 is Relation-like Seg x2 -defined Seg x2 -defined {x3} -valued Function-like constant total total V30( Seg x2,{x3}) finite FinSequence-like FinSubsequence-like V95() Element of bool [:(Seg x2),{x3}:]
{x3} is non empty finite V95() set
[:(Seg x2),{x3}:] is Relation-like finite V95() set
bool [:(Seg x2),{x3}:] is finite V39() V95() set
X * is non empty functional FinSequence-membered FinSequenceSet of X
{ b₁ where b₁ is Relation-like NAT -defined X -valued Function-like finite FinSequence-like FinSubsequence-like V95() Element of X * : len b₁ = x1 } is set
f is Relation-like NAT -defined X -valued Function-like finite FinSequence-like FinSubsequence-like V95() Element of X *
len f is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
proj2 (x2 |-> x3) is finite V95() set
f is Relation-like NAT -defined X -valued Function-like finite FinSequence-like FinSubsequence-like V95() Element of X *
len f is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
X is non empty V79() ManySortedSign
the carrier of X is non empty set
S is non empty V79() ManySortedSign
X +* S is non empty V79() strict ManySortedSign
the carrier of (X +* S) is non empty set
x1 is Element of the carrier of X
the carrier of S is non empty set
the carrier of X \/ the carrier of S is non empty set
S is non empty V79() ManySortedSign
the carrier of S is non empty set
X is non empty V79() ManySortedSign
X +* S is non empty V79() strict ManySortedSign
the carrier of (X +* S) is non empty set
x1 is Element of the carrier of S
the carrier of X is non empty set
the carrier of X \/ the carrier of S is non empty set
X is non empty finite V95() set
the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set is Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set
1 -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
[:(1 -tuples_on X),X:] is Relation-like set
bool [:(1 -tuples_on X),X:] is set
the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:] is Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:]
1GateCircStr ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:]) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
1GateCircuit ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:]) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:])) ( 1GateCircStr ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:])) ( 1GateCircStr ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:])) MSAlgebra over 1GateCircStr ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:])
the carrier of (1GateCircStr ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:])) is non empty finite V95() set
the Sorts of (1GateCircuit ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:])) is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:])) -defined Function-like total set
the carrier of (1GateCircStr ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:])) --> X is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:])) -defined {X} -valued Function-like constant total V30( the carrier of (1GateCircStr ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:])),{X}) finite V95() Element of bool [: the carrier of (1GateCircStr ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:])),{X}:]
{X} is non empty finite V39() V95() set
[: the carrier of (1GateCircStr ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:])),{X}:] is Relation-like finite V95() set
bool [: the carrier of (1GateCircStr ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:])),{X}:] is finite V39() V95() set
the_value_of the Sorts of (1GateCircuit ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:])) is set
X is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
S is non empty finite V95() set
X -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
[:(X -tuples_on S),S:] is Relation-like set
bool [:(X -tuples_on S),S:] is set
x1 is Relation-like X -tuples_on S -defined S -valued Function-like V30(X -tuples_on S,S) Element of bool [:(X -tuples_on S),S:]
x2 is Relation-like NAT -defined Function-like finite V42(X) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (x2,x1) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
1GateCircuit (x2,x1) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (x2,x1)) ( 1GateCircStr (x2,x1)) ( 1GateCircStr (x2,x1)) MSAlgebra over 1GateCircStr (x2,x1)
x3 is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (x2,x1)) ( 1GateCircStr (x2,x1)) ( 1GateCircStr (x2,x1)) MSAlgebra over 1GateCircStr (x2,x1)
the Sorts of x3 is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (x2,x1)) -defined Function-like total set
the carrier of (1GateCircStr (x2,x1)) is non empty finite V95() set
the_value_of the Sorts of x3 is set
the carrier of (1GateCircStr (x2,x1)) --> S is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (x2,x1)) -defined {S} -valued Function-like constant total V30( the carrier of (1GateCircStr (x2,x1)),{S}) finite V95() Element of bool [: the carrier of (1GateCircStr (x2,x1)),{S}:]
{S} is non empty finite V39() V95() set
[: the carrier of (1GateCircStr (x2,x1)),{S}:] is Relation-like finite V95() set
bool [: the carrier of (1GateCircStr (x2,x1)),{S}:] is finite V39() V95() set
X is non empty finite V95() set
the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set is Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set
1 -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
[:(1 -tuples_on X),X:] is Relation-like set
bool [:(1 -tuples_on X),X:] is set
the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:] is Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:]
1GateCircStr ( the Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set , the Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:]) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
X is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
S is non empty finite V95() set
X -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
[:(X -tuples_on S),S:] is Relation-like set
bool [:(X -tuples_on S),S:] is set
x1 is Relation-like X -tuples_on S -defined S -valued Function-like V30(X -tuples_on S,S) Element of bool [:(X -tuples_on S),S:]
x2 is Relation-like NAT -defined Function-like finite V42(X) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (x2,x1) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
x1 is finite-yielding MSAlgebra over S
the Sorts of x1 is non empty Relation-like the carrier of S -defined Function-like total set
the carrier of S is non empty set
the_value_of the Sorts of x1 is set
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
x1 is finite-yielding (X,S)
the Sorts of x1 is non empty Relation-like the carrier of S -defined Function-like total set
the carrier of S is non empty set
the_value_of the Sorts of x1 is set
proj1 the Sorts of x1 is non empty set
x2 is set
the Sorts of x1 . x2 is set
X is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
S is non empty finite V95() set
X -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
[:(X -tuples_on S),S:] is Relation-like set
bool [:(X -tuples_on S),S:] is set
x1 is Relation-like X -tuples_on S -defined S -valued Function-like V30(X -tuples_on S,S) Element of bool [:(X -tuples_on S),S:]
x2 is Relation-like NAT -defined Function-like finite V42(X) FinSequence-like FinSubsequence-like V95() set
1GateCircuit (x2,x1) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (x2,x1)) ( 1GateCircStr (x2,x1)) ( 1GateCircStr (x2,x1)) MSAlgebra over 1GateCircStr (x2,x1)
1GateCircStr (x2,x1) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
(X,S,x1,x2) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (S)
the Sorts of (1GateCircuit (x2,x1)) is non empty Relation-like non-empty non empty-yielding the carrier of (X,S,x1,x2) -defined Function-like total set
the carrier of (X,S,x1,x2) is non empty finite V95() set
the_value_of the Sorts of (1GateCircuit (x2,x1)) is set
the Sorts of (1GateCircuit (x2,x1)) is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (x2,x1)) -defined Function-like total set
the carrier of (1GateCircStr (x2,x1)) is non empty finite V95() set
the carrier of (X,S,x1,x2) --> S is non empty Relation-like non-empty non empty-yielding the carrier of (X,S,x1,x2) -defined {S} -valued Function-like constant total V30( the carrier of (X,S,x1,x2),{S}) finite V95() Element of bool [: the carrier of (X,S,x1,x2),{S}:]
{S} is non empty finite V39() V95() set
[: the carrier of (X,S,x1,x2),{S}:] is Relation-like finite V95() set
bool [: the carrier of (X,S,x1,x2),{S}:] is finite V39() V95() set
the_value_of the Sorts of (1GateCircuit (x2,x1)) is set
X is non empty finite V95() set
S is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (X)
x1 is finite-yielding MSAlgebra over S
the Sorts of x1 is non empty Relation-like the carrier of S -defined Function-like total set
the carrier of S is non empty finite V95() set
the_value_of the Sorts of x1 is set
the Charact of x1 is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding V34() ManySortedFunction of the Arity of S * ( the Sorts of x1 #), the ResultSort of S * the Sorts of x1
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding V34() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered FinSequenceSet of the carrier of S
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Sorts of x1 # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ( the Sorts of x1 #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of x1 is non empty Relation-like the carrier' of S -defined Function-like total set
MSAlgebra(# the Sorts of x1, the Charact of x1 #) is strict MSAlgebra over S
x3 is finite-yielding MSAlgebra over S
the Charact of x3 is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding V34() ManySortedFunction of the Arity of S * ( the Sorts of x3 #), the ResultSort of S * the Sorts of x3
the Sorts of x3 is non empty Relation-like the carrier of S -defined Function-like total set
the Sorts of x3 # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ( the Sorts of x3 #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S * the Sorts of x3 is non empty Relation-like the carrier' of S -defined Function-like total set
f is set
f `1 is set
the Charact of x3 . f is Relation-like Function-like set
[(f `1),( the Charact of x3 . f)] is pair non empty set
{(f `1),( the Charact of x3 . f)} is non empty finite V95() set
{(f `1)} is non empty finite V95() set
{{(f `1),( the Charact of x3 . f)},{(f `1)}} is non empty finite V39() V95() set
b is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
a is non empty finite V95() set
b -tuples_on a is non empty functional FinSequence-membered FinSequenceSet of a
[:(b -tuples_on a),a:] is Relation-like set
bool [:(b -tuples_on a),a:] is set
g is Relation-like b -tuples_on a -defined a -valued Function-like V30(b -tuples_on a,a) Element of bool [:(b -tuples_on a),a:]
c is Relation-like NAT -defined Function-like finite V42(b) FinSequence-like FinSubsequence-like V95() set
(b,a,g,c) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (a)
f is non-empty finite-yielding gate`2=den (X,S)
proj1 the Arity of S is set
proj1 the Sorts of x1 is non empty set
the Sorts of f is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the carrier of S --> X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined {X} -valued Function-like constant total V30( the carrier of S,{X}) finite V95() Element of bool [: the carrier of S,{X}:]
{X} is non empty finite V39() V95() set
[: the carrier of S,{X}:] is Relation-like finite V95() set
bool [: the carrier of S,{X}:] is finite V39() V95() set
[c,g] is pair non empty set
{c,g} is non empty functional finite V95() set
{c} is non empty functional finite V39() V93() V95() set
{{c,g},{c}} is non empty finite V39() V95() set
1GateCircuit (c,g) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (c,g)) ( 1GateCircStr (c,g)) ( 1GateCircStr (c,g)) MSAlgebra over 1GateCircStr (c,g)
1GateCircStr (c,g) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
{[c,g]} is non empty Relation-like Function-like finite V95() set
[c,g] `1 is set
the Charact of (1GateCircuit (c,g)) is non empty Relation-like the carrier' of (1GateCircStr (c,g)) -defined Function-like total Function-yielding V34() ManySortedFunction of the Arity of (1GateCircStr (c,g)) * ( the Sorts of (1GateCircuit (c,g)) #), the ResultSort of (1GateCircStr (c,g)) * the Sorts of (1GateCircuit (c,g))
the carrier' of (1GateCircStr (c,g)) is non empty set
the Arity of (1GateCircStr (c,g)) is Relation-like the carrier' of (1GateCircStr (c,g)) -defined the carrier of (1GateCircStr (c,g)) * -valued Function-like V30( the carrier' of (1GateCircStr (c,g)), the carrier of (1GateCircStr (c,g)) * ) Function-yielding V34() Element of bool [: the carrier' of (1GateCircStr (c,g)),( the carrier of (1GateCircStr (c,g)) *):]
the carrier of (1GateCircStr (c,g)) is non empty finite V95() set
the carrier of (1GateCircStr (c,g)) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (1GateCircStr (c,g))
[: the carrier' of (1GateCircStr (c,g)),( the carrier of (1GateCircStr (c,g)) *):] is Relation-like set
bool [: the carrier' of (1GateCircStr (c,g)),( the carrier of (1GateCircStr (c,g)) *):] is set
the Sorts of (1GateCircuit (c,g)) is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (c,g)) -defined Function-like total set
the Sorts of (1GateCircuit (c,g)) # is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (c,g)) * -defined Function-like total set
the Arity of (1GateCircStr (c,g)) * ( the Sorts of (1GateCircuit (c,g)) #) is non empty Relation-like non-empty non empty-yielding the carrier' of (1GateCircStr (c,g)) -defined Function-like total set
the ResultSort of (1GateCircStr (c,g)) is Relation-like the carrier' of (1GateCircStr (c,g)) -defined the carrier of (1GateCircStr (c,g)) -valued Function-like V30( the carrier' of (1GateCircStr (c,g)), the carrier of (1GateCircStr (c,g))) Element of bool [: the carrier' of (1GateCircStr (c,g)), the carrier of (1GateCircStr (c,g)):]
[: the carrier' of (1GateCircStr (c,g)), the carrier of (1GateCircStr (c,g)):] is Relation-like set
bool [: the carrier' of (1GateCircStr (c,g)), the carrier of (1GateCircStr (c,g)):] is set
the ResultSort of (1GateCircStr (c,g)) * the Sorts of (1GateCircuit (c,g)) is non empty Relation-like non-empty non empty-yielding the carrier' of (1GateCircStr (c,g)) -defined Function-like total set
the Charact of (1GateCircuit (c,g)) . [c,g] is Relation-like Function-like set
[([c,g] `1),( the Charact of (1GateCircuit (c,g)) . [c,g])] is pair non empty set
{([c,g] `1),( the Charact of (1GateCircuit (c,g)) . [c,g])} is non empty finite V95() set
{([c,g] `1)} is non empty finite V95() set
{{([c,g] `1),( the Charact of (1GateCircuit (c,g)) . [c,g])},{([c,g] `1)}} is non empty finite V39() V95() set
the Arity of S . [c,g] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V95() set
proj1 the ResultSort of S is set
the ResultSort of S * the Sorts of f is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
( the ResultSort of S * the Sorts of f) . [c,g] is set
the ResultSort of S . [c,g] is set
the Sorts of f . ( the ResultSort of S . [c,g]) is set
proj1 the Sorts of f is non empty set
the Charact of f is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding V34() ManySortedFunction of the Arity of S * ( the Sorts of f #), the ResultSort of S * the Sorts of f
the Sorts of f # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ( the Sorts of f #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the Charact of f . [c,g] is Relation-like Function-like set
[([c,g] `1),( the Charact of f . [c,g])] is pair non empty set
{([c,g] `1),( the Charact of f . [c,g])} is non empty finite V95() set
{{([c,g] `1),( the Charact of f . [c,g])},{([c,g] `1)}} is non empty finite V39() V95() set
proj1 ( the Charact of f . [c,g]) is set
proj1 g is set
( the Arity of S * ( the Sorts of f #)) . [c,g] is set
[:(( the Arity of S * ( the Sorts of f #)) . [c,g]),(( the ResultSort of S * the Sorts of f) . [c,g]):] is Relation-like set
bool [:(( the Arity of S * ( the Sorts of f #)) . [c,g]),(( the ResultSort of S * the Sorts of f) . [c,g]):] is set
x is Relation-like NAT -defined the carrier of S -valued Function-like finite FinSequence-like FinSubsequence-like V95() FinSequence of the carrier of S
( the Sorts of f #) . x is set
len x is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
(len x) -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
k is set
the Charact of f . k is Relation-like Function-like set
the Charact of (1GateCircuit (c,g)) . k is Relation-like Function-like set
b -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
<*> X is non pair empty Relation-like non-empty empty-yielding NAT -defined X -valued Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() Function-yielding V34() finite finite-yielding V39() FinSequence-like FinSubsequence-like FinSequence-membered V47() V92() V95() non with_pair ext-real V140() V141() V142() V143() V144() V145() V146() V149() V150() V151() V152() V153() FinSequence of X
{(<*> X)} is non empty functional finite V39() V93() V95() non with_pair V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() set
<*> a is non pair empty Relation-like non-empty empty-yielding NAT -defined a -valued Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() Function-yielding V34() finite finite-yielding V39() FinSequence-like FinSubsequence-like FinSequence-membered V47() V92() V95() non with_pair ext-real V140() V141() V142() V143() V144() V145() V146() V149() V150() V151() V152() V153() FinSequence of a
{(<*> a)} is non empty functional finite V39() V93() V95() non with_pair V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() set
proj2 ( the Charact of f . [c,g]) is set
[:(b -tuples_on X),X:] is Relation-like set
bool [:(b -tuples_on X),X:] is set
k is Relation-like b -tuples_on X -defined X -valued Function-like V30(b -tuples_on X,X) Element of bool [:(b -tuples_on X),X:]
1GateCircuit (c,k) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (c,k)) ( 1GateCircStr (c,k)) ( 1GateCircStr (c,k)) MSAlgebra over 1GateCircStr (c,k)
1GateCircStr (c,k) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
the Charact of (1GateCircuit (c,k)) is non empty Relation-like the carrier' of (1GateCircStr (c,k)) -defined Function-like total Function-yielding V34() ManySortedFunction of the Arity of (1GateCircStr (c,k)) * ( the Sorts of (1GateCircuit (c,k)) #), the ResultSort of (1GateCircStr (c,k)) * the Sorts of (1GateCircuit (c,k))
the carrier' of (1GateCircStr (c,k)) is non empty set
the Arity of (1GateCircStr (c,k)) is Relation-like the carrier' of (1GateCircStr (c,k)) -defined the carrier of (1GateCircStr (c,k)) * -valued Function-like V30( the carrier' of (1GateCircStr (c,k)), the carrier of (1GateCircStr (c,k)) * ) Function-yielding V34() Element of bool [: the carrier' of (1GateCircStr (c,k)),( the carrier of (1GateCircStr (c,k)) *):]
the carrier of (1GateCircStr (c,k)) is non empty finite V95() set
the carrier of (1GateCircStr (c,k)) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (1GateCircStr (c,k))
[: the carrier' of (1GateCircStr (c,k)),( the carrier of (1GateCircStr (c,k)) *):] is Relation-like set
bool [: the carrier' of (1GateCircStr (c,k)),( the carrier of (1GateCircStr (c,k)) *):] is set
the Sorts of (1GateCircuit (c,k)) is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (c,k)) -defined Function-like total set
the Sorts of (1GateCircuit (c,k)) # is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (c,k)) * -defined Function-like total set
the Arity of (1GateCircStr (c,k)) * ( the Sorts of (1GateCircuit (c,k)) #) is non empty Relation-like non-empty non empty-yielding the carrier' of (1GateCircStr (c,k)) -defined Function-like total set
the ResultSort of (1GateCircStr (c,k)) is Relation-like the carrier' of (1GateCircStr (c,k)) -defined the carrier of (1GateCircStr (c,k)) -valued Function-like V30( the carrier' of (1GateCircStr (c,k)), the carrier of (1GateCircStr (c,k))) Element of bool [: the carrier' of (1GateCircStr (c,k)), the carrier of (1GateCircStr (c,k)):]
[: the carrier' of (1GateCircStr (c,k)), the carrier of (1GateCircStr (c,k)):] is Relation-like set
bool [: the carrier' of (1GateCircStr (c,k)), the carrier of (1GateCircStr (c,k)):] is set
the ResultSort of (1GateCircStr (c,k)) * the Sorts of (1GateCircuit (c,k)) is non empty Relation-like non-empty non empty-yielding the carrier' of (1GateCircStr (c,k)) -defined Function-like total set
the Charact of (1GateCircuit (c,k)) . [c,g] is Relation-like Function-like set
[([c,g] `1),( the Charact of (1GateCircuit (c,k)) . [c,g])] is pair non empty set
{([c,g] `1),( the Charact of (1GateCircuit (c,k)) . [c,g])} is non empty finite V95() set
{{([c,g] `1),( the Charact of (1GateCircuit (c,k)) . [c,g])},{([c,g] `1)}} is non empty finite V39() V95() set
x is set
the Charact of f . x is Relation-like Function-like set
the Charact of (1GateCircuit (c,k)) . x is Relation-like Function-like set
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
x1 is finite-yielding MSAlgebra over S
the Sorts of x1 is non empty Relation-like the carrier of S -defined Function-like total set
the carrier of S is non empty set
the_value_of the Sorts of x1 is set
the Charact of x1 is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding V34() ManySortedFunction of the Arity of S * ( the Sorts of x1 #), the ResultSort of S * the Sorts of x1
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding V34() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered FinSequenceSet of the carrier of S
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Sorts of x1 # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ( the Sorts of x1 #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of x1 is non empty Relation-like the carrier' of S -defined Function-like total set
MSAlgebra(# the Sorts of x1, the Charact of x1 #) is strict MSAlgebra over S
x3 is finite-yielding MSAlgebra over S
the Charact of x3 is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding V34() ManySortedFunction of the Arity of S * ( the Sorts of x3 #), the ResultSort of S * the Sorts of x3
the Sorts of x3 is non empty Relation-like the carrier of S -defined Function-like total set
the Sorts of x3 # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ( the Sorts of x3 #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S * the Sorts of x3 is non empty Relation-like the carrier' of S -defined Function-like total set
f is set
f `1 is set
the Charact of x3 . f is Relation-like Function-like set
[(f `1),( the Charact of x3 . f)] is pair non empty set
{(f `1),( the Charact of x3 . f)} is non empty finite V95() set
{(f `1)} is non empty finite V95() set
{{(f `1),( the Charact of x3 . f)},{(f `1)}} is non empty finite V39() V95() set
f is non-empty finite-yielding gate`2=den (X,S)
X is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
S is non empty finite V95() set
X -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
[:(X -tuples_on S),S:] is Relation-like set
bool [:(X -tuples_on S),S:] is set
x1 is Relation-like X -tuples_on S -defined S -valued Function-like V30(X -tuples_on S,S) Element of bool [:(X -tuples_on S),S:]
x2 is Relation-like NAT -defined Function-like finite V42(X) FinSequence-like FinSubsequence-like V95() set
1GateCircuit (x2,x1) is strict non-empty finite-yielding gate`2=den ( 1GateCircStr (x2,x1)) ( 1GateCircStr (x2,x1)) ( 1GateCircStr (x2,x1)) MSAlgebra over 1GateCircStr (x2,x1)
1GateCircStr (x2,x1) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
(X,S,x1,x2) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (S)
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
x1 is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
x2 is non-empty finite-yielding gate`2=den (X,S)
x3 is non-empty finite-yielding gate`2=den (X,x1)
the Sorts of x2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the carrier of S is non empty set
the Sorts of x3 is non empty Relation-like non-empty non empty-yielding the carrier of x1 -defined Function-like total set
the carrier of x1 is non empty set
the Charact of x2 is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding V34() ManySortedFunction of the Arity of S * ( the Sorts of x2 #), the ResultSort of S * the Sorts of x2
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding V34() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered FinSequenceSet of the carrier of S
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Sorts of x2 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ( the Sorts of x2 #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of x2 is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the Charact of x3 is non empty Relation-like the carrier' of x1 -defined Function-like total Function-yielding V34() ManySortedFunction of the Arity of x1 * ( the Sorts of x3 #), the ResultSort of x1 * the Sorts of x3
the carrier' of x1 is non empty set
the Arity of x1 is Relation-like the carrier' of x1 -defined the carrier of x1 * -valued Function-like V30( the carrier' of x1, the carrier of x1 * ) Function-yielding V34() Element of bool [: the carrier' of x1,( the carrier of x1 *):]
the carrier of x1 * is non empty functional FinSequence-membered FinSequenceSet of the carrier of x1
[: the carrier' of x1,( the carrier of x1 *):] is Relation-like set
bool [: the carrier' of x1,( the carrier of x1 *):] is set
the Sorts of x3 # is non empty Relation-like non-empty non empty-yielding the carrier of x1 * -defined Function-like total set
the Arity of x1 * ( the Sorts of x3 #) is non empty Relation-like non-empty non empty-yielding the carrier' of x1 -defined Function-like total set
the ResultSort of x1 is Relation-like the carrier' of x1 -defined the carrier of x1 -valued Function-like V30( the carrier' of x1, the carrier of x1) Element of bool [: the carrier' of x1, the carrier of x1:]
[: the carrier' of x1, the carrier of x1:] is Relation-like set
bool [: the carrier' of x1, the carrier of x1:] is set
the ResultSort of x1 * the Sorts of x3 is non empty Relation-like non-empty non empty-yielding the carrier' of x1 -defined Function-like total set
the_value_of the Sorts of x3 is set
proj1 the Sorts of x3 is non empty set
(proj1 the Sorts of x3) --> X is non empty Relation-like non-empty non empty-yielding proj1 the Sorts of x3 -defined {X} -valued Function-like constant total V30( proj1 the Sorts of x3,{X}) Element of bool [:(proj1 the Sorts of x3),{X}:]
{X} is non empty finite V39() V95() set
[:(proj1 the Sorts of x3),{X}:] is Relation-like set
bool [:(proj1 the Sorts of x3),{X}:] is set
the_value_of the Sorts of x2 is set
proj1 the Sorts of x2 is non empty set
(proj1 the Sorts of x2) --> X is non empty Relation-like non-empty non empty-yielding proj1 the Sorts of x2 -defined {X} -valued Function-like constant total V30( proj1 the Sorts of x2,{X}) Element of bool [:(proj1 the Sorts of x2),{X}:]
[:(proj1 the Sorts of x2),{X}:] is Relation-like set
bool [:(proj1 the Sorts of x2),{X}:] is set
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
x1 is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
S +* x1 is non empty non void V79() strict Circuit-like unsplit gate`1=arity ManySortedSign
the carrier of (S +* x1) is non empty set
the carrier of S is non empty set
the carrier of x1 is non empty set
the carrier of S \/ the carrier of x1 is non empty set
x2 is non-empty finite-yielding gate`2=den (X,S)
x3 is non-empty finite-yielding gate`2=den (X,x1)
x2 +* x3 is strict non-empty MSAlgebra over S +* x1
the Sorts of x2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
proj1 the Sorts of x2 is non empty set
the Sorts of x3 is non empty Relation-like non-empty non empty-yielding the carrier of x1 -defined Function-like total set
proj1 the Sorts of x3 is non empty set
the Sorts of (x2 +* x3) is non empty Relation-like non-empty non empty-yielding the carrier of (S +* x1) -defined Function-like total set
the Sorts of x2 +* the Sorts of x3 is non empty Relation-like the carrier of S \/ the carrier of x1 -defined Function-like total set
f is set
the Sorts of (x2 +* x3) . f is set
the Sorts of x2 . f is set
the Sorts of x3 . f is set
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
x1 is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
S +* x1 is non empty non void V79() strict Circuit-like unsplit gate`1=arity ManySortedSign
the carrier' of (S +* x1) is non empty set
the carrier' of S is non empty set
the carrier' of x1 is non empty set
the carrier' of S \/ the carrier' of x1 is non empty set
x2 is non-empty finite-yielding gate`2=den (X,S)
x3 is non-empty finite-yielding gate`2=den (X,x1)
x2 +* x3 is strict non-empty MSAlgebra over S +* x1
the Charact of x2 is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding V34() ManySortedFunction of the Arity of S * ( the Sorts of x2 #), the ResultSort of S * the Sorts of x2
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding V34() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S is non empty set
the carrier of S * is non empty functional FinSequence-membered FinSequenceSet of the carrier of S
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Sorts of x2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of x2 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ( the Sorts of x2 #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of x2 is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
proj1 the Charact of x2 is non empty set
the Charact of x3 is non empty Relation-like the carrier' of x1 -defined Function-like total Function-yielding V34() ManySortedFunction of the Arity of x1 * ( the Sorts of x3 #), the ResultSort of x1 * the Sorts of x3
the Arity of x1 is Relation-like the carrier' of x1 -defined the carrier of x1 * -valued Function-like V30( the carrier' of x1, the carrier of x1 * ) Function-yielding V34() Element of bool [: the carrier' of x1,( the carrier of x1 *):]
the carrier of x1 is non empty set
the carrier of x1 * is non empty functional FinSequence-membered FinSequenceSet of the carrier of x1
[: the carrier' of x1,( the carrier of x1 *):] is Relation-like set
bool [: the carrier' of x1,( the carrier of x1 *):] is set
the Sorts of x3 is non empty Relation-like non-empty non empty-yielding the carrier of x1 -defined Function-like total set
the Sorts of x3 # is non empty Relation-like non-empty non empty-yielding the carrier of x1 * -defined Function-like total set
the Arity of x1 * ( the Sorts of x3 #) is non empty Relation-like non-empty non empty-yielding the carrier' of x1 -defined Function-like total set
the ResultSort of x1 is Relation-like the carrier' of x1 -defined the carrier of x1 -valued Function-like V30( the carrier' of x1, the carrier of x1) Element of bool [: the carrier' of x1, the carrier of x1:]
[: the carrier' of x1, the carrier of x1:] is Relation-like set
bool [: the carrier' of x1, the carrier of x1:] is set
the ResultSort of x1 * the Sorts of x3 is non empty Relation-like non-empty non empty-yielding the carrier' of x1 -defined Function-like total set
proj1 the Charact of x3 is non empty set
the Charact of (x2 +* x3) is non empty Relation-like the carrier' of (S +* x1) -defined Function-like total Function-yielding V34() ManySortedFunction of the Arity of (S +* x1) * ( the Sorts of (x2 +* x3) #), the ResultSort of (S +* x1) * the Sorts of (x2 +* x3)
the Arity of (S +* x1) is Relation-like the carrier' of (S +* x1) -defined the carrier of (S +* x1) * -valued Function-like V30( the carrier' of (S +* x1), the carrier of (S +* x1) * ) Function-yielding V34() Element of bool [: the carrier' of (S +* x1),( the carrier of (S +* x1) *):]
the carrier of (S +* x1) is non empty set
the carrier of (S +* x1) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (S +* x1)
[: the carrier' of (S +* x1),( the carrier of (S +* x1) *):] is Relation-like set
bool [: the carrier' of (S +* x1),( the carrier of (S +* x1) *):] is set
the Sorts of (x2 +* x3) is non empty Relation-like non-empty non empty-yielding the carrier of (S +* x1) -defined Function-like total set
the Sorts of (x2 +* x3) # is non empty Relation-like non-empty non empty-yielding the carrier of (S +* x1) * -defined Function-like total set
the Arity of (S +* x1) * ( the Sorts of (x2 +* x3) #) is non empty Relation-like non-empty non empty-yielding the carrier' of (S +* x1) -defined Function-like total set
the ResultSort of (S +* x1) is Relation-like the carrier' of (S +* x1) -defined the carrier of (S +* x1) -valued Function-like V30( the carrier' of (S +* x1), the carrier of (S +* x1)) Element of bool [: the carrier' of (S +* x1), the carrier of (S +* x1):]
[: the carrier' of (S +* x1), the carrier of (S +* x1):] is Relation-like set
bool [: the carrier' of (S +* x1), the carrier of (S +* x1):] is set
the ResultSort of (S +* x1) * the Sorts of (x2 +* x3) is non empty Relation-like non-empty non empty-yielding the carrier' of (S +* x1) -defined Function-like total set
the Charact of x2 +* the Charact of x3 is non empty Relation-like the carrier' of S \/ the carrier' of x1 -defined Function-like total Function-yielding V34() ManySortedFunction of ( the Arity of S * ( the Sorts of x2 #)) +* ( the Arity of x1 * ( the Sorts of x3 #)),( the ResultSort of S * the Sorts of x2) +* ( the ResultSort of x1 * the Sorts of x3)
( the Arity of S * ( the Sorts of x2 #)) +* ( the Arity of x1 * ( the Sorts of x3 #)) is non empty Relation-like the carrier' of S \/ the carrier' of x1 -defined Function-like total set
( the ResultSort of S * the Sorts of x2) +* ( the ResultSort of x1 * the Sorts of x3) is non empty Relation-like the carrier' of S \/ the carrier' of x1 -defined Function-like total set
f is set
f `1 is set
the Charact of (x2 +* x3) . f is Relation-like Function-like set
[(f `1),( the Charact of (x2 +* x3) . f)] is pair non empty set
{(f `1),( the Charact of (x2 +* x3) . f)} is non empty finite V95() set
{(f `1)} is non empty finite V95() set
{{(f `1),( the Charact of (x2 +* x3) . f)},{(f `1)}} is non empty finite V39() V95() set
the Charact of x2 . f is Relation-like Function-like set
the Charact of x3 . f is Relation-like Function-like set
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
x1 is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
S +* x1 is non empty non void V79() strict Circuit-like unsplit gate`1=arity ManySortedSign
x2 is non-empty finite-yielding gate`2=den (X,S)
x3 is non-empty finite-yielding gate`2=den (X,x1)
x2 +* x3 is strict non-empty MSAlgebra over S +* x1
the Sorts of (x2 +* x3) is non empty Relation-like non-empty non empty-yielding the carrier of (S +* x1) -defined Function-like total set
the carrier of (S +* x1) is non empty set
the_value_of the Sorts of (x2 +* x3) is set
the Sorts of x2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the carrier of S is non empty set
proj1 the Sorts of x2 is non empty set
the_value_of the Sorts of x2 is set
(proj1 the Sorts of x2) --> X is non empty Relation-like non-empty non empty-yielding proj1 the Sorts of x2 -defined {X} -valued Function-like constant total V30( proj1 the Sorts of x2,{X}) Element of bool [:(proj1 the Sorts of x2),{X}:]
{X} is non empty finite V39() V95() set
[:(proj1 the Sorts of x2),{X}:] is Relation-like set
bool [:(proj1 the Sorts of x2),{X}:] is set
the Sorts of x3 is non empty Relation-like non-empty non empty-yielding the carrier of x1 -defined Function-like total set
the carrier of x1 is non empty set
the_value_of the Sorts of x3 is set
proj1 the Sorts of x3 is non empty set
(proj1 the Sorts of x3) --> X is non empty Relation-like non-empty non empty-yielding proj1 the Sorts of x3 -defined {X} -valued Function-like constant total V30( proj1 the Sorts of x3,{X}) Element of bool [:(proj1 the Sorts of x3),{X}:]
[:(proj1 the Sorts of x3),{X}:] is Relation-like set
bool [:(proj1 the Sorts of x3),{X}:] is set
f is finite-yielding MSAlgebra over S +* x1
the Sorts of f is non empty Relation-like the carrier of (S +* x1) -defined Function-like total set
the Sorts of x2 +* the Sorts of x3 is non empty Relation-like the carrier of S \/ the carrier of x1 -defined Function-like total set
the carrier of S \/ the carrier of x1 is non empty set
the Sorts of x2 \/ the Sorts of x3 is non empty Relation-like set
(proj1 the Sorts of x2) \/ (proj1 the Sorts of x3) is non empty set
[:((proj1 the Sorts of x2) \/ (proj1 the Sorts of x3)),{X}:] is Relation-like set
the carrier of S \/ (proj1 the Sorts of x3) is non empty set
( the carrier of S \/ (proj1 the Sorts of x3)) --> X is non empty Relation-like non-empty non empty-yielding the carrier of S \/ (proj1 the Sorts of x3) -defined {X} -valued Function-like constant total V30( the carrier of S \/ (proj1 the Sorts of x3),{X}) Element of bool [:( the carrier of S \/ (proj1 the Sorts of x3)),{X}:]
[:( the carrier of S \/ (proj1 the Sorts of x3)),{X}:] is Relation-like set
bool [:( the carrier of S \/ (proj1 the Sorts of x3)),{X}:] is set
X is non empty finite V79() ManySortedSign
S is non empty finite V79() ManySortedSign
X +* S is non empty V79() strict ManySortedSign
the carrier of (X +* S) is non empty set
the carrier of X is non empty finite V95() set
the carrier of S is non empty finite V95() set
the carrier of X \/ the carrier of S is non empty finite V95() set
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
x1 is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
S +* x1 is non empty non void V79() strict Circuit-like unsplit gate`1=arity ManySortedSign
x2 is finite-yielding MSAlgebra over x1
the Sorts of x2 is non empty Relation-like the carrier of x1 -defined Function-like total set
the carrier of x1 is non empty set
the_value_of the Sorts of x2 is set
f is finite-yielding MSAlgebra over S
the Sorts of f is non empty Relation-like the carrier of S -defined Function-like total set
the carrier of S is non empty set
the_value_of the Sorts of f is set
a is non-empty finite-yielding gate`2=den (X,S)
x3 is non-empty finite-yielding gate`2=den (X,x1)
a +* x3 is strict non-empty MSAlgebra over S +* x1
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
x1 is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
S +* x1 is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den ManySortedSign
x2 is finite-yielding MSAlgebra over x1
the Sorts of x2 is non empty Relation-like the carrier of x1 -defined Function-like total set
the carrier of x1 is non empty set
the_value_of the Sorts of x2 is set
f is finite-yielding MSAlgebra over S
the Sorts of f is non empty Relation-like the carrier of S -defined Function-like total set
the carrier of S is non empty set
the_value_of the Sorts of f is set
a is non-empty finite-yielding gate`2=den (X,S)
x3 is non-empty finite-yielding gate`2=den (X,x1)
a +* x3 is strict non-empty MSAlgebra over S +* x1
b is finite-yielding MSAlgebra over S +* x1
the Sorts of b is non empty Relation-like the carrier of (S +* x1) -defined Function-like total set
the carrier of (S +* x1) is non empty set
the_value_of the Sorts of b is set
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
x1 is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
x2 is non-empty finite-yielding gate`2=den (X,S)
x3 is non-empty finite-yielding gate`2=den (X,x1)
x2 +* x3 is strict non-empty MSAlgebra over S +* x1
S +* x1 is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den ManySortedSign
(X,S,x1) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (X)
the Sorts of (x2 +* x3) is non empty Relation-like non-empty non empty-yielding the carrier of (S +* x1) -defined Function-like total set
the carrier of (S +* x1) is non empty set
the_value_of the Sorts of (x2 +* x3) is set
X is set
the_rank_of X is V17() V18() V19() set
S is set
[X,S] is pair non empty set
{X,S} is non empty finite V95() set
{X} is non empty finite V95() set
{{X,S},{X}} is non empty finite V39() V95() set
the_rank_of [X,S] is V17() V18() V19() set
the_rank_of S is V17() V18() V19() set
the_rank_of {X} is V17() V18() V19() set
the_rank_of {{X,S},{X}} is V17() V18() V19() set
the_rank_of {X,S} is V17() V18() V19() set
X is non empty finite non void V79() Circuit-like unsplit gate`1=arity gate`2=den ManySortedSign
the carrier' of X is non empty set
the carrier of X is non empty finite V95() set
S is Relation-like set
x1 is non-empty finite-yielding MSAlgebra over X
x2 is set
field S is set
proj1 S is set
proj2 S is set
(proj1 S) \/ (proj2 S) is set
the Element of x2 is Element of x2
a is set
f is set
the_rank_of f is V17() V18() V19() set
b is set
f is set
the_rank_of the Element of x2 is V17() V18() V19() set
inf f is V17() V18() V19() set
a is set
the_rank_of a is V17() V18() V19() set
b is set
[a,b] is pair non empty set
{a,b} is non empty finite V95() set
{a} is non empty finite V95() set
{{a,b},{a}} is non empty finite V39() V95() set
the_rank_of b is V17() V18() V19() set
a `1 is set
the Charact of x1 is non empty Relation-like the carrier' of X -defined Function-like total Function-yielding V34() ManySortedFunction of the Arity of X * ( the Sorts of x1 #), the ResultSort of X * the Sorts of x1
the Arity of X is Relation-like the carrier' of X -defined the carrier of X * -valued Function-like V30( the carrier' of X, the carrier of X * ) Function-yielding V34() Element of bool [: the carrier' of X,( the carrier of X *):]
the carrier of X * is non empty functional FinSequence-membered FinSequenceSet of the carrier of X
[: the carrier' of X,( the carrier of X *):] is Relation-like set
bool [: the carrier' of X,( the carrier of X *):] is set
the Sorts of x1 is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
the Sorts of x1 # is non empty Relation-like non-empty non empty-yielding the carrier of X * -defined Function-like total set
the Arity of X * ( the Sorts of x1 #) is non empty Relation-like non-empty non empty-yielding the carrier' of X -defined Function-like total set
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
the ResultSort of X * the Sorts of x1 is non empty Relation-like non-empty non empty-yielding the carrier' of X -defined Function-like total set
the Charact of x1 . a is Relation-like Function-like set
[(a `1),( the Charact of x1 . a)] is pair non empty set
{(a `1),( the Charact of x1 . a)} is non empty finite V95() set
{(a `1)} is non empty finite V95() set
{{(a `1),( the Charact of x1 . a)},{(a `1)}} is non empty finite V39() V95() set
the_rank_of (a `1) is V17() V18() V19() set
proj2 (a `1) is set
c is set
[c,b] is pair non empty set
{c,b} is non empty finite V95() set
{c} is non empty finite V95() set
{{c,b},{c}} is non empty finite V39() V95() set
the_rank_of [c,b] is V17() V18() V19() set
the Sorts of x1 is non empty Relation-like non-empty non empty-yielding the carrier of X -defined Function-like total set
K246( the Sorts of x1) is non empty functional V93() V94() set
proj2 S is set
x2 is set
x3 is set
[x3,x2] is pair non empty set
{x3,x2} is non empty finite V95() set
{x3} is non empty finite V95() set
{{x3,x2},{x3}} is non empty finite V39() V95() set
field S is set
proj1 S is set
(proj1 S) \/ (proj2 S) is set
x2 is set
[x2,x2] is pair non empty set
{x2,x2} is non empty finite V95() set
{x2} is non empty finite V95() set
{{x2,x2},{x2}} is non empty finite V39() V95() set
x2 is set
x3 is set
[x2,x3] is pair non empty set
{x2,x3} is non empty finite V95() set
{x2} is non empty finite V95() set
{{x2,x3},{x2}} is non empty finite V39() V95() set
the carrier of X \/ the carrier of X is non empty finite V95() set
x2 is set
x3 is set
f is set
f is set
[x2,f] is pair non empty set
{x2,f} is non empty finite V95() set
{x2} is non empty finite V95() set
{{x2,f},{x2}} is non empty finite V39() V95() set
a is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
f is Relation-like Function-like set
proj1 f is set
proj2 f is set
a is set
b is set
f . b is set
c is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
the Element of x3 is Element of x3
[x2, the Element of x3] is pair non empty set
{x2, the Element of x3} is non empty finite V95() set
{x2} is non empty finite V95() set
{{x2, the Element of x3},{x2}} is non empty finite V39() V95() set
a is non empty finite V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
sup a is non pair V17() V18() V19() V23() V47() ext-real V153() set
g is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
g + 1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
k is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
a1 is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
Following (a1,k) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(Following (a1,k)) . x2 is set
x is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (a1,x) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(Following (a1,x)) . x2 is set
k is non pair V17() V18() V19() V23() V47() ext-real V153() set
k + k is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
c is Element of the carrier' of X
the_arity_of c is Relation-like NAT -defined the carrier of X -valued Function-like finite FinSequence-like FinSubsequence-like V95() Element of the carrier of X *
the carrier of X * is non empty functional FinSequence-membered FinSequenceSet of the carrier of X
proj2 (the_arity_of c) is finite V95() set
Following (a1,g) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
x is set
the Arity of X is Relation-like the carrier' of X -defined the carrier of X * -valued Function-like V30( the carrier' of X, the carrier of X * ) Function-yielding V34() Element of bool [: the carrier' of X,( the carrier of X *):]
[: the carrier' of X,( the carrier of X *):] is Relation-like set
bool [: the carrier' of X,( the carrier of X *):] is set
the Arity of X . c is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V95() Element of the carrier of X *
c `2 is Relation-like Function-like set
[( the Arity of X . c),(c `2)] is pair non empty set
{( the Arity of X . c),(c `2)} is non empty functional finite V95() set
{( the Arity of X . c)} is non empty functional finite V39() V93() V95() set
{{( the Arity of X . c),(c `2)},{( the Arity of X . c)}} is non empty finite V39() V95() set
[(the_arity_of c),(c `2)] is pair non empty set
{(the_arity_of c),(c `2)} is non empty functional finite V95() set
{(the_arity_of c)} is non empty functional finite V39() V93() V95() set
{{(the_arity_of c),(c `2)},{(the_arity_of c)}} is non empty finite V39() V95() set
the_rank_of x is V17() V18() V19() set
the_rank_of c is V17() V18() V19() set
x2 `1 is set
proj2 (x2 `1) is set
[c,x] is pair non empty set
{c,x} is non empty finite V95() set
{c} is non empty finite V95() set
{{c,x},{c}} is non empty finite V39() V95() set
f . x is set
l is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
k is non pair V17() V18() V19() V23() V47() ext-real V153() set
g + k is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following ((Following (a1,g)),k) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(Following ((Following (a1,g)),k)) . x is set
Following (a1,(g + k)) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(Following (a1,(g + k))) . x is set
Following (a1,l) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(Following (a1,l)) . x is set
(Following (a1,g)) . x is set
the_result_sort_of c is Element of the carrier of X
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
the ResultSort of X . c is Element of the carrier of X
Following (Following (a1,g)) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
k is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following ((Following (a1,k)),k) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(Following ((Following (a1,k)),k)) . x2 is set
a is non pair non empty V17() V18() V19() V23() V47() ext-real positive V140() V141() V142() V143() V144() V145() V147() V149() V153() Element of NAT
b is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
Following (b,a) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(Following (b,a)) . x2 is set
c is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (b,c) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(Following (b,c)) . x2 is set
g is non pair V17() V18() V19() V23() V47() ext-real V153() set
a + g is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
InnerVertices X is finite V95() Element of bool the carrier of X
bool the carrier of X is finite V39() V95() set
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
K488( the carrier of X, the ResultSort of X) is finite V95() Element of bool the carrier of X
id the carrier' of X is non empty Relation-like the carrier' of X -defined the carrier' of X -valued Function-like one-to-one total Element of bool [: the carrier' of X, the carrier' of X:]
[: the carrier' of X, the carrier' of X:] is Relation-like set
bool [: the carrier' of X, the carrier' of X:] is set
proj2 (id the carrier' of X) is non empty set
a1 is Element of the carrier' of X
the_arity_of a1 is Relation-like NAT -defined the carrier of X -valued Function-like finite FinSequence-like FinSubsequence-like V95() Element of the carrier of X *
the carrier of X * is non empty functional FinSequence-membered FinSequenceSet of the carrier of X
proj2 (the_arity_of a1) is finite V95() set
x is set
the Arity of X is Relation-like the carrier' of X -defined the carrier of X * -valued Function-like V30( the carrier' of X, the carrier of X * ) Function-yielding V34() Element of bool [: the carrier' of X,( the carrier of X *):]
[: the carrier' of X,( the carrier of X *):] is Relation-like set
bool [: the carrier' of X,( the carrier of X *):] is set
the Arity of X . a1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V95() Element of the carrier of X *
a1 `2 is Relation-like Function-like set
[( the Arity of X . a1),(a1 `2)] is pair non empty set
{( the Arity of X . a1),(a1 `2)} is non empty functional finite V95() set
{( the Arity of X . a1)} is non empty functional finite V39() V93() V95() set
{{( the Arity of X . a1),(a1 `2)},{( the Arity of X . a1)}} is non empty finite V39() V95() set
[(the_arity_of a1),(a1 `2)] is pair non empty set
{(the_arity_of a1),(a1 `2)} is non empty functional finite V95() set
{(the_arity_of a1)} is non empty functional finite V39() V93() V95() set
{{(the_arity_of a1),(a1 `2)},{(the_arity_of a1)}} is non empty finite V39() V95() set
the_rank_of x is V17() V18() V19() set
the_rank_of a1 is V17() V18() V19() set
x2 `1 is set
proj2 (x2 `1) is set
[a1,x] is pair non empty set
{a1,x} is non empty finite V95() set
{a1} is non empty finite V95() set
{{a1,x},{a1}} is non empty finite V39() V95() set
Following b is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
the_result_sort_of a1 is Element of the carrier of X
the ResultSort of X . a1 is Element of the carrier of X
k is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following ((Following (b,a)),k) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(Following ((Following (b,a)),k)) . x2 is set
InputVertices X is finite V95() Element of bool the carrier of X
the carrier of X \ K488( the carrier of X, the ResultSort of X) is finite V95() Element of bool the carrier of X
b . x2 is set
(InputVertices X) \/ (InnerVertices X) is finite V95() Element of bool the carrier of X
x2 is set
x3 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
x2 is Relation-like Function-like set
proj1 x2 is set
proj2 x2 is set
x3 is set
f is set
x2 . f is set
a is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
x3 is non empty finite V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
sup x3 is non pair V17() V18() V19() V23() V47() ext-real V153() set
f is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
a is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
Following (a,f) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
b is set
x2 . b is set
c is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
f + 1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
(Following (a,f)) . b is set
Following (a,c) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(Following (a,c)) . b is set
Following (a,(f + 1)) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(Following (a,(f + 1))) . b is set
Following (Following (a,f)) is non empty Relation-like the carrier of X -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(Following (Following (a,f))) . b is set
proj1 (Following (a,f)) is non empty set
proj1 (Following (Following (a,f))) is non empty set
X is non empty finite V95() set
S is non empty finite non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
x1 is non-empty finite-yielding gate`2=den (X,S)
F₁() is non empty set
1 -tuples_on F₁() is non empty functional FinSequence-membered FinSequenceSet of F₁()
[:(1 -tuples_on F₁()),F₁():] is Relation-like set
bool [:(1 -tuples_on F₁()),F₁():] is set
X is Relation-like 1 -tuples_on F₁() -defined F₁() -valued Function-like V30(1 -tuples_on F₁(),F₁()) Element of bool [:(1 -tuples_on F₁()),F₁():]
x1 is Element of F₁()
<*x1*> is non empty Relation-like NAT -defined F₁() -valued Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() FinSequence of F₁()
S is Relation-like 1 -tuples_on F₁() -defined F₁() -valued Function-like V30(1 -tuples_on F₁(),F₁()) Element of bool [:(1 -tuples_on F₁()),F₁():]
S . <*x1*> is set
x2 is Relation-like NAT -defined F₁() -valued Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() Element of 1 -tuples_on F₁()
x2 . 1 is set
F₂((x2 . 1)) is Element of F₁()
F₂(x1) is Element of F₁()
S is Relation-like 1 -tuples_on F₁() -defined F₁() -valued Function-like V30(1 -tuples_on F₁(),F₁()) Element of bool [:(1 -tuples_on F₁()),F₁():]
x1 is Relation-like 1 -tuples_on F₁() -defined F₁() -valued Function-like V30(1 -tuples_on F₁(),F₁()) Element of bool [:(1 -tuples_on F₁()),F₁():]
x2 is Relation-like NAT -defined F₁() -valued Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() Element of 1 -tuples_on F₁()
x3 is Element of F₁()
<*x3*> is non empty Relation-like NAT -defined F₁() -valued Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() FinSequence of F₁()
S . x2 is Element of F₁()
F₂(x3) is Element of F₁()
x1 . x2 is Element of F₁()
F₁() is non empty set
2 -tuples_on F₁() is non empty functional FinSequence-membered FinSequenceSet of F₁()
[:(2 -tuples_on F₁()),F₁():] is Relation-like set
bool [:(2 -tuples_on F₁()),F₁():] is set
X is Relation-like 2 -tuples_on F₁() -defined F₁() -valued Function-like V30(2 -tuples_on F₁(),F₁()) Element of bool [:(2 -tuples_on F₁()),F₁():]
x1 is Element of F₁()
x2 is Element of F₁()
<*x1,x2*> is non empty Relation-like NAT -defined F₁() -valued Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() FinSequence of F₁()
S is Relation-like 2 -tuples_on F₁() -defined F₁() -valued Function-like V30(2 -tuples_on F₁(),F₁()) Element of bool [:(2 -tuples_on F₁()),F₁():]
S . <*x1,x2*> is set
x3 is Relation-like NAT -defined F₁() -valued Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() Element of 2 -tuples_on F₁()
x3 . 1 is set
x3 . 2 is set
F₂((x3 . 1),(x3 . 2)) is Element of F₁()
F₂(x1,(x3 . 2)) is Element of F₁()
F₂(x1,x2) is Element of F₁()
S is Relation-like 2 -tuples_on F₁() -defined F₁() -valued Function-like V30(2 -tuples_on F₁(),F₁()) Element of bool [:(2 -tuples_on F₁()),F₁():]
x1 is Relation-like 2 -tuples_on F₁() -defined F₁() -valued Function-like V30(2 -tuples_on F₁(),F₁()) Element of bool [:(2 -tuples_on F₁()),F₁():]
x2 is Relation-like NAT -defined F₁() -valued Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() Element of 2 -tuples_on F₁()
x3 is Element of F₁()
f is Element of F₁()
<*x3,f*> is non empty Relation-like NAT -defined F₁() -valued Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() FinSequence of F₁()
S . x2 is Element of F₁()
F₂(x3,f) is Element of F₁()
x1 . x2 is Element of F₁()
F₁() is non empty set
3 -tuples_on F₁() is non empty functional FinSequence-membered FinSequenceSet of F₁()
[:(3 -tuples_on F₁()),F₁():] is Relation-like set
bool [:(3 -tuples_on F₁()),F₁():] is set
X is Relation-like 3 -tuples_on F₁() -defined F₁() -valued Function-like V30(3 -tuples_on F₁(),F₁()) Element of bool [:(3 -tuples_on F₁()),F₁():]
x1 is Element of F₁()
x2 is Element of F₁()
x3 is Element of F₁()
<*x1,x2,x3*> is non empty Relation-like NAT -defined F₁() -valued Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() FinSequence of F₁()
S is Relation-like 3 -tuples_on F₁() -defined F₁() -valued Function-like V30(3 -tuples_on F₁(),F₁()) Element of bool [:(3 -tuples_on F₁()),F₁():]
S . <*x1,x2,x3*> is set
f is Relation-like NAT -defined F₁() -valued Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() Element of 3 -tuples_on F₁()
f . 1 is set
f . 2 is set
f . 3 is set
F₂((f . 1),(f . 2),(f . 3)) is Element of F₁()
F₂(x1,(f . 2),(f . 3)) is Element of F₁()
F₂(x1,x2,(f . 3)) is Element of F₁()
F₂(x1,x2,x3) is Element of F₁()
S is Relation-like 3 -tuples_on F₁() -defined F₁() -valued Function-like V30(3 -tuples_on F₁(),F₁()) Element of bool [:(3 -tuples_on F₁()),F₁():]
x1 is Relation-like 3 -tuples_on F₁() -defined F₁() -valued Function-like V30(3 -tuples_on F₁(),F₁()) Element of bool [:(3 -tuples_on F₁()),F₁():]
x2 is Relation-like NAT -defined F₁() -valued Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() Element of 3 -tuples_on F₁()
x3 is Element of F₁()
f is Element of F₁()
a is Element of F₁()
<*x3,f,a*> is non empty Relation-like NAT -defined F₁() -valued Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() FinSequence of F₁()
S . x2 is Element of F₁()
F₂(x3,f,a) is Element of F₁()
x1 . x2 is Element of F₁()
X is Relation-like Function-like set
proj1 X is set
S is set
x1 is set
x2 is set
x3 is set
<*S,x1,x2,x3*> is non empty Relation-like NAT -defined Function-like finite V42(4) FinSequence-like FinSubsequence-like V95() set
<*S,x1,x2,x3*> * X is Relation-like NAT -defined Function-like finite V95() set
X . S is set
X . x1 is set
X . x2 is set
X . x3 is set
<*(X . S),(X . x1),(X . x2),(X . x3)*> is non empty Relation-like NAT -defined Function-like finite V42(4) FinSequence-like FinSubsequence-like V95() set
proj2 X is set
proj2 <*S,x1,x2,x3*> is non empty finite V95() set
f is non empty set
b is set
{S,x1,x2,x3} is finite V95() set
a is non empty set
[:f,a:] is Relation-like set
bool [:f,a:] is set
b is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like V95() FinSequence of f
c is Relation-like f -defined a -valued Function-like V30(f,a) Element of bool [:f,a:]
c * b is Relation-like NAT -defined a -valued Function-like finite FinSequence-like FinSubsequence-like V95() FinSequence of a
dom (c * b) is finite V95() V140() V141() V142() V143() V144() V145() V149() V150() V151() Element of bool NAT
dom b is finite V95() V140() V141() V142() V143() V144() V145() V149() V150() V151() Element of bool NAT
g is non pair V17() V18() V19() V23() V47() ext-real V153() set
b . g is set
(c * b) . g is set
c . S is set
<*(X . S),(X . x1),(X . x2),(X . x3)*> . g is set
b . g is set
(c * b) . g is set
c . x1 is set
<*(X . S),(X . x1),(X . x2),(X . x3)*> . g is set
b . g is set
(c * b) . g is set
c . x2 is set
<*(X . S),(X . x1),(X . x2),(X . x3)*> . g is set
b . g is set
(c * b) . g is set
c . x3 is set
<*(X . S),(X . x1),(X . x2),(X . x3)*> . g is set
dom <*(X . S),(X . x1),(X . x2),(X . x3)*> is non empty finite V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
X is Relation-like Function-like set
proj1 X is set
S is set
x1 is set
x2 is set
x3 is set
f is set
<*S,x1,x2,x3,f*> is non empty Relation-like NAT -defined Function-like finite V42(5) FinSequence-like FinSubsequence-like V95() set
<*S,x1,x2,x3,f*> * X is Relation-like NAT -defined Function-like finite V95() set
X . S is set
X . x1 is set
X . x2 is set
X . x3 is set
X . f is set
<*(X . S),(X . x1),(X . x2),(X . x3),(X . f)*> is non empty Relation-like NAT -defined Function-like finite V42(5) FinSequence-like FinSubsequence-like V95() set
proj2 X is set
proj2 <*S,x1,x2,x3,f*> is non empty finite V95() set
a is non empty set
c is set
{S,x1,x2,x3,f} is finite V95() set
b is non empty set
[:a,b:] is Relation-like set
bool [:a,b:] is set
c is Relation-like NAT -defined a -valued Function-like finite FinSequence-like FinSubsequence-like V95() FinSequence of a
g is Relation-like a -defined b -valued Function-like V30(a,b) Element of bool [:a,b:]
g * c is Relation-like NAT -defined b -valued Function-like finite FinSequence-like FinSubsequence-like V95() FinSequence of b
dom (g * c) is finite V95() V140() V141() V142() V143() V144() V145() V149() V150() V151() Element of bool NAT
dom c is finite V95() V140() V141() V142() V143() V144() V145() V149() V150() V151() Element of bool NAT
k is non pair V17() V18() V19() V23() V47() ext-real V153() set
c . k is set
(g * c) . k is set
g . S is set
<*(X . S),(X . x1),(X . x2),(X . x3),(X . f)*> . k is set
c . k is set
(g * c) . k is set
g . x1 is set
<*(X . S),(X . x1),(X . x2),(X . x3),(X . f)*> . k is set
c . k is set
(g * c) . k is set
g . x2 is set
<*(X . S),(X . x1),(X . x2),(X . x3),(X . f)*> . k is set
c . k is set
(g * c) . k is set
g . x3 is set
<*(X . S),(X . x1),(X . x2),(X . x3),(X . f)*> . k is set
c . k is set
(g * c) . k is set
g . f is set
<*(X . S),(X . x1),(X . x2),(X . x3),(X . f)*> . k is set
dom <*(X . S),(X . x1),(X . x2),(X . x3),(X . f)*> is non empty finite V95() V140() V141() V142() V143() V144() V145() V147() V148() V149() V150() V151() Element of bool NAT
F₂() is non empty finite V95() set
1 -tuples_on F₂() is non empty functional FinSequence-membered FinSequenceSet of F₂()
[:(1 -tuples_on F₂()),F₂():] is Relation-like set
bool [:(1 -tuples_on F₂()),F₂():] is set
F₄() is Relation-like 1 -tuples_on F₂() -defined F₂() -valued Function-like V30(1 -tuples_on F₂(),F₂()) Element of bool [:(1 -tuples_on F₂()),F₂():]
F₁() is set
<*F₁()*> is non empty Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (<*F₁()*>,F₄()) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
the carrier of (1GateCircStr (<*F₁()*>,F₄())) is non empty finite V95() set
(1,F₂(),F₄(),<*F₁()*>) is strict strict non-empty non-empty finite-yielding finite-yielding gate`2=den gate`2=den ( 1GateCircStr (<*F₁()*>,F₄())) ((1,F₂(),F₄(),<*F₁()*>)) ( 1GateCircStr (<*F₁()*>,F₄())) (F₂(),(1,F₂(),F₄(),<*F₁()*>))
(1,F₂(),F₄(),<*F₁()*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (F₂())
the Sorts of (1,F₂(),F₄(),<*F₁()*>) is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (<*F₁()*>,F₄())) -defined Function-like total set
K246( the Sorts of (1,F₂(),F₄(),<*F₁()*>)) is non empty functional V93() V94() set
((1,F₂(),F₄(),<*F₁()*>)) is pair non empty Element of the carrier of (1,F₂(),F₄(),<*F₁()*>)
the carrier of (1,F₂(),F₄(),<*F₁()*>) is non empty finite V95() set
the carrier' of (1,F₂(),F₄(),<*F₁()*>) is non empty set
union the carrier' of (1,F₂(),F₄(),<*F₁()*>) is set
S is non empty Relation-like the carrier of (1GateCircStr (<*F₁()*>,F₄())) -defined Function-like the Sorts of (1,F₂(),F₄(),<*F₁()*>) -compatible total Element of K246( the Sorts of (1,F₂(),F₄(),<*F₁()*>))
S . F₁() is set
((1GateCircStr (<*F₁()*>,F₄())),(1,F₂(),F₄(),<*F₁()*>),S) is non empty Relation-like the carrier of (1GateCircStr (<*F₁()*>,F₄())) -defined Function-like the Sorts of (1,F₂(),F₄(),<*F₁()*>) -compatible total Element of K246( the Sorts of (1,F₂(),F₄(),<*F₁()*>))
((1GateCircStr (<*F₁()*>,F₄())),(1,F₂(),F₄(),<*F₁()*>),S) . ((1,F₂(),F₄(),<*F₁()*>)) is set
proj1 S is non empty set
proj2 <*F₁()*> is non empty finite V95() set
[<*F₁()*>,F₄()] is pair non empty set
{<*F₁()*>,F₄()} is non empty functional finite V95() set
{<*F₁()*>} is non empty functional finite V39() V93() V95() set
{{<*F₁()*>,F₄()},{<*F₁()*>}} is non empty finite V39() V95() set
{[<*F₁()*>,F₄()]} is non empty Relation-like Function-like finite V95() set
(proj2 <*F₁()*>) \/ {[<*F₁()*>,F₄()]} is non empty finite V95() set
{F₁()} is non empty finite V95() set
{F₁()} \/ {[<*F₁()*>,F₄()]} is non empty finite V95() set
{F₁(),[<*F₁()*>,F₄()]} is non empty finite V95() set
x1 is Element of F₂()
F₃(x1) is Element of F₂()
<*F₁()*> * S is Relation-like NAT -defined Function-like finite V95() set
<*x1*> is non empty Relation-like NAT -defined F₂() -valued Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() FinSequence of F₂()
Following S is non empty Relation-like the carrier of (1GateCircStr (<*F₁()*>,F₄())) -defined Function-like the Sorts of (1,F₂(),F₄(),<*F₁()*>) -compatible total Element of K246( the Sorts of (1,F₂(),F₄(),<*F₁()*>))
(Following S) . ((1,F₂(),F₄(),<*F₁()*>)) is set
(Following S) . [<*F₁()*>,F₄()] is set
F₄() . (<*F₁()*> * S) is set
F₃() is non empty finite V95() set
2 -tuples_on F₃() is non empty functional FinSequence-membered FinSequenceSet of F₃()
[:(2 -tuples_on F₃()),F₃():] is Relation-like set
bool [:(2 -tuples_on F₃()),F₃():] is set
F₅() is Relation-like 2 -tuples_on F₃() -defined F₃() -valued Function-like V30(2 -tuples_on F₃(),F₃()) Element of bool [:(2 -tuples_on F₃()),F₃():]
F₁() is set
F₂() is set
<*F₁(),F₂()*> is non empty Relation-like NAT -defined Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (<*F₁(),F₂()*>,F₅()) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
the carrier of (1GateCircStr (<*F₁(),F₂()*>,F₅())) is non empty finite V95() set
(2,F₃(),F₅(),<*F₁(),F₂()*>) is strict strict non-empty non-empty finite-yielding finite-yielding gate`2=den gate`2=den ( 1GateCircStr (<*F₁(),F₂()*>,F₅())) ((2,F₃(),F₅(),<*F₁(),F₂()*>)) ( 1GateCircStr (<*F₁(),F₂()*>,F₅())) (F₃(),(2,F₃(),F₅(),<*F₁(),F₂()*>))
(2,F₃(),F₅(),<*F₁(),F₂()*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (F₃())
the Sorts of (2,F₃(),F₅(),<*F₁(),F₂()*>) is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (<*F₁(),F₂()*>,F₅())) -defined Function-like total set
K246( the Sorts of (2,F₃(),F₅(),<*F₁(),F₂()*>)) is non empty functional V93() V94() set
((2,F₃(),F₅(),<*F₁(),F₂()*>)) is pair non empty Element of the carrier of (2,F₃(),F₅(),<*F₁(),F₂()*>)
the carrier of (2,F₃(),F₅(),<*F₁(),F₂()*>) is non empty finite V95() set
the carrier' of (2,F₃(),F₅(),<*F₁(),F₂()*>) is non empty set
union the carrier' of (2,F₃(),F₅(),<*F₁(),F₂()*>) is set
S is non empty Relation-like the carrier of (1GateCircStr (<*F₁(),F₂()*>,F₅())) -defined Function-like the Sorts of (2,F₃(),F₅(),<*F₁(),F₂()*>) -compatible total Element of K246( the Sorts of (2,F₃(),F₅(),<*F₁(),F₂()*>))
S . F₁() is set
S . F₂() is set
((1GateCircStr (<*F₁(),F₂()*>,F₅())),(2,F₃(),F₅(),<*F₁(),F₂()*>),S) is non empty Relation-like the carrier of (1GateCircStr (<*F₁(),F₂()*>,F₅())) -defined Function-like the Sorts of (2,F₃(),F₅(),<*F₁(),F₂()*>) -compatible total Element of K246( the Sorts of (2,F₃(),F₅(),<*F₁(),F₂()*>))
((1GateCircStr (<*F₁(),F₂()*>,F₅())),(2,F₃(),F₅(),<*F₁(),F₂()*>),S) . ((2,F₃(),F₅(),<*F₁(),F₂()*>)) is set
proj1 S is non empty set
proj2 <*F₁(),F₂()*> is non empty finite V95() set
[<*F₁(),F₂()*>,F₅()] is pair non empty set
{<*F₁(),F₂()*>,F₅()} is non empty functional finite V95() set
{<*F₁(),F₂()*>} is non empty functional finite V39() V93() V95() set
{{<*F₁(),F₂()*>,F₅()},{<*F₁(),F₂()*>}} is non empty finite V39() V95() set
{[<*F₁(),F₂()*>,F₅()]} is non empty Relation-like Function-like finite V95() set
(proj2 <*F₁(),F₂()*>) \/ {[<*F₁(),F₂()*>,F₅()]} is non empty finite V95() set
{F₁(),F₂()} is non empty finite V95() set
{F₁(),F₂()} \/ {[<*F₁(),F₂()*>,F₅()]} is non empty finite V95() set
{F₁(),F₂(),[<*F₁(),F₂()*>,F₅()]} is finite V95() set
x1 is Element of F₃()
x2 is Element of F₃()
F₄(x1,x2) is Element of F₃()
<*F₁(),F₂()*> * S is Relation-like NAT -defined Function-like finite V95() set
<*x1,x2*> is non empty Relation-like NAT -defined F₃() -valued Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() FinSequence of F₃()
Following S is non empty Relation-like the carrier of (1GateCircStr (<*F₁(),F₂()*>,F₅())) -defined Function-like the Sorts of (2,F₃(),F₅(),<*F₁(),F₂()*>) -compatible total Element of K246( the Sorts of (2,F₃(),F₅(),<*F₁(),F₂()*>))
(Following S) . ((2,F₃(),F₅(),<*F₁(),F₂()*>)) is set
(Following S) . [<*F₁(),F₂()*>,F₅()] is set
F₅() . (<*F₁(),F₂()*> * S) is set
F₄() is non empty finite V95() set
3 -tuples_on F₄() is non empty functional FinSequence-membered FinSequenceSet of F₄()
[:(3 -tuples_on F₄()),F₄():] is Relation-like set
bool [:(3 -tuples_on F₄()),F₄():] is set
F₆() is Relation-like 3 -tuples_on F₄() -defined F₄() -valued Function-like V30(3 -tuples_on F₄(),F₄()) Element of bool [:(3 -tuples_on F₄()),F₄():]
F₁() is set
F₂() is set
F₃() is set
<*F₁(),F₂(),F₃()*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (<*F₁(),F₂(),F₃()*>,F₆()) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
the carrier of (1GateCircStr (<*F₁(),F₂(),F₃()*>,F₆())) is non empty finite V95() set
(3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>) is strict strict non-empty non-empty finite-yielding finite-yielding gate`2=den gate`2=den ( 1GateCircStr (<*F₁(),F₂(),F₃()*>,F₆())) ((3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>)) ( 1GateCircStr (<*F₁(),F₂(),F₃()*>,F₆())) (F₄(),(3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>))
(3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (F₄())
the Sorts of (3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>) is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (<*F₁(),F₂(),F₃()*>,F₆())) -defined Function-like total set
K246( the Sorts of (3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>)) is non empty functional V93() V94() set
((3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>)) is pair non empty Element of the carrier of (3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>)
the carrier of (3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>) is non empty finite V95() set
the carrier' of (3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>) is non empty set
union the carrier' of (3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>) is set
S is non empty Relation-like the carrier of (1GateCircStr (<*F₁(),F₂(),F₃()*>,F₆())) -defined Function-like the Sorts of (3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>) -compatible total Element of K246( the Sorts of (3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>))
S . F₁() is set
S . F₂() is set
S . F₃() is set
((1GateCircStr (<*F₁(),F₂(),F₃()*>,F₆())),(3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>),S) is non empty Relation-like the carrier of (1GateCircStr (<*F₁(),F₂(),F₃()*>,F₆())) -defined Function-like the Sorts of (3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>) -compatible total Element of K246( the Sorts of (3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>))
((1GateCircStr (<*F₁(),F₂(),F₃()*>,F₆())),(3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>),S) . ((3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>)) is set
proj1 S is non empty set
proj2 <*F₁(),F₂(),F₃()*> is non empty finite V95() set
[<*F₁(),F₂(),F₃()*>,F₆()] is pair non empty set
{<*F₁(),F₂(),F₃()*>,F₆()} is non empty functional finite V95() set
{<*F₁(),F₂(),F₃()*>} is non empty functional finite V39() V93() V95() set
{{<*F₁(),F₂(),F₃()*>,F₆()},{<*F₁(),F₂(),F₃()*>}} is non empty finite V39() V95() set
{[<*F₁(),F₂(),F₃()*>,F₆()]} is non empty Relation-like Function-like finite V95() set
(proj2 <*F₁(),F₂(),F₃()*>) \/ {[<*F₁(),F₂(),F₃()*>,F₆()]} is non empty finite V95() set
{F₁(),F₂(),F₃()} is finite V95() set
{F₁(),F₂(),F₃()} \/ {[<*F₁(),F₂(),F₃()*>,F₆()]} is non empty finite V95() set
{F₁(),F₂(),F₃(),[<*F₁(),F₂(),F₃()*>,F₆()]} is finite V95() set
x1 is Element of F₄()
x2 is Element of F₄()
x3 is Element of F₄()
F₅(x1,x2,x3) is Element of F₄()
<*F₁(),F₂(),F₃()*> * S is Relation-like NAT -defined Function-like finite V95() set
<*x1,x2,x3*> is non empty Relation-like NAT -defined F₄() -valued Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() FinSequence of F₄()
Following S is non empty Relation-like the carrier of (1GateCircStr (<*F₁(),F₂(),F₃()*>,F₆())) -defined Function-like the Sorts of (3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>) -compatible total Element of K246( the Sorts of (3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>))
(Following S) . ((3,F₄(),F₆(),<*F₁(),F₂(),F₃()*>)) is set
(Following S) . [<*F₁(),F₂(),F₃()*>,F₆()] is set
F₆() . (<*F₁(),F₂(),F₃()*> * S) is set
F₅() is non empty finite V95() set
4 -tuples_on F₅() is non empty functional FinSequence-membered FinSequenceSet of F₅()
[:(4 -tuples_on F₅()),F₅():] is Relation-like set
bool [:(4 -tuples_on F₅()),F₅():] is set
F₇() is Relation-like 4 -tuples_on F₅() -defined F₅() -valued Function-like V30(4 -tuples_on F₅(),F₅()) Element of bool [:(4 -tuples_on F₅()),F₅():]
F₁() is set
F₂() is set
F₃() is set
F₄() is set
<*F₁(),F₂(),F₃(),F₄()*> is non empty Relation-like NAT -defined Function-like finite V42(4) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (<*F₁(),F₂(),F₃(),F₄()*>,F₇()) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
the carrier of (1GateCircStr (<*F₁(),F₂(),F₃(),F₄()*>,F₇())) is non empty finite V95() set
(4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>) is strict strict non-empty non-empty finite-yielding finite-yielding gate`2=den gate`2=den ( 1GateCircStr (<*F₁(),F₂(),F₃(),F₄()*>,F₇())) ((4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>)) ( 1GateCircStr (<*F₁(),F₂(),F₃(),F₄()*>,F₇())) (F₅(),(4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>))
(4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (F₅())
the Sorts of (4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>) is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (<*F₁(),F₂(),F₃(),F₄()*>,F₇())) -defined Function-like total set
K246( the Sorts of (4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>)) is non empty functional V93() V94() set
((4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>)) is pair non empty Element of the carrier of (4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>)
the carrier of (4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>) is non empty finite V95() set
the carrier' of (4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>) is non empty set
union the carrier' of (4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>) is set
S is non empty Relation-like the carrier of (1GateCircStr (<*F₁(),F₂(),F₃(),F₄()*>,F₇())) -defined Function-like the Sorts of (4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>) -compatible total Element of K246( the Sorts of (4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>))
S . F₁() is set
S . F₂() is set
S . F₃() is set
S . F₄() is set
((1GateCircStr (<*F₁(),F₂(),F₃(),F₄()*>,F₇())),(4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>),S) is non empty Relation-like the carrier of (1GateCircStr (<*F₁(),F₂(),F₃(),F₄()*>,F₇())) -defined Function-like the Sorts of (4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>) -compatible total Element of K246( the Sorts of (4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>))
((1GateCircStr (<*F₁(),F₂(),F₃(),F₄()*>,F₇())),(4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>),S) . ((4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>)) is set
proj1 S is non empty set
proj2 <*F₁(),F₂(),F₃(),F₄()*> is non empty finite V95() set
[<*F₁(),F₂(),F₃(),F₄()*>,F₇()] is pair non empty set
{<*F₁(),F₂(),F₃(),F₄()*>,F₇()} is non empty functional finite V95() set
{<*F₁(),F₂(),F₃(),F₄()*>} is non empty functional finite V39() V93() V95() set
{{<*F₁(),F₂(),F₃(),F₄()*>,F₇()},{<*F₁(),F₂(),F₃(),F₄()*>}} is non empty finite V39() V95() set
{[<*F₁(),F₂(),F₃(),F₄()*>,F₇()]} is non empty Relation-like Function-like finite V95() set
(proj2 <*F₁(),F₂(),F₃(),F₄()*>) \/ {[<*F₁(),F₂(),F₃(),F₄()*>,F₇()]} is non empty finite V95() set
{F₁(),F₂(),F₃(),F₄()} is finite V95() set
{F₁(),F₂(),F₃(),F₄()} \/ {[<*F₁(),F₂(),F₃(),F₄()*>,F₇()]} is non empty finite V95() set
{[<*F₁(),F₂(),F₃(),F₄()*>,F₇()],F₁(),F₂(),F₃(),F₄()} is finite V95() set
x1 is Element of F₅()
x2 is Element of F₅()
x3 is Element of F₅()
f is Element of F₅()
F₆(x1,x2,x3,f) is Element of F₅()
<*F₁(),F₂(),F₃(),F₄()*> * S is Relation-like NAT -defined Function-like finite V95() set
<*x1,x2,x3,f*> is non empty Relation-like NAT -defined F₅() -valued Function-like finite V42(4) FinSequence-like FinSubsequence-like V95() FinSequence of F₅()
Following S is non empty Relation-like the carrier of (1GateCircStr (<*F₁(),F₂(),F₃(),F₄()*>,F₇())) -defined Function-like the Sorts of (4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>) -compatible total Element of K246( the Sorts of (4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>))
(Following S) . ((4,F₅(),F₇(),<*F₁(),F₂(),F₃(),F₄()*>)) is set
(Following S) . [<*F₁(),F₂(),F₃(),F₄()*>,F₇()] is set
F₇() . (<*F₁(),F₂(),F₃(),F₄()*> * S) is set
F₆() is non empty finite V95() set
5 -tuples_on F₆() is non empty functional FinSequence-membered FinSequenceSet of F₆()
[:(5 -tuples_on F₆()),F₆():] is Relation-like set
bool [:(5 -tuples_on F₆()),F₆():] is set
F₈() is Relation-like 5 -tuples_on F₆() -defined F₆() -valued Function-like V30(5 -tuples_on F₆(),F₆()) Element of bool [:(5 -tuples_on F₆()),F₆():]
F₁() is set
F₂() is set
F₃() is set
F₄() is set
F₅() is set
<*F₁(),F₂(),F₃(),F₄(),F₅()*> is non empty Relation-like NAT -defined Function-like finite V42(5) FinSequence-like FinSubsequence-like V95() set
1GateCircStr (<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈()) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
the carrier of (1GateCircStr (<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈())) is non empty finite V95() set
(5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) is strict strict non-empty non-empty finite-yielding finite-yielding gate`2=den gate`2=den ( 1GateCircStr (<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈())) ((5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) ( 1GateCircStr (<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈())) (F₆(),(5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))
(5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (F₆())
the Sorts of (5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈())) -defined Function-like total set
K246( the Sorts of (5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is non empty functional V93() V94() set
((5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is pair non empty Element of the carrier of (5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)
the carrier of (5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) is non empty finite V95() set
the carrier' of (5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) is non empty set
union the carrier' of (5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) is set
S is non empty Relation-like the carrier of (1GateCircStr (<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈())) -defined Function-like the Sorts of (5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) -compatible total Element of K246( the Sorts of (5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))
S . F₁() is set
S . F₂() is set
S . F₃() is set
S . F₄() is set
S . F₅() is set
((1GateCircStr (<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈())),(5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),S) is non empty Relation-like the carrier of (1GateCircStr (<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈())) -defined Function-like the Sorts of (5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) -compatible total Element of K246( the Sorts of (5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))
((1GateCircStr (<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈())),(5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),S) . ((5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is set
proj1 S is non empty set
proj2 <*F₁(),F₂(),F₃(),F₄(),F₅()*> is non empty finite V95() set
[<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈()] is pair non empty set
{<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈()} is non empty functional finite V95() set
{<*F₁(),F₂(),F₃(),F₄(),F₅()*>} is non empty functional finite V39() V93() V95() set
{{<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈()},{<*F₁(),F₂(),F₃(),F₄(),F₅()*>}} is non empty finite V39() V95() set
{[<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈()]} is non empty Relation-like Function-like finite V95() set
(proj2 <*F₁(),F₂(),F₃(),F₄(),F₅()*>) \/ {[<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈()]} is non empty finite V95() set
{F₁(),F₂(),F₃(),F₄(),F₅()} is finite V95() set
{F₁(),F₂(),F₃(),F₄(),F₅()} \/ {[<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈()]} is non empty finite V95() set
{F₁(),F₂(),F₃(),F₄(),F₅(),[<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈()]} is finite V95() set
x1 is Element of F₆()
x2 is Element of F₆()
x3 is Element of F₆()
f is Element of F₆()
a is Element of F₆()
F₇(x1,x2,x3,f,a) is Element of F₆()
<*F₁(),F₂(),F₃(),F₄(),F₅()*> * S is Relation-like NAT -defined Function-like finite V95() set
<*x1,x2,x3,f,a*> is non empty Relation-like NAT -defined F₆() -valued Function-like finite V42(5) FinSequence-like FinSubsequence-like V95() FinSequence of F₆()
Following S is non empty Relation-like the carrier of (1GateCircStr (<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈())) -defined Function-like the Sorts of (5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) -compatible total Element of K246( the Sorts of (5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))
(Following S) . ((5,F₆(),F₈(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is set
(Following S) . [<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₈()] is set
F₈() . (<*F₁(),F₂(),F₃(),F₄(),F₅()*> * S) is set
X is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
S is non empty finite V95() set
X -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
[:(X -tuples_on S),S:] is Relation-like set
bool [:(X -tuples_on S),S:] is set
x1 is Relation-like X -tuples_on S -defined S -valued Function-like V30(X -tuples_on S,S) Element of bool [:(X -tuples_on S),S:]
x2 is Relation-like NAT -defined Function-like finite V42(X) FinSequence-like FinSubsequence-like V95() set
proj2 x2 is finite V95() set
(X,S,x1,x2) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (S)
((X,S,x1,x2)) is pair non empty Element of the carrier of (X,S,x1,x2)
the carrier of (X,S,x1,x2) is non empty finite V95() set
the carrier' of (X,S,x1,x2) is non empty set
union the carrier' of (X,S,x1,x2) is set
x3 is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (S)
the carrier of x3 is non empty set
InputVertices x3 is Element of bool the carrier of x3
bool the carrier of x3 is set
the ResultSort of x3 is Relation-like the carrier' of x3 -defined the carrier of x3 -valued Function-like V30( the carrier' of x3, the carrier of x3) Element of bool [: the carrier' of x3, the carrier of x3:]
the carrier' of x3 is non empty set
[: the carrier' of x3, the carrier of x3:] is Relation-like set
bool [: the carrier' of x3, the carrier of x3:] is set
K488( the carrier of x3, the ResultSort of x3) is Element of bool the carrier of x3
the carrier of x3 \ K488( the carrier of x3, the ResultSort of x3) is Element of bool the carrier of x3
(S,x3,(X,S,x1,x2)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (S)
InputVertices (S,x3,(X,S,x1,x2)) is Element of bool the carrier of (S,x3,(X,S,x1,x2))
the carrier of (S,x3,(X,S,x1,x2)) is non empty set
bool the carrier of (S,x3,(X,S,x1,x2)) is set
the ResultSort of (S,x3,(X,S,x1,x2)) is Relation-like the carrier' of (S,x3,(X,S,x1,x2)) -defined the carrier of (S,x3,(X,S,x1,x2)) -valued Function-like V30( the carrier' of (S,x3,(X,S,x1,x2)), the carrier of (S,x3,(X,S,x1,x2))) Element of bool [: the carrier' of (S,x3,(X,S,x1,x2)), the carrier of (S,x3,(X,S,x1,x2)):]
the carrier' of (S,x3,(X,S,x1,x2)) is non empty set
[: the carrier' of (S,x3,(X,S,x1,x2)), the carrier of (S,x3,(X,S,x1,x2)):] is Relation-like set
bool [: the carrier' of (S,x3,(X,S,x1,x2)), the carrier of (S,x3,(X,S,x1,x2)):] is set
K488( the carrier of (S,x3,(X,S,x1,x2)), the ResultSort of (S,x3,(X,S,x1,x2))) is Element of bool the carrier of (S,x3,(X,S,x1,x2))
the carrier of (S,x3,(X,S,x1,x2)) \ K488( the carrier of (S,x3,(X,S,x1,x2)), the ResultSort of (S,x3,(X,S,x1,x2))) is Element of bool the carrier of (S,x3,(X,S,x1,x2))
InnerVertices x3 is Element of bool the carrier of x3
(InputVertices x3) \/ (InnerVertices x3) is Element of bool the carrier of x3
InnerVertices (X,S,x1,x2) is finite V95() Element of bool the carrier of (X,S,x1,x2)
bool the carrier of (X,S,x1,x2) is finite V39() V95() set
the ResultSort of (X,S,x1,x2) is Relation-like the carrier' of (X,S,x1,x2) -defined the carrier of (X,S,x1,x2) -valued Function-like V30( the carrier' of (X,S,x1,x2), the carrier of (X,S,x1,x2)) Element of bool [: the carrier' of (X,S,x1,x2), the carrier of (X,S,x1,x2):]
[: the carrier' of (X,S,x1,x2), the carrier of (X,S,x1,x2):] is Relation-like set
bool [: the carrier' of (X,S,x1,x2), the carrier of (X,S,x1,x2):] is set
K488( the carrier of (X,S,x1,x2), the ResultSort of (X,S,x1,x2)) is finite V95() Element of bool the carrier of (X,S,x1,x2)
(InputVertices x3) \ (InnerVertices (X,S,x1,x2)) is Element of bool the carrier of x3
InputVertices (X,S,x1,x2) is finite V95() Element of bool the carrier of (X,S,x1,x2)
the carrier of (X,S,x1,x2) \ K488( the carrier of (X,S,x1,x2), the ResultSort of (X,S,x1,x2)) is finite V95() Element of bool the carrier of (X,S,x1,x2)
(InputVertices (X,S,x1,x2)) \ (InnerVertices x3) is finite V95() Element of bool the carrier of (X,S,x1,x2)
((InputVertices x3) \ (InnerVertices (X,S,x1,x2))) \/ ((InputVertices (X,S,x1,x2)) \ (InnerVertices x3)) is set
(proj2 x2) \ (InnerVertices x3) is finite V95() Element of bool (proj2 x2)
bool (proj2 x2) is finite V39() V95() set
((InputVertices x3) \ (InnerVertices (X,S,x1,x2))) \/ ((proj2 x2) \ (InnerVertices x3)) is set
{((X,S,x1,x2))} is non empty Relation-like finite V95() set
(InputVertices x3) \ {((X,S,x1,x2))} is Element of bool the carrier of x3
((InputVertices x3) \ {((X,S,x1,x2))}) \/ ((proj2 x2) \ (InnerVertices x3)) is set
(InputVertices x3) \/ ((proj2 x2) \ (InnerVertices x3)) is set
X is set
S is set
X \/ S is set
x1 is non empty finite V95() set
x2 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
x2 -tuples_on x1 is non empty functional FinSequence-membered FinSequenceSet of x1
[:(x2 -tuples_on x1),x1:] is Relation-like set
bool [:(x2 -tuples_on x1),x1:] is set
x3 is Relation-like x2 -tuples_on x1 -defined x1 -valued Function-like V30(x2 -tuples_on x1,x1) Element of bool [:(x2 -tuples_on x1),x1:]
f is Relation-like NAT -defined Function-like finite V42(x2) FinSequence-like FinSubsequence-like V95() set
proj2 f is finite V95() set
(x2,x1,x3,f) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (x1)
((x2,x1,x3,f)) is pair non empty Element of the carrier of (x2,x1,x3,f)
the carrier of (x2,x1,x3,f) is non empty finite V95() set
the carrier' of (x2,x1,x3,f) is non empty set
union the carrier' of (x2,x1,x3,f) is set
a is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (x1)
the carrier of a is non empty set
InnerVertices a is Element of bool the carrier of a
bool the carrier of a is set
the ResultSort of a is Relation-like the carrier' of a -defined the carrier of a -valued Function-like V30( the carrier' of a, the carrier of a) Element of bool [: the carrier' of a, the carrier of a:]
the carrier' of a is non empty set
[: the carrier' of a, the carrier of a:] is Relation-like set
bool [: the carrier' of a, the carrier of a:] is set
K488( the carrier of a, the ResultSort of a) is Element of bool the carrier of a
InputVertices a is Element of bool the carrier of a
the carrier of a \ K488( the carrier of a, the ResultSort of a) is Element of bool the carrier of a
(x1,a,(x2,x1,x3,f)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (x1)
InputVertices (x1,a,(x2,x1,x3,f)) is Element of bool the carrier of (x1,a,(x2,x1,x3,f))
the carrier of (x1,a,(x2,x1,x3,f)) is non empty set
bool the carrier of (x1,a,(x2,x1,x3,f)) is set
the ResultSort of (x1,a,(x2,x1,x3,f)) is Relation-like the carrier' of (x1,a,(x2,x1,x3,f)) -defined the carrier of (x1,a,(x2,x1,x3,f)) -valued Function-like V30( the carrier' of (x1,a,(x2,x1,x3,f)), the carrier of (x1,a,(x2,x1,x3,f))) Element of bool [: the carrier' of (x1,a,(x2,x1,x3,f)), the carrier of (x1,a,(x2,x1,x3,f)):]
the carrier' of (x1,a,(x2,x1,x3,f)) is non empty set
[: the carrier' of (x1,a,(x2,x1,x3,f)), the carrier of (x1,a,(x2,x1,x3,f)):] is Relation-like set
bool [: the carrier' of (x1,a,(x2,x1,x3,f)), the carrier of (x1,a,(x2,x1,x3,f)):] is set
K488( the carrier of (x1,a,(x2,x1,x3,f)), the ResultSort of (x1,a,(x2,x1,x3,f))) is Element of bool the carrier of (x1,a,(x2,x1,x3,f))
the carrier of (x1,a,(x2,x1,x3,f)) \ K488( the carrier of (x1,a,(x2,x1,x3,f)), the ResultSort of (x1,a,(x2,x1,x3,f))) is Element of bool the carrier of (x1,a,(x2,x1,x3,f))
(InputVertices a) \/ S is set
(InputVertices a) \/ (InnerVertices a) is Element of bool the carrier of a
InnerVertices (x2,x1,x3,f) is finite V95() Element of bool the carrier of (x2,x1,x3,f)
bool the carrier of (x2,x1,x3,f) is finite V39() V95() set
the ResultSort of (x2,x1,x3,f) is Relation-like the carrier' of (x2,x1,x3,f) -defined the carrier of (x2,x1,x3,f) -valued Function-like V30( the carrier' of (x2,x1,x3,f), the carrier of (x2,x1,x3,f)) Element of bool [: the carrier' of (x2,x1,x3,f), the carrier of (x2,x1,x3,f):]
[: the carrier' of (x2,x1,x3,f), the carrier of (x2,x1,x3,f):] is Relation-like set
bool [: the carrier' of (x2,x1,x3,f), the carrier of (x2,x1,x3,f):] is set
K488( the carrier of (x2,x1,x3,f), the ResultSort of (x2,x1,x3,f)) is finite V95() Element of bool the carrier of (x2,x1,x3,f)
(InputVertices a) \ (InnerVertices (x2,x1,x3,f)) is Element of bool the carrier of a
InputVertices (x2,x1,x3,f) is finite V95() Element of bool the carrier of (x2,x1,x3,f)
the carrier of (x2,x1,x3,f) \ K488( the carrier of (x2,x1,x3,f), the ResultSort of (x2,x1,x3,f)) is finite V95() Element of bool the carrier of (x2,x1,x3,f)
(InputVertices (x2,x1,x3,f)) \ (InnerVertices a) is finite V95() Element of bool the carrier of (x2,x1,x3,f)
((InputVertices a) \ (InnerVertices (x2,x1,x3,f))) \/ ((InputVertices (x2,x1,x3,f)) \ (InnerVertices a)) is set
(proj2 f) \ (InnerVertices a) is finite V95() Element of bool (proj2 f)
bool (proj2 f) is finite V39() V95() set
((InputVertices a) \ (InnerVertices (x2,x1,x3,f))) \/ ((proj2 f) \ (InnerVertices a)) is set
X \ (InnerVertices a) is Element of bool X
bool X is set
(X \ (InnerVertices a)) \/ S is set
((InputVertices a) \ (InnerVertices (x2,x1,x3,f))) \/ ((X \ (InnerVertices a)) \/ S) is set
((InputVertices a) \ (InnerVertices (x2,x1,x3,f))) \/ (X \ (InnerVertices a)) is set
(((InputVertices a) \ (InnerVertices (x2,x1,x3,f))) \/ (X \ (InnerVertices a))) \/ S is set
{((x2,x1,x3,f))} is non empty Relation-like finite V95() set
(InputVertices a) \ {((x2,x1,x3,f))} is Element of bool the carrier of a
((InputVertices a) \ {((x2,x1,x3,f))}) \/ (X \ (InnerVertices a)) is set
(((InputVertices a) \ {((x2,x1,x3,f))}) \/ (X \ (InnerVertices a))) \/ S is set
(InputVertices a) \/ (X \ (InnerVertices a)) is set
((InputVertices a) \/ (X \ (InnerVertices a))) \/ S is set
X is set
<*X*> is non empty Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set
S is non empty finite V95() set
1 -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
[:(1 -tuples_on S),S:] is Relation-like set
bool [:(1 -tuples_on S),S:] is set
x2 is Relation-like 1 -tuples_on S -defined S -valued Function-like V30(1 -tuples_on S,S) Element of bool [:(1 -tuples_on S),S:]
(1,S,x2,<*X*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (S)
((1,S,x2,<*X*>)) is pair non empty Element of the carrier of (1,S,x2,<*X*>)
the carrier of (1,S,x2,<*X*>) is non empty finite V95() set
the carrier' of (1,S,x2,<*X*>) is non empty set
union the carrier' of (1,S,x2,<*X*>) is set
x3 is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (S)
the carrier of x3 is non empty set
InputVertices x3 is Element of bool the carrier of x3
bool the carrier of x3 is set
the ResultSort of x3 is Relation-like the carrier' of x3 -defined the carrier of x3 -valued Function-like V30( the carrier' of x3, the carrier of x3) Element of bool [: the carrier' of x3, the carrier of x3:]
the carrier' of x3 is non empty set
[: the carrier' of x3, the carrier of x3:] is Relation-like set
bool [: the carrier' of x3, the carrier of x3:] is set
K488( the carrier of x3, the ResultSort of x3) is Element of bool the carrier of x3
the carrier of x3 \ K488( the carrier of x3, the ResultSort of x3) is Element of bool the carrier of x3
(S,x3,(1,S,x2,<*X*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (S)
InputVertices (S,x3,(1,S,x2,<*X*>)) is Element of bool the carrier of (S,x3,(1,S,x2,<*X*>))
the carrier of (S,x3,(1,S,x2,<*X*>)) is non empty set
bool the carrier of (S,x3,(1,S,x2,<*X*>)) is set
the ResultSort of (S,x3,(1,S,x2,<*X*>)) is Relation-like the carrier' of (S,x3,(1,S,x2,<*X*>)) -defined the carrier of (S,x3,(1,S,x2,<*X*>)) -valued Function-like V30( the carrier' of (S,x3,(1,S,x2,<*X*>)), the carrier of (S,x3,(1,S,x2,<*X*>))) Element of bool [: the carrier' of (S,x3,(1,S,x2,<*X*>)), the carrier of (S,x3,(1,S,x2,<*X*>)):]
the carrier' of (S,x3,(1,S,x2,<*X*>)) is non empty set
[: the carrier' of (S,x3,(1,S,x2,<*X*>)), the carrier of (S,x3,(1,S,x2,<*X*>)):] is Relation-like set
bool [: the carrier' of (S,x3,(1,S,x2,<*X*>)), the carrier of (S,x3,(1,S,x2,<*X*>)):] is set
K488( the carrier of (S,x3,(1,S,x2,<*X*>)), the ResultSort of (S,x3,(1,S,x2,<*X*>))) is Element of bool the carrier of (S,x3,(1,S,x2,<*X*>))
the carrier of (S,x3,(1,S,x2,<*X*>)) \ K488( the carrier of (S,x3,(1,S,x2,<*X*>)), the ResultSort of (S,x3,(1,S,x2,<*X*>))) is Element of bool the carrier of (S,x3,(1,S,x2,<*X*>))
{X} is non empty finite V95() set
proj2 <*X*> is non empty finite V95() set
X is set
S is set
<*X,S*> is non empty Relation-like NAT -defined Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() set
{S} is non empty finite V95() set
x1 is non empty finite V95() set
2 -tuples_on x1 is non empty functional FinSequence-membered FinSequenceSet of x1
[:(2 -tuples_on x1),x1:] is Relation-like set
bool [:(2 -tuples_on x1),x1:] is set
x3 is Relation-like 2 -tuples_on x1 -defined x1 -valued Function-like V30(2 -tuples_on x1,x1) Element of bool [:(2 -tuples_on x1),x1:]
(2,x1,x3,<*X,S*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (x1)
((2,x1,x3,<*X,S*>)) is pair non empty Element of the carrier of (2,x1,x3,<*X,S*>)
the carrier of (2,x1,x3,<*X,S*>) is non empty finite V95() set
the carrier' of (2,x1,x3,<*X,S*>) is non empty set
union the carrier' of (2,x1,x3,<*X,S*>) is set
f is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (x1)
the carrier of f is non empty set
InnerVertices f is Element of bool the carrier of f
bool the carrier of f is set
the ResultSort of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V30( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the carrier' of f is non empty set
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
K488( the carrier of f, the ResultSort of f) is Element of bool the carrier of f
InputVertices f is Element of bool the carrier of f
the carrier of f \ K488( the carrier of f, the ResultSort of f) is Element of bool the carrier of f
(x1,f,(2,x1,x3,<*X,S*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (x1)
InputVertices (x1,f,(2,x1,x3,<*X,S*>)) is Element of bool the carrier of (x1,f,(2,x1,x3,<*X,S*>))
the carrier of (x1,f,(2,x1,x3,<*X,S*>)) is non empty set
bool the carrier of (x1,f,(2,x1,x3,<*X,S*>)) is set
the ResultSort of (x1,f,(2,x1,x3,<*X,S*>)) is Relation-like the carrier' of (x1,f,(2,x1,x3,<*X,S*>)) -defined the carrier of (x1,f,(2,x1,x3,<*X,S*>)) -valued Function-like V30( the carrier' of (x1,f,(2,x1,x3,<*X,S*>)), the carrier of (x1,f,(2,x1,x3,<*X,S*>))) Element of bool [: the carrier' of (x1,f,(2,x1,x3,<*X,S*>)), the carrier of (x1,f,(2,x1,x3,<*X,S*>)):]
the carrier' of (x1,f,(2,x1,x3,<*X,S*>)) is non empty set
[: the carrier' of (x1,f,(2,x1,x3,<*X,S*>)), the carrier of (x1,f,(2,x1,x3,<*X,S*>)):] is Relation-like set
bool [: the carrier' of (x1,f,(2,x1,x3,<*X,S*>)), the carrier of (x1,f,(2,x1,x3,<*X,S*>)):] is set
K488( the carrier of (x1,f,(2,x1,x3,<*X,S*>)), the ResultSort of (x1,f,(2,x1,x3,<*X,S*>))) is Element of bool the carrier of (x1,f,(2,x1,x3,<*X,S*>))
the carrier of (x1,f,(2,x1,x3,<*X,S*>)) \ K488( the carrier of (x1,f,(2,x1,x3,<*X,S*>)), the ResultSort of (x1,f,(2,x1,x3,<*X,S*>))) is Element of bool the carrier of (x1,f,(2,x1,x3,<*X,S*>))
(InputVertices f) \/ {S} is non empty set
proj2 <*X,S*> is non empty finite V95() set
{X,S} is non empty finite V95() set
{X} is non empty finite V95() set
{X} \/ {S} is non empty finite V95() set
S is set
X is set
<*X,S*> is non empty Relation-like NAT -defined Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() set
{X} is non empty finite V95() set
x1 is non empty finite V95() set
2 -tuples_on x1 is non empty functional FinSequence-membered FinSequenceSet of x1
[:(2 -tuples_on x1),x1:] is Relation-like set
bool [:(2 -tuples_on x1),x1:] is set
x3 is Relation-like 2 -tuples_on x1 -defined x1 -valued Function-like V30(2 -tuples_on x1,x1) Element of bool [:(2 -tuples_on x1),x1:]
(2,x1,x3,<*X,S*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (x1)
((2,x1,x3,<*X,S*>)) is pair non empty Element of the carrier of (2,x1,x3,<*X,S*>)
the carrier of (2,x1,x3,<*X,S*>) is non empty finite V95() set
the carrier' of (2,x1,x3,<*X,S*>) is non empty set
union the carrier' of (2,x1,x3,<*X,S*>) is set
f is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (x1)
the carrier of f is non empty set
InnerVertices f is Element of bool the carrier of f
bool the carrier of f is set
the ResultSort of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V30( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the carrier' of f is non empty set
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
K488( the carrier of f, the ResultSort of f) is Element of bool the carrier of f
InputVertices f is Element of bool the carrier of f
the carrier of f \ K488( the carrier of f, the ResultSort of f) is Element of bool the carrier of f
(x1,f,(2,x1,x3,<*X,S*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (x1)
InputVertices (x1,f,(2,x1,x3,<*X,S*>)) is Element of bool the carrier of (x1,f,(2,x1,x3,<*X,S*>))
the carrier of (x1,f,(2,x1,x3,<*X,S*>)) is non empty set
bool the carrier of (x1,f,(2,x1,x3,<*X,S*>)) is set
the ResultSort of (x1,f,(2,x1,x3,<*X,S*>)) is Relation-like the carrier' of (x1,f,(2,x1,x3,<*X,S*>)) -defined the carrier of (x1,f,(2,x1,x3,<*X,S*>)) -valued Function-like V30( the carrier' of (x1,f,(2,x1,x3,<*X,S*>)), the carrier of (x1,f,(2,x1,x3,<*X,S*>))) Element of bool [: the carrier' of (x1,f,(2,x1,x3,<*X,S*>)), the carrier of (x1,f,(2,x1,x3,<*X,S*>)):]
the carrier' of (x1,f,(2,x1,x3,<*X,S*>)) is non empty set
[: the carrier' of (x1,f,(2,x1,x3,<*X,S*>)), the carrier of (x1,f,(2,x1,x3,<*X,S*>)):] is Relation-like set
bool [: the carrier' of (x1,f,(2,x1,x3,<*X,S*>)), the carrier of (x1,f,(2,x1,x3,<*X,S*>)):] is set
K488( the carrier of (x1,f,(2,x1,x3,<*X,S*>)), the ResultSort of (x1,f,(2,x1,x3,<*X,S*>))) is Element of bool the carrier of (x1,f,(2,x1,x3,<*X,S*>))
the carrier of (x1,f,(2,x1,x3,<*X,S*>)) \ K488( the carrier of (x1,f,(2,x1,x3,<*X,S*>)), the ResultSort of (x1,f,(2,x1,x3,<*X,S*>))) is Element of bool the carrier of (x1,f,(2,x1,x3,<*X,S*>))
(InputVertices f) \/ {X} is non empty set
proj2 <*X,S*> is non empty finite V95() set
{X,S} is non empty finite V95() set
{S} is non empty finite V95() set
{X} \/ {S} is non empty finite V95() set
X is set
S is set
<*X,S*> is non empty Relation-like NAT -defined Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() set
x1 is non empty finite V95() set
2 -tuples_on x1 is non empty functional FinSequence-membered FinSequenceSet of x1
[:(2 -tuples_on x1),x1:] is Relation-like set
bool [:(2 -tuples_on x1),x1:] is set
x2 is Relation-like 2 -tuples_on x1 -defined x1 -valued Function-like V30(2 -tuples_on x1,x1) Element of bool [:(2 -tuples_on x1),x1:]
(2,x1,x2,<*X,S*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (x1)
((2,x1,x2,<*X,S*>)) is pair non empty Element of the carrier of (2,x1,x2,<*X,S*>)
the carrier of (2,x1,x2,<*X,S*>) is non empty finite V95() set
the carrier' of (2,x1,x2,<*X,S*>) is non empty set
union the carrier' of (2,x1,x2,<*X,S*>) is set
proj2 <*X,S*> is non empty finite V95() set
{X,S} is non empty finite V95() set
x3 is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (x1)
the carrier of x3 is non empty set
InputVertices x3 is Element of bool the carrier of x3
bool the carrier of x3 is set
the ResultSort of x3 is Relation-like the carrier' of x3 -defined the carrier of x3 -valued Function-like V30( the carrier' of x3, the carrier of x3) Element of bool [: the carrier' of x3, the carrier of x3:]
the carrier' of x3 is non empty set
[: the carrier' of x3, the carrier of x3:] is Relation-like set
bool [: the carrier' of x3, the carrier of x3:] is set
K488( the carrier of x3, the ResultSort of x3) is Element of bool the carrier of x3
the carrier of x3 \ K488( the carrier of x3, the ResultSort of x3) is Element of bool the carrier of x3
(x1,x3,(2,x1,x2,<*X,S*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (x1)
InputVertices (x1,x3,(2,x1,x2,<*X,S*>)) is Element of bool the carrier of (x1,x3,(2,x1,x2,<*X,S*>))
the carrier of (x1,x3,(2,x1,x2,<*X,S*>)) is non empty set
bool the carrier of (x1,x3,(2,x1,x2,<*X,S*>)) is set
the ResultSort of (x1,x3,(2,x1,x2,<*X,S*>)) is Relation-like the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)) -defined the carrier of (x1,x3,(2,x1,x2,<*X,S*>)) -valued Function-like V30( the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)), the carrier of (x1,x3,(2,x1,x2,<*X,S*>))) Element of bool [: the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)), the carrier of (x1,x3,(2,x1,x2,<*X,S*>)):]
the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)) is non empty set
[: the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)), the carrier of (x1,x3,(2,x1,x2,<*X,S*>)):] is Relation-like set
bool [: the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)), the carrier of (x1,x3,(2,x1,x2,<*X,S*>)):] is set
K488( the carrier of (x1,x3,(2,x1,x2,<*X,S*>)), the ResultSort of (x1,x3,(2,x1,x2,<*X,S*>))) is Element of bool the carrier of (x1,x3,(2,x1,x2,<*X,S*>))
the carrier of (x1,x3,(2,x1,x2,<*X,S*>)) \ K488( the carrier of (x1,x3,(2,x1,x2,<*X,S*>)), the ResultSort of (x1,x3,(2,x1,x2,<*X,S*>))) is Element of bool the carrier of (x1,x3,(2,x1,x2,<*X,S*>))
X is set
S is set
x1 is set
<*X,S,x1*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
{S,x1} is non empty finite V95() set
x2 is non empty finite V95() set
3 -tuples_on x2 is non empty functional FinSequence-membered FinSequenceSet of x2
[:(3 -tuples_on x2),x2:] is Relation-like set
bool [:(3 -tuples_on x2),x2:] is set
f is Relation-like 3 -tuples_on x2 -defined x2 -valued Function-like V30(3 -tuples_on x2,x2) Element of bool [:(3 -tuples_on x2),x2:]
(3,x2,f,<*X,S,x1*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (x2)
((3,x2,f,<*X,S,x1*>)) is pair non empty Element of the carrier of (3,x2,f,<*X,S,x1*>)
the carrier of (3,x2,f,<*X,S,x1*>) is non empty finite V95() set
the carrier' of (3,x2,f,<*X,S,x1*>) is non empty set
union the carrier' of (3,x2,f,<*X,S,x1*>) is set
a is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (x2)
the carrier of a is non empty set
InnerVertices a is Element of bool the carrier of a
bool the carrier of a is set
the ResultSort of a is Relation-like the carrier' of a -defined the carrier of a -valued Function-like V30( the carrier' of a, the carrier of a) Element of bool [: the carrier' of a, the carrier of a:]
the carrier' of a is non empty set
[: the carrier' of a, the carrier of a:] is Relation-like set
bool [: the carrier' of a, the carrier of a:] is set
K488( the carrier of a, the ResultSort of a) is Element of bool the carrier of a
InputVertices a is Element of bool the carrier of a
the carrier of a \ K488( the carrier of a, the ResultSort of a) is Element of bool the carrier of a
(x2,a,(3,x2,f,<*X,S,x1*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (x2)
InputVertices (x2,a,(3,x2,f,<*X,S,x1*>)) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) is non empty set
bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) is set
the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>)) is Relation-like the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)) -defined the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) -valued Function-like V30( the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))) Element of bool [: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):]
the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)) is non empty set
[: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):] is Relation-like set
bool [: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):] is set
K488( the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)), the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>))) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) \ K488( the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)), the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>))) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
(InputVertices a) \/ {S,x1} is non empty set
proj2 <*X,S,x1*> is non empty finite V95() set
{X,S,x1} is finite V95() set
{X} is non empty finite V95() set
{X} \/ {S,x1} is non empty finite V95() set
S is set
X is set
x1 is set
<*X,S,x1*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
{X,x1} is non empty finite V95() set
x2 is non empty finite V95() set
3 -tuples_on x2 is non empty functional FinSequence-membered FinSequenceSet of x2
[:(3 -tuples_on x2),x2:] is Relation-like set
bool [:(3 -tuples_on x2),x2:] is set
f is Relation-like 3 -tuples_on x2 -defined x2 -valued Function-like V30(3 -tuples_on x2,x2) Element of bool [:(3 -tuples_on x2),x2:]
(3,x2,f,<*X,S,x1*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (x2)
((3,x2,f,<*X,S,x1*>)) is pair non empty Element of the carrier of (3,x2,f,<*X,S,x1*>)
the carrier of (3,x2,f,<*X,S,x1*>) is non empty finite V95() set
the carrier' of (3,x2,f,<*X,S,x1*>) is non empty set
union the carrier' of (3,x2,f,<*X,S,x1*>) is set
a is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (x2)
the carrier of a is non empty set
InnerVertices a is Element of bool the carrier of a
bool the carrier of a is set
the ResultSort of a is Relation-like the carrier' of a -defined the carrier of a -valued Function-like V30( the carrier' of a, the carrier of a) Element of bool [: the carrier' of a, the carrier of a:]
the carrier' of a is non empty set
[: the carrier' of a, the carrier of a:] is Relation-like set
bool [: the carrier' of a, the carrier of a:] is set
K488( the carrier of a, the ResultSort of a) is Element of bool the carrier of a
InputVertices a is Element of bool the carrier of a
the carrier of a \ K488( the carrier of a, the ResultSort of a) is Element of bool the carrier of a
(x2,a,(3,x2,f,<*X,S,x1*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (x2)
InputVertices (x2,a,(3,x2,f,<*X,S,x1*>)) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) is non empty set
bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) is set
the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>)) is Relation-like the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)) -defined the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) -valued Function-like V30( the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))) Element of bool [: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):]
the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)) is non empty set
[: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):] is Relation-like set
bool [: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):] is set
K488( the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)), the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>))) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) \ K488( the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)), the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>))) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
(InputVertices a) \/ {X,x1} is non empty set
proj2 <*X,S,x1*> is non empty finite V95() set
{X,S,x1} is finite V95() set
{S,X,x1} is finite V95() set
{S} is non empty finite V95() set
{S} \/ {X,x1} is non empty finite V95() set
x1 is set
X is set
S is set
<*X,S,x1*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
{X,S} is non empty finite V95() set
x2 is non empty finite V95() set
3 -tuples_on x2 is non empty functional FinSequence-membered FinSequenceSet of x2
[:(3 -tuples_on x2),x2:] is Relation-like set
bool [:(3 -tuples_on x2),x2:] is set
f is Relation-like 3 -tuples_on x2 -defined x2 -valued Function-like V30(3 -tuples_on x2,x2) Element of bool [:(3 -tuples_on x2),x2:]
(3,x2,f,<*X,S,x1*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (x2)
((3,x2,f,<*X,S,x1*>)) is pair non empty Element of the carrier of (3,x2,f,<*X,S,x1*>)
the carrier of (3,x2,f,<*X,S,x1*>) is non empty finite V95() set
the carrier' of (3,x2,f,<*X,S,x1*>) is non empty set
union the carrier' of (3,x2,f,<*X,S,x1*>) is set
a is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (x2)
the carrier of a is non empty set
InnerVertices a is Element of bool the carrier of a
bool the carrier of a is set
the ResultSort of a is Relation-like the carrier' of a -defined the carrier of a -valued Function-like V30( the carrier' of a, the carrier of a) Element of bool [: the carrier' of a, the carrier of a:]
the carrier' of a is non empty set
[: the carrier' of a, the carrier of a:] is Relation-like set
bool [: the carrier' of a, the carrier of a:] is set
K488( the carrier of a, the ResultSort of a) is Element of bool the carrier of a
InputVertices a is Element of bool the carrier of a
the carrier of a \ K488( the carrier of a, the ResultSort of a) is Element of bool the carrier of a
(x2,a,(3,x2,f,<*X,S,x1*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (x2)
InputVertices (x2,a,(3,x2,f,<*X,S,x1*>)) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) is non empty set
bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) is set
the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>)) is Relation-like the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)) -defined the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) -valued Function-like V30( the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))) Element of bool [: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):]
the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)) is non empty set
[: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):] is Relation-like set
bool [: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):] is set
K488( the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)), the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>))) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) \ K488( the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)), the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>))) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
(InputVertices a) \/ {X,S} is non empty set
proj2 <*X,S,x1*> is non empty finite V95() set
{X,S,x1} is finite V95() set
{x1} is non empty finite V95() set
{X,S} \/ {x1} is non empty finite V95() set
X is set
S is set
x1 is set
<*X,S,x1*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
{x1} is non empty finite V95() set
x2 is non empty finite V95() set
3 -tuples_on x2 is non empty functional FinSequence-membered FinSequenceSet of x2
[:(3 -tuples_on x2),x2:] is Relation-like set
bool [:(3 -tuples_on x2),x2:] is set
f is Relation-like 3 -tuples_on x2 -defined x2 -valued Function-like V30(3 -tuples_on x2,x2) Element of bool [:(3 -tuples_on x2),x2:]
(3,x2,f,<*X,S,x1*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (x2)
((3,x2,f,<*X,S,x1*>)) is pair non empty Element of the carrier of (3,x2,f,<*X,S,x1*>)
the carrier of (3,x2,f,<*X,S,x1*>) is non empty finite V95() set
the carrier' of (3,x2,f,<*X,S,x1*>) is non empty set
union the carrier' of (3,x2,f,<*X,S,x1*>) is set
a is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (x2)
the carrier of a is non empty set
InnerVertices a is Element of bool the carrier of a
bool the carrier of a is set
the ResultSort of a is Relation-like the carrier' of a -defined the carrier of a -valued Function-like V30( the carrier' of a, the carrier of a) Element of bool [: the carrier' of a, the carrier of a:]
the carrier' of a is non empty set
[: the carrier' of a, the carrier of a:] is Relation-like set
bool [: the carrier' of a, the carrier of a:] is set
K488( the carrier of a, the ResultSort of a) is Element of bool the carrier of a
InputVertices a is Element of bool the carrier of a
the carrier of a \ K488( the carrier of a, the ResultSort of a) is Element of bool the carrier of a
(x2,a,(3,x2,f,<*X,S,x1*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (x2)
InputVertices (x2,a,(3,x2,f,<*X,S,x1*>)) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) is non empty set
bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) is set
the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>)) is Relation-like the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)) -defined the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) -valued Function-like V30( the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))) Element of bool [: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):]
the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)) is non empty set
[: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):] is Relation-like set
bool [: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):] is set
K488( the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)), the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>))) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) \ K488( the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)), the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>))) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
(InputVertices a) \/ {x1} is non empty set
proj2 <*X,S,x1*> is non empty finite V95() set
{X,S,x1} is finite V95() set
{X,S} is non empty finite V95() set
{X,S} \/ {x1} is non empty finite V95() set
X is set
x1 is set
S is set
<*X,S,x1*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
{S} is non empty finite V95() set
x2 is non empty finite V95() set
3 -tuples_on x2 is non empty functional FinSequence-membered FinSequenceSet of x2
[:(3 -tuples_on x2),x2:] is Relation-like set
bool [:(3 -tuples_on x2),x2:] is set
f is Relation-like 3 -tuples_on x2 -defined x2 -valued Function-like V30(3 -tuples_on x2,x2) Element of bool [:(3 -tuples_on x2),x2:]
(3,x2,f,<*X,S,x1*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (x2)
((3,x2,f,<*X,S,x1*>)) is pair non empty Element of the carrier of (3,x2,f,<*X,S,x1*>)
the carrier of (3,x2,f,<*X,S,x1*>) is non empty finite V95() set
the carrier' of (3,x2,f,<*X,S,x1*>) is non empty set
union the carrier' of (3,x2,f,<*X,S,x1*>) is set
a is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (x2)
the carrier of a is non empty set
InnerVertices a is Element of bool the carrier of a
bool the carrier of a is set
the ResultSort of a is Relation-like the carrier' of a -defined the carrier of a -valued Function-like V30( the carrier' of a, the carrier of a) Element of bool [: the carrier' of a, the carrier of a:]
the carrier' of a is non empty set
[: the carrier' of a, the carrier of a:] is Relation-like set
bool [: the carrier' of a, the carrier of a:] is set
K488( the carrier of a, the ResultSort of a) is Element of bool the carrier of a
InputVertices a is Element of bool the carrier of a
the carrier of a \ K488( the carrier of a, the ResultSort of a) is Element of bool the carrier of a
(x2,a,(3,x2,f,<*X,S,x1*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (x2)
InputVertices (x2,a,(3,x2,f,<*X,S,x1*>)) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) is non empty set
bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) is set
the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>)) is Relation-like the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)) -defined the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) -valued Function-like V30( the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))) Element of bool [: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):]
the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)) is non empty set
[: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):] is Relation-like set
bool [: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):] is set
K488( the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)), the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>))) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) \ K488( the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)), the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>))) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
(InputVertices a) \/ {S} is non empty set
proj2 <*X,S,x1*> is non empty finite V95() set
{X,S,x1} is finite V95() set
{S,X,x1} is finite V95() set
{X,x1} is non empty finite V95() set
{S} \/ {X,x1} is non empty finite V95() set
S is set
x1 is set
X is set
<*X,S,x1*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
{X} is non empty finite V95() set
x2 is non empty finite V95() set
3 -tuples_on x2 is non empty functional FinSequence-membered FinSequenceSet of x2
[:(3 -tuples_on x2),x2:] is Relation-like set
bool [:(3 -tuples_on x2),x2:] is set
f is Relation-like 3 -tuples_on x2 -defined x2 -valued Function-like V30(3 -tuples_on x2,x2) Element of bool [:(3 -tuples_on x2),x2:]
(3,x2,f,<*X,S,x1*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (x2)
((3,x2,f,<*X,S,x1*>)) is pair non empty Element of the carrier of (3,x2,f,<*X,S,x1*>)
the carrier of (3,x2,f,<*X,S,x1*>) is non empty finite V95() set
the carrier' of (3,x2,f,<*X,S,x1*>) is non empty set
union the carrier' of (3,x2,f,<*X,S,x1*>) is set
a is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (x2)
the carrier of a is non empty set
InnerVertices a is Element of bool the carrier of a
bool the carrier of a is set
the ResultSort of a is Relation-like the carrier' of a -defined the carrier of a -valued Function-like V30( the carrier' of a, the carrier of a) Element of bool [: the carrier' of a, the carrier of a:]
the carrier' of a is non empty set
[: the carrier' of a, the carrier of a:] is Relation-like set
bool [: the carrier' of a, the carrier of a:] is set
K488( the carrier of a, the ResultSort of a) is Element of bool the carrier of a
InputVertices a is Element of bool the carrier of a
the carrier of a \ K488( the carrier of a, the ResultSort of a) is Element of bool the carrier of a
(x2,a,(3,x2,f,<*X,S,x1*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (x2)
InputVertices (x2,a,(3,x2,f,<*X,S,x1*>)) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) is non empty set
bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) is set
the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>)) is Relation-like the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)) -defined the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) -valued Function-like V30( the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))) Element of bool [: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):]
the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)) is non empty set
[: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):] is Relation-like set
bool [: the carrier' of (x2,a,(3,x2,f,<*X,S,x1*>)), the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)):] is set
K488( the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)), the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>))) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)) \ K488( the carrier of (x2,a,(3,x2,f,<*X,S,x1*>)), the ResultSort of (x2,a,(3,x2,f,<*X,S,x1*>))) is Element of bool the carrier of (x2,a,(3,x2,f,<*X,S,x1*>))
(InputVertices a) \/ {X} is non empty set
proj2 <*X,S,x1*> is non empty finite V95() set
{X,S,x1} is finite V95() set
{S,x1} is non empty finite V95() set
{X} \/ {S,x1} is non empty finite V95() set
X is set
S is set
x1 is set
<*X,S,x1*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
x2 is non empty finite V95() set
3 -tuples_on x2 is non empty functional FinSequence-membered FinSequenceSet of x2
[:(3 -tuples_on x2),x2:] is Relation-like set
bool [:(3 -tuples_on x2),x2:] is set
x3 is Relation-like 3 -tuples_on x2 -defined x2 -valued Function-like V30(3 -tuples_on x2,x2) Element of bool [:(3 -tuples_on x2),x2:]
(3,x2,x3,<*X,S,x1*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (x2)
((3,x2,x3,<*X,S,x1*>)) is pair non empty Element of the carrier of (3,x2,x3,<*X,S,x1*>)
the carrier of (3,x2,x3,<*X,S,x1*>) is non empty finite V95() set
the carrier' of (3,x2,x3,<*X,S,x1*>) is non empty set
union the carrier' of (3,x2,x3,<*X,S,x1*>) is set
f is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den (x2)
the carrier of f is non empty set
InputVertices f is Element of bool the carrier of f
bool the carrier of f is set
the ResultSort of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V30( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the carrier' of f is non empty set
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
K488( the carrier of f, the ResultSort of f) is Element of bool the carrier of f
the carrier of f \ K488( the carrier of f, the ResultSort of f) is Element of bool the carrier of f
(x2,f,(3,x2,x3,<*X,S,x1*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (x2)
InputVertices (x2,f,(3,x2,x3,<*X,S,x1*>)) is Element of bool the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>))
the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)) is non empty set
bool the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)) is set
the ResultSort of (x2,f,(3,x2,x3,<*X,S,x1*>)) is Relation-like the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)) -defined the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)) -valued Function-like V30( the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)), the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>))) Element of bool [: the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)), the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)):]
the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)) is non empty set
[: the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)), the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)):] is Relation-like set
bool [: the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)), the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)):] is set
K488( the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)), the ResultSort of (x2,f,(3,x2,x3,<*X,S,x1*>))) is Element of bool the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>))
the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)) \ K488( the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)), the ResultSort of (x2,f,(3,x2,x3,<*X,S,x1*>))) is Element of bool the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>))
{X,S} is non empty finite V95() set
{x1} is non empty finite V95() set
proj2 <*X,S,x1*> is non empty finite V95() set
{X,S,x1} is finite V95() set
{X,S} \/ {x1} is non empty finite V95() set
X is non empty finite V95() set
S is non empty finite non void V79() Circuit-like unsplit gate`1=arity gate`2=den (X)
InputVertices S is finite V95() Element of bool the carrier of S
the carrier of S is non empty finite V95() set
bool the carrier of S is finite V39() V95() set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K488( the carrier of S, the ResultSort of S) is finite V95() Element of bool the carrier of S
the carrier of S \ K488( the carrier of S, the ResultSort of S) is finite V95() Element of bool the carrier of S
x1 is non-empty finite-yielding gate`2=den (S) (S) (X,S)
the Sorts of x1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
K246( the Sorts of x1) is non empty functional V93() V94() set
x2 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
x2 -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
[:(x2 -tuples_on X),X:] is Relation-like set
bool [:(x2 -tuples_on X),X:] is set
x3 is Relation-like x2 -tuples_on X -defined X -valued Function-like V30(x2 -tuples_on X,X) Element of bool [:(x2 -tuples_on X),X:]
f is Relation-like NAT -defined Function-like finite V42(x2) FinSequence-like FinSubsequence-like V95() set
(x2,X,x3,f) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (X)
((x2,X,x3,f)) is pair non empty Element of the carrier of (x2,X,x3,f)
the carrier of (x2,X,x3,f) is non empty finite V95() set
the carrier' of (x2,X,x3,f) is non empty set
union the carrier' of (x2,X,x3,f) is set
(X,S,(x2,X,x3,f)) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (X)
the carrier of (X,S,(x2,X,x3,f)) is non empty finite V95() set
(x2,X,x3,f) is strict strict non-empty non-empty finite-yielding finite-yielding gate`2=den gate`2=den ( 1GateCircStr (f,x3)) ((x2,X,x3,f)) ( 1GateCircStr (f,x3)) (X,(x2,X,x3,f))
1GateCircStr (f,x3) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
(X,S,(x2,X,x3,f),x1,(x2,X,x3,f)) is strict non-empty finite-yielding gate`2=den ((X,S,(x2,X,x3,f))) ((X,S,(x2,X,x3,f))) (X,(X,S,(x2,X,x3,f)))
the Sorts of (X,S,(x2,X,x3,f),x1,(x2,X,x3,f)) is non empty Relation-like non-empty non empty-yielding the carrier of (X,S,(x2,X,x3,f)) -defined Function-like total set
K246( the Sorts of (X,S,(x2,X,x3,f),x1,(x2,X,x3,f))) is non empty functional V93() V94() set
InnerVertices (x2,X,x3,f) is finite V95() Element of bool the carrier of (x2,X,x3,f)
bool the carrier of (x2,X,x3,f) is finite V39() V95() set
the ResultSort of (x2,X,x3,f) is Relation-like the carrier' of (x2,X,x3,f) -defined the carrier of (x2,X,x3,f) -valued Function-like V30( the carrier' of (x2,X,x3,f), the carrier of (x2,X,x3,f)) Element of bool [: the carrier' of (x2,X,x3,f), the carrier of (x2,X,x3,f):]
[: the carrier' of (x2,X,x3,f), the carrier of (x2,X,x3,f):] is Relation-like set
bool [: the carrier' of (x2,X,x3,f), the carrier of (x2,X,x3,f):] is set
K488( the carrier of (x2,X,x3,f), the ResultSort of (x2,X,x3,f)) is finite V95() Element of bool the carrier of (x2,X,x3,f)
{((x2,X,x3,f))} is non empty Relation-like finite V95() set
a is non empty Relation-like the carrier of (X,S,(x2,X,x3,f)) -defined Function-like the Sorts of (X,S,(x2,X,x3,f),x1,(x2,X,x3,f)) -compatible total Element of K246( the Sorts of (X,S,(x2,X,x3,f),x1,(x2,X,x3,f)))
a | the carrier of S is Relation-like the carrier of S -defined the carrier of (X,S,(x2,X,x3,f)) -defined Function-like the Sorts of (X,S,(x2,X,x3,f),x1,(x2,X,x3,f)) -compatible finite V95() set
((X,S,(x2,X,x3,f)),(X,S,(x2,X,x3,f),x1,(x2,X,x3,f)),a) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
b is non empty Relation-like the carrier of S -defined Function-like the Sorts of x1 -compatible total Element of K246( the Sorts of x1)
(S,x1,b) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
1 + (S,x1,b) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
the Sorts of (x2,X,x3,f) is non empty Relation-like non-empty non empty-yielding the carrier of (x2,X,x3,f) -defined Function-like total set
the carrier of (1GateCircStr (f,x3)) is non empty finite V95() set
the Sorts of (x2,X,x3,f) is non empty Relation-like non-empty non empty-yielding the carrier of (1GateCircStr (f,x3)) -defined Function-like total set
K246( the Sorts of (x2,X,x3,f)) is non empty functional V93() V94() set
Following (a,(S,x1,b)) is non empty Relation-like the carrier of (X,S,(x2,X,x3,f)) -defined Function-like the Sorts of (X,S,(x2,X,x3,f),x1,(x2,X,x3,f)) -compatible total Element of K246( the Sorts of (X,S,(x2,X,x3,f),x1,(x2,X,x3,f)))
(Following (a,(S,x1,b))) | the carrier of (x2,X,x3,f) is Relation-like the carrier of (x2,X,x3,f) -defined the carrier of (X,S,(x2,X,x3,f)) -defined Function-like the Sorts of (X,S,(x2,X,x3,f),x1,(x2,X,x3,f)) -compatible finite V95() set
c is non empty Relation-like the carrier of (1GateCircStr (f,x3)) -defined Function-like the Sorts of (x2,X,x3,f) -compatible total Element of K246( the Sorts of (x2,X,x3,f))
((1GateCircStr (f,x3)),(x2,X,x3,f),c) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
(S,x1,b) + ((1GateCircStr (f,x3)),(x2,X,x3,f),c) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
F₂() is non empty finite V95() set
F₄() is non empty finite non void V79() Circuit-like unsplit gate`1=arity gate`2=den (F₂())
1 -tuples_on F₂() is non empty functional FinSequence-membered FinSequenceSet of F₂()
[:(1 -tuples_on F₂()),F₂():] is Relation-like set
bool [:(1 -tuples_on F₂()),F₂():] is set
F₆() is Relation-like 1 -tuples_on F₂() -defined F₂() -valued Function-like V30(1 -tuples_on F₂(),F₂()) Element of bool [:(1 -tuples_on F₂()),F₂():]
F₁() is set
<*F₁()*> is non empty Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set
(1,F₂(),F₆(),<*F₁()*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (F₂())
((1,F₂(),F₆(),<*F₁()*>)) is pair non empty Element of the carrier of (1,F₂(),F₆(),<*F₁()*>)
the carrier of (1,F₂(),F₆(),<*F₁()*>) is non empty finite V95() set
the carrier' of (1,F₂(),F₆(),<*F₁()*>) is non empty set
union the carrier' of (1,F₂(),F₆(),<*F₁()*>) is set
InputVertices F₄() is finite V95() Element of bool the carrier of F₄()
the carrier of F₄() is non empty finite V95() set
bool the carrier of F₄() is finite V39() V95() set
the ResultSort of F₄() is Relation-like the carrier' of F₄() -defined the carrier of F₄() -valued Function-like V30( the carrier' of F₄(), the carrier of F₄()) Element of bool [: the carrier' of F₄(), the carrier of F₄():]
the carrier' of F₄() is non empty set
[: the carrier' of F₄(), the carrier of F₄():] is Relation-like set
bool [: the carrier' of F₄(), the carrier of F₄():] is set
K488( the carrier of F₄(), the ResultSort of F₄()) is finite V95() Element of bool the carrier of F₄()
the carrier of F₄() \ K488( the carrier of F₄(), the ResultSort of F₄()) is finite V95() Element of bool the carrier of F₄()
(F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (F₂())
the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) is non empty finite V95() set
F₅() is non-empty finite-yielding gate`2=den (F<sub>4</sub>()) (F<sub>4</sub>()) (F<sub>2</sub>(),F<sub>4</sub>())
(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>) is strict strict non-empty non-empty finite-yielding finite-yielding gate`2=den gate`2=den ( 1GateCircStr (<*F<sub>1</sub>()*>,F<sub>6</sub>())) ((1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)) ( 1GateCircStr (<*F<sub>1</sub>()*>,F<sub>6</sub>())) (F<sub>2</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>))
1GateCircStr (<*F<sub>1</sub>()*>,F<sub>6</sub>()) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
(F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>),F<sub>5</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)) is strict non-empty finite-yielding gate`2=den ((F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>))) ((F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>))) (F₂(),(F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)))
the Sorts of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)) is non empty Relation-like non-empty non empty-yielding the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) -defined Function-like total set
K246( the Sorts of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>))) is non empty functional V93() V94() set
the Sorts of F₅() is non empty Relation-like non-empty non empty-yielding the carrier of F₄() -defined Function-like total set
K246( the Sorts of F₅()) is non empty functional V93() V94() set
InnerVertices F₄() is finite V95() Element of bool the carrier of F₄()
S is non empty Relation-like the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) -defined Function-like the Sorts of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)) -compatible total Element of K246( the Sorts of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)))
S | the carrier of F₄() is Relation-like the carrier of F₄() -defined the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) -defined Function-like the Sorts of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)) -compatible finite V95() set
S . F₁() is set
((F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)),(F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)),S) is non empty Relation-like the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) -defined Function-like the Sorts of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)) -compatible total Element of K246( the Sorts of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)))
((F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)),(F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)),S) . ((1,F₂(),F₆(),<*F₁()*>)) is set
x1 is non empty Relation-like the carrier of F₄() -defined Function-like the Sorts of F₅() -compatible total Element of K246( the Sorts of F₅())
(F₄(),F₅(),x1) is non empty Relation-like the carrier of F₄() -defined Function-like the Sorts of F₅() -compatible total Element of K246( the Sorts of F₅())
(F₄(),F₅(),x1) . F₁() is set
proj2 <*F₁()*> is non empty finite V95() set
{F₁()} is non empty finite V95() set
InputVertices (1,F₂(),F₆(),<*F₁()*>) is finite V95() Element of bool the carrier of (1,F₂(),F₆(),<*F₁()*>)
bool the carrier of (1,F₂(),F₆(),<*F₁()*>) is finite V39() V95() set
the ResultSort of (1,F₂(),F₆(),<*F₁()*>) is Relation-like the carrier' of (1,F₂(),F₆(),<*F₁()*>) -defined the carrier of (1,F₂(),F₆(),<*F₁()*>) -valued Function-like V30( the carrier' of (1,F₂(),F₆(),<*F₁()*>), the carrier of (1,F₂(),F₆(),<*F₁()*>)) Element of bool [: the carrier' of (1,F₂(),F₆(),<*F₁()*>), the carrier of (1,F₂(),F₆(),<*F₁()*>):]
[: the carrier' of (1,F₂(),F₆(),<*F₁()*>), the carrier of (1,F₂(),F₆(),<*F₁()*>):] is Relation-like set
bool [: the carrier' of (1,F₂(),F₆(),<*F₁()*>), the carrier of (1,F₂(),F₆(),<*F₁()*>):] is set
K488( the carrier of (1,F₂(),F₆(),<*F₁()*>), the ResultSort of (1,F₂(),F₆(),<*F₁()*>)) is finite V95() Element of bool the carrier of (1,F₂(),F₆(),<*F₁()*>)
the carrier of (1,F₂(),F₆(),<*F₁()*>) \ K488( the carrier of (1,F₂(),F₆(),<*F₁()*>), the ResultSort of (1,F₂(),F₆(),<*F₁()*>)) is finite V95() Element of bool the carrier of (1,F₂(),F₆(),<*F₁()*>)
(InputVertices (1,F₂(),F₆(),<*F₁()*>)) \ (InnerVertices F₄()) is finite V95() Element of bool the carrier of (1,F₂(),F₆(),<*F₁()*>)
InnerVertices (1,F₂(),F₆(),<*F₁()*>) is finite V95() Element of bool the carrier of (1,F₂(),F₆(),<*F₁()*>)
{((1,F₂(),F₆(),<*F₁()*>))} is non empty Relation-like finite V95() set
(F₄(),F₅(),x1) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (S,(F₄(),F₅(),x1)) is non empty Relation-like the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) -defined Function-like the Sorts of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)) -compatible total Element of K246( the Sorts of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)))
(Following (S,(F₄(),F₅(),x1))) | the carrier of F₄() is Relation-like the carrier of F₄() -defined the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) -defined Function-like the Sorts of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)) -compatible finite V95() set
Following (x1,(F₄(),F₅(),x1)) is non empty Relation-like the carrier of F₄() -defined Function-like the Sorts of F₅() -compatible total Element of K246( the Sorts of F₅())
InputVertices (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) is finite V95() Element of bool the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>))
bool the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) is finite V39() V95() set
the ResultSort of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) is Relation-like the carrier' of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) -defined the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) -valued Function-like V30( the carrier' of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)), the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>))) Element of bool [: the carrier' of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)), the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)):]
the carrier' of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) is non empty set
[: the carrier' of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)), the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)):] is Relation-like set
bool [: the carrier' of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)), the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)):] is set
K488( the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)), the ResultSort of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>))) is finite V95() Element of bool the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>))
the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) \ K488( the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)), the ResultSort of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>))) is finite V95() Element of bool the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>))
(InputVertices F₄()) \/ ((InputVertices (1,F₂(),F₆(),<*F₁()*>)) \ (InnerVertices F₄())) is finite V95() set
x2 is Element of F₂()
F₃(x2) is Element of F₂()
(Following (S,(F₄(),F₅(),x1))) . F₁() is set
[<*F₁()*>,F₆()] is pair non empty set
{<*F₁()*>,F₆()} is non empty functional finite V95() set
{<*F₁()*>} is non empty functional finite V39() V93() V95() set
{{<*F₁()*>,F₆()},{<*F₁()*>}} is non empty finite V39() V95() set
{[<*F₁()*>,F₆()]} is non empty Relation-like Function-like finite V95() set
the carrier' of F₄() \/ {[<*F₁()*>,F₆()]} is non empty set
x3 is Element of the carrier' of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>))
the_result_sort_of x3 is Element of the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>))
the ResultSort of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) . x3 is Element of the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>))
x3 `2 is Relation-like Function-like set
the carrier of F<sub>4</sub>() \/ the carrier of (1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>) is non empty finite V95() set
the carrier of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>))
the Arity of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)) is Relation-like the carrier' of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)) -defined the carrier of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)) * -valued Function-like V30( the carrier' of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)), the carrier of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)) * ) Function-yielding V34() Element of bool [: the carrier' of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)),( the carrier of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)) *):]
[: the carrier' of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)),( the carrier of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)) *):] is Relation-like set
bool [: the carrier' of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)),( the carrier of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)) *):] is set
the Arity of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)) . x3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V95() Element of the carrier of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)) *
[( the Arity of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)) . x3),(x3 `2)] is pair non empty set
{( the Arity of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) . x3),(x3 `2)} is non empty functional finite V95() set
{( the Arity of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)) . x3)} is non empty functional finite V39() V93() V95() set
{{( the Arity of (F<sub>2</sub>(),F<sub>4</sub>(),(1,F<sub>2</sub>(),F<sub>6</sub>(),<*F<sub>1</sub>()*>)) . x3),(x3 `2)},{( the Arity of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) . x3)}} is non empty finite V39() V95() set
the_arity_of x3 is Relation-like NAT -defined the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) -valued Function-like finite FinSequence-like FinSubsequence-like V95() Element of the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) *
proj1 (Following (S,(F₄(),F₅(),x1))) is non empty set
<*F₁()*> * (Following (S,(F₄(),F₅(),x1))) is Relation-like NAT -defined Function-like finite V95() set
<*x2*> is non empty Relation-like NAT -defined F₂() -valued Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() FinSequence of F₂()
((F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)),(F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)),S) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
1 + (F₄(),F₅(),x1) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (S,(1 + (F₄(),F₅(),x1))) is non empty Relation-like the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) -defined Function-like the Sorts of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)) -compatible total Element of K246( the Sorts of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)))
(Following (S,(1 + (F₄(),F₅(),x1)))) . ((1,F₂(),F₆(),<*F₁()*>)) is set
Following (Following (S,(F₄(),F₅(),x1))) is non empty Relation-like the carrier of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>)) -defined Function-like the Sorts of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)) -compatible total Element of K246( the Sorts of (F₂(),F₄(),(1,F₂(),F₆(),<*F₁()*>),F₅(),(1,F₂(),F₆(),<*F₁()*>)))
(Following (Following (S,(F₄(),F₅(),x1)))) . x3 is set
F₆() . (<*F₁()*> * (Following (S,(F₄(),F₅(),x1)))) is set
F₃() is non empty finite V95() set
F₅() is non empty finite non void V79() Circuit-like unsplit gate`1=arity gate`2=den (F₃())
2 -tuples_on F₃() is non empty functional FinSequence-membered FinSequenceSet of F₃()
[:(2 -tuples_on F₃()),F₃():] is Relation-like set
bool [:(2 -tuples_on F₃()),F₃():] is set
F₇() is Relation-like 2 -tuples_on F₃() -defined F₃() -valued Function-like V30(2 -tuples_on F₃(),F₃()) Element of bool [:(2 -tuples_on F₃()),F₃():]
F₁() is set
F₂() is set
<*F₁(),F₂()*> is non empty Relation-like NAT -defined Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() set
(2,F₃(),F₇(),<*F₁(),F₂()*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (F₃())
((2,F₃(),F₇(),<*F₁(),F₂()*>)) is pair non empty Element of the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>)
the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>) is non empty finite V95() set
the carrier' of (2,F₃(),F₇(),<*F₁(),F₂()*>) is non empty set
union the carrier' of (2,F₃(),F₇(),<*F₁(),F₂()*>) is set
InputVertices F₅() is finite V95() Element of bool the carrier of F₅()
the carrier of F₅() is non empty finite V95() set
bool the carrier of F₅() is finite V39() V95() set
the ResultSort of F₅() is Relation-like the carrier' of F₅() -defined the carrier of F₅() -valued Function-like V30( the carrier' of F₅(), the carrier of F₅()) Element of bool [: the carrier' of F₅(), the carrier of F₅():]
the carrier' of F₅() is non empty set
[: the carrier' of F₅(), the carrier of F₅():] is Relation-like set
bool [: the carrier' of F₅(), the carrier of F₅():] is set
K488( the carrier of F₅(), the ResultSort of F₅()) is finite V95() Element of bool the carrier of F₅()
the carrier of F₅() \ K488( the carrier of F₅(), the ResultSort of F₅()) is finite V95() Element of bool the carrier of F₅()
(F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (F₃())
the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) is non empty finite V95() set
F₆() is non-empty finite-yielding gate`2=den (F<sub>5</sub>()) (F<sub>5</sub>()) (F<sub>3</sub>(),F<sub>5</sub>())
(2,F<sub>3</sub>(),F<sub>7</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>()*>) is strict strict non-empty non-empty finite-yielding finite-yielding gate`2=den gate`2=den ( 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>()*>,F<sub>7</sub>())) ((2,F<sub>3</sub>(),F<sub>7</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>()*>)) ( 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>()*>,F<sub>7</sub>())) (F<sub>3</sub>(),(2,F<sub>3</sub>(),F<sub>7</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>()*>))
1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>()*>,F<sub>7</sub>()) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
(F<sub>3</sub>(),F<sub>5</sub>(),(2,F<sub>3</sub>(),F<sub>7</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>()*>),F<sub>6</sub>(),(2,F<sub>3</sub>(),F<sub>7</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>()*>)) is strict non-empty finite-yielding gate`2=den ((F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>))) ((F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>))) (F₃(),(F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)))
the Sorts of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) is non empty Relation-like non-empty non empty-yielding the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -defined Function-like total set
K246( the Sorts of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>))) is non empty functional V93() V94() set
the Sorts of F₆() is non empty Relation-like non-empty non empty-yielding the carrier of F₅() -defined Function-like total set
K246( the Sorts of F₆()) is non empty functional V93() V94() set
InnerVertices F₅() is finite V95() Element of bool the carrier of F₅()
S is non empty Relation-like the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -defined Function-like the Sorts of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -compatible total Element of K246( the Sorts of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)))
S | the carrier of F₅() is Relation-like the carrier of F₅() -defined the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -defined Function-like the Sorts of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -compatible finite V95() set
S . F₁() is set
S . F₂() is set
((F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)),(F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)),S) is non empty Relation-like the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -defined Function-like the Sorts of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -compatible total Element of K246( the Sorts of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)))
((F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)),(F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)),S) . ((2,F₃(),F₇(),<*F₁(),F₂()*>)) is set
x1 is non empty Relation-like the carrier of F₅() -defined Function-like the Sorts of F₆() -compatible total Element of K246( the Sorts of F₆())
(F₅(),F₆(),x1) is non empty Relation-like the carrier of F₅() -defined Function-like the Sorts of F₆() -compatible total Element of K246( the Sorts of F₆())
(F₅(),F₆(),x1) . F₁() is set
(F₅(),F₆(),x1) . F₂() is set
InnerVertices (2,F₃(),F₇(),<*F₁(),F₂()*>) is finite V95() Element of bool the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>)
bool the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>) is finite V39() V95() set
the ResultSort of (2,F₃(),F₇(),<*F₁(),F₂()*>) is Relation-like the carrier' of (2,F₃(),F₇(),<*F₁(),F₂()*>) -defined the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>) -valued Function-like V30( the carrier' of (2,F₃(),F₇(),<*F₁(),F₂()*>), the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>)) Element of bool [: the carrier' of (2,F₃(),F₇(),<*F₁(),F₂()*>), the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>):]
[: the carrier' of (2,F₃(),F₇(),<*F₁(),F₂()*>), the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>):] is Relation-like set
bool [: the carrier' of (2,F₃(),F₇(),<*F₁(),F₂()*>), the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>):] is set
K488( the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>), the ResultSort of (2,F₃(),F₇(),<*F₁(),F₂()*>)) is finite V95() Element of bool the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>)
{((2,F₃(),F₇(),<*F₁(),F₂()*>))} is non empty Relation-like finite V95() set
(F₅(),F₆(),x1) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (S,(F₅(),F₆(),x1)) is non empty Relation-like the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -defined Function-like the Sorts of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -compatible total Element of K246( the Sorts of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)))
(Following (S,(F₅(),F₆(),x1))) | the carrier of F₅() is Relation-like the carrier of F₅() -defined the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -defined Function-like the Sorts of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -compatible finite V95() set
Following (x1,(F₅(),F₆(),x1)) is non empty Relation-like the carrier of F₅() -defined Function-like the Sorts of F₆() -compatible total Element of K246( the Sorts of F₆())
[<*F₁(),F₂()*>,F₇()] is pair non empty set
{<*F₁(),F₂()*>,F₇()} is non empty functional finite V95() set
{<*F₁(),F₂()*>} is non empty functional finite V39() V93() V95() set
{{<*F₁(),F₂()*>,F₇()},{<*F₁(),F₂()*>}} is non empty finite V39() V95() set
{[<*F₁(),F₂()*>,F₇()]} is non empty Relation-like Function-like finite V95() set
the carrier' of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) is non empty set
the carrier' of F₅() \/ {[<*F₁(),F₂()*>,F₇()]} is non empty set
x3 is Element of F₃()
f is Element of F₃()
F₄(x3,f) is Element of F₃()
InputVertices (2,F₃(),F₇(),<*F₁(),F₂()*>) is finite V95() Element of bool the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>)
the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>) \ K488( the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>), the ResultSort of (2,F₃(),F₇(),<*F₁(),F₂()*>)) is finite V95() Element of bool the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>)
proj2 <*F₁(),F₂()*> is non empty finite V95() set
InputVertices (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) is finite V95() Element of bool the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>))
bool the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) is finite V39() V95() set
the ResultSort of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) is Relation-like the carrier' of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -defined the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -valued Function-like V30( the carrier' of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)), the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>))) Element of bool [: the carrier' of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)), the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)):]
[: the carrier' of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)), the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)):] is Relation-like set
bool [: the carrier' of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)), the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)):] is set
K488( the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)), the ResultSort of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>))) is finite V95() Element of bool the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>))
the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) \ K488( the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)), the ResultSort of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>))) is finite V95() Element of bool the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>))
(InputVertices (2,F₃(),F₇(),<*F₁(),F₂()*>)) \ (InnerVertices F₅()) is finite V95() Element of bool the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>)
(InputVertices F₅()) \/ ((InputVertices (2,F₃(),F₇(),<*F₁(),F₂()*>)) \ (InnerVertices F₅())) is finite V95() set
{F₁(),F₂()} is non empty finite V95() set
(Following (S,(F₅(),F₆(),x1))) . F₂() is set
(Following (S,(F₅(),F₆(),x1))) . F₁() is set
x2 is Element of the carrier' of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>))
the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>))
the Arity of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) is Relation-like the carrier' of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -defined the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) * -valued Function-like V30( the carrier' of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)), the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) * ) Function-yielding V34() Element of bool [: the carrier' of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)),( the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) *):]
[: the carrier' of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)),( the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) *):] is Relation-like set
bool [: the carrier' of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)),( the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) *):] is set
the Arity of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) . x2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V95() Element of the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) *
x2 `2 is Relation-like Function-like set
[( the Arity of (F<sub>3</sub>(),F<sub>5</sub>(),(2,F<sub>3</sub>(),F<sub>7</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>()*>)) . x2),(x2 `2)] is pair non empty set
{( the Arity of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) . x2),(x2 `2)} is non empty functional finite V95() set
{( the Arity of (F<sub>3</sub>(),F<sub>5</sub>(),(2,F<sub>3</sub>(),F<sub>7</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>()*>)) . x2)} is non empty functional finite V39() V93() V95() set
{{( the Arity of (F<sub>3</sub>(),F<sub>5</sub>(),(2,F<sub>3</sub>(),F<sub>7</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>()*>)) . x2),(x2 `2)},{( the Arity of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) . x2)}} is non empty finite V39() V95() set
the_arity_of x2 is Relation-like NAT -defined the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -valued Function-like finite FinSequence-like FinSubsequence-like V95() Element of the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) *
the carrier of F₅() \/ the carrier of (2,F₃(),F₇(),<*F₁(),F₂()*>) is non empty finite V95() set
proj1 (Following (S,(F₅(),F₆(),x1))) is non empty set
<*F₁(),F₂()*> * (Following (S,(F₅(),F₆(),x1))) is Relation-like NAT -defined Function-like finite V95() set
<*x3,f*> is non empty Relation-like NAT -defined F₃() -valued Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() FinSequence of F₃()
the_result_sort_of x2 is Element of the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>))
the ResultSort of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) . x2 is Element of the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>))
((F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)),(F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)),S) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
1 + (F₅(),F₆(),x1) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (S,(1 + (F₅(),F₆(),x1))) is non empty Relation-like the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -defined Function-like the Sorts of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -compatible total Element of K246( the Sorts of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)))
(Following (S,(1 + (F₅(),F₆(),x1)))) . ((2,F₃(),F₇(),<*F₁(),F₂()*>)) is set
Following (Following (S,(F₅(),F₆(),x1))) is non empty Relation-like the carrier of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -defined Function-like the Sorts of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)) -compatible total Element of K246( the Sorts of (F₃(),F₅(),(2,F₃(),F₇(),<*F₁(),F₂()*>),F₆(),(2,F₃(),F₇(),<*F₁(),F₂()*>)))
(Following (Following (S,(F₅(),F₆(),x1)))) . x2 is set
F₇() . (<*F₁(),F₂()*> * (Following (S,(F₅(),F₆(),x1)))) is set
F₄() is non empty finite V95() set
F₆() is non empty finite non void V79() Circuit-like unsplit gate`1=arity gate`2=den (F₄())
3 -tuples_on F₄() is non empty functional FinSequence-membered FinSequenceSet of F₄()
[:(3 -tuples_on F₄()),F₄():] is Relation-like set
bool [:(3 -tuples_on F₄()),F₄():] is set
F₈() is Relation-like 3 -tuples_on F₄() -defined F₄() -valued Function-like V30(3 -tuples_on F₄(),F₄()) Element of bool [:(3 -tuples_on F₄()),F₄():]
F₁() is set
F₂() is set
F₃() is set
<*F₁(),F₂(),F₃()*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (F₄())
((3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) is pair non empty Element of the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)
the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>) is non empty finite V95() set
the carrier' of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>) is non empty set
union the carrier' of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>) is set
InputVertices F₆() is finite V95() Element of bool the carrier of F₆()
the carrier of F₆() is non empty finite V95() set
bool the carrier of F₆() is finite V39() V95() set
the ResultSort of F₆() is Relation-like the carrier' of F₆() -defined the carrier of F₆() -valued Function-like V30( the carrier' of F₆(), the carrier of F₆()) Element of bool [: the carrier' of F₆(), the carrier of F₆():]
the carrier' of F₆() is non empty set
[: the carrier' of F₆(), the carrier of F₆():] is Relation-like set
bool [: the carrier' of F₆(), the carrier of F₆():] is set
K488( the carrier of F₆(), the ResultSort of F₆()) is finite V95() Element of bool the carrier of F₆()
the carrier of F₆() \ K488( the carrier of F₆(), the ResultSort of F₆()) is finite V95() Element of bool the carrier of F₆()
(F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (F₄())
the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) is non empty finite V95() set
F₇() is non-empty finite-yielding gate`2=den (F<sub>6</sub>()) (F<sub>6</sub>()) (F<sub>4</sub>(),F<sub>6</sub>())
(3,F<sub>4</sub>(),F<sub>8</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>()*>) is strict strict non-empty non-empty finite-yielding finite-yielding gate`2=den gate`2=den ( 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>()*>,F<sub>8</sub>())) ((3,F<sub>4</sub>(),F<sub>8</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>()*>)) ( 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>()*>,F<sub>8</sub>())) (F<sub>4</sub>(),(3,F<sub>4</sub>(),F<sub>8</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>()*>))
1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>()*>,F<sub>8</sub>()) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
(F<sub>4</sub>(),F<sub>6</sub>(),(3,F<sub>4</sub>(),F<sub>8</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>()*>),F<sub>7</sub>(),(3,F<sub>4</sub>(),F<sub>8</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>()*>)) is strict non-empty finite-yielding gate`2=den ((F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>))) ((F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>))) (F₄(),(F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)))
the Sorts of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) is non empty Relation-like non-empty non empty-yielding the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -defined Function-like total set
K246( the Sorts of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>))) is non empty functional V93() V94() set
the Sorts of F₇() is non empty Relation-like non-empty non empty-yielding the carrier of F₆() -defined Function-like total set
K246( the Sorts of F₇()) is non empty functional V93() V94() set
InnerVertices F₆() is finite V95() Element of bool the carrier of F₆()
S is non empty Relation-like the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -defined Function-like the Sorts of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -compatible total Element of K246( the Sorts of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)))
S | the carrier of F₆() is Relation-like the carrier of F₆() -defined the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -defined Function-like the Sorts of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -compatible finite V95() set
S . F₁() is set
S . F₂() is set
S . F₃() is set
((F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)),(F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)),S) is non empty Relation-like the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -defined Function-like the Sorts of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -compatible total Element of K246( the Sorts of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)))
((F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)),(F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)),S) . ((3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) is set
x1 is non empty Relation-like the carrier of F₆() -defined Function-like the Sorts of F₇() -compatible total Element of K246( the Sorts of F₇())
(F₆(),F₇(),x1) is non empty Relation-like the carrier of F₆() -defined Function-like the Sorts of F₇() -compatible total Element of K246( the Sorts of F₇())
(F₆(),F₇(),x1) . F₁() is set
(F₆(),F₇(),x1) . F₂() is set
(F₆(),F₇(),x1) . F₃() is set
InnerVertices (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>) is finite V95() Element of bool the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)
bool the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>) is finite V39() V95() set
the ResultSort of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>) is Relation-like the carrier' of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>) -defined the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>) -valued Function-like V30( the carrier' of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>), the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) Element of bool [: the carrier' of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>), the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>):]
[: the carrier' of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>), the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>):] is Relation-like set
bool [: the carrier' of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>), the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>):] is set
K488( the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>), the ResultSort of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) is finite V95() Element of bool the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)
{((3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>))} is non empty Relation-like finite V95() set
(F₆(),F₇(),x1) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (S,(F₆(),F₇(),x1)) is non empty Relation-like the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -defined Function-like the Sorts of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -compatible total Element of K246( the Sorts of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)))
(Following (S,(F₆(),F₇(),x1))) | the carrier of F₆() is Relation-like the carrier of F₆() -defined the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -defined Function-like the Sorts of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -compatible finite V95() set
Following (x1,(F₆(),F₇(),x1)) is non empty Relation-like the carrier of F₆() -defined Function-like the Sorts of F₇() -compatible total Element of K246( the Sorts of F₇())
InputVertices (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) is finite V95() Element of bool the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>))
bool the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) is finite V39() V95() set
the ResultSort of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) is Relation-like the carrier' of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -defined the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -valued Function-like V30( the carrier' of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)), the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>))) Element of bool [: the carrier' of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)), the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)):]
the carrier' of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) is non empty set
[: the carrier' of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)), the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)):] is Relation-like set
bool [: the carrier' of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)), the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)):] is set
K488( the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)), the ResultSort of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>))) is finite V95() Element of bool the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>))
the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) \ K488( the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)), the ResultSort of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>))) is finite V95() Element of bool the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>))
InputVertices (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>) is finite V95() Element of bool the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)
the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>) \ K488( the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>), the ResultSort of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) is finite V95() Element of bool the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)
(InputVertices (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) \ (InnerVertices F₆()) is finite V95() Element of bool the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)
(InputVertices F₆()) \/ ((InputVertices (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) \ (InnerVertices F₆())) is finite V95() set
[<*F₁(),F₂(),F₃()*>,F₈()] is pair non empty set
{<*F₁(),F₂(),F₃()*>,F₈()} is non empty functional finite V95() set
{<*F₁(),F₂(),F₃()*>} is non empty functional finite V39() V93() V95() set
{{<*F₁(),F₂(),F₃()*>,F₈()},{<*F₁(),F₂(),F₃()*>}} is non empty finite V39() V95() set
{[<*F₁(),F₂(),F₃()*>,F₈()]} is non empty Relation-like Function-like finite V95() set
the carrier' of F₆() \/ {[<*F₁(),F₂(),F₃()*>,F₈()]} is non empty set
x3 is Element of F₄()
f is Element of F₄()
a is Element of F₄()
F₅(x3,f,a) is Element of F₄()
proj2 <*F₁(),F₂(),F₃()*> is non empty finite V95() set
x2 is Element of the carrier' of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>))
the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>))
the Arity of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) is Relation-like the carrier' of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -defined the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) * -valued Function-like V30( the carrier' of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)), the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) * ) Function-yielding V34() Element of bool [: the carrier' of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)),( the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) *):]
[: the carrier' of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)),( the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) *):] is Relation-like set
bool [: the carrier' of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)),( the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) *):] is set
the Arity of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) . x2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V95() Element of the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) *
x2 `2 is Relation-like Function-like set
[( the Arity of (F<sub>4</sub>(),F<sub>6</sub>(),(3,F<sub>4</sub>(),F<sub>8</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>()*>)) . x2),(x2 `2)] is pair non empty set
{( the Arity of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) . x2),(x2 `2)} is non empty functional finite V95() set
{( the Arity of (F<sub>4</sub>(),F<sub>6</sub>(),(3,F<sub>4</sub>(),F<sub>8</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>()*>)) . x2)} is non empty functional finite V39() V93() V95() set
{{( the Arity of (F<sub>4</sub>(),F<sub>6</sub>(),(3,F<sub>4</sub>(),F<sub>8</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>()*>)) . x2),(x2 `2)},{( the Arity of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) . x2)}} is non empty finite V39() V95() set
the_arity_of x2 is Relation-like NAT -defined the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -valued Function-like finite FinSequence-like FinSubsequence-like V95() Element of the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) *
the carrier of F₆() \/ the carrier of (3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>) is non empty finite V95() set
{F₁(),F₂(),F₃()} is finite V95() set
(Following (S,(F₆(),F₇(),x1))) . F₃() is set
proj1 (Following (S,(F₆(),F₇(),x1))) is non empty set
(Following (S,(F₆(),F₇(),x1))) . F₁() is set
(Following (S,(F₆(),F₇(),x1))) . F₂() is set
<*F₁(),F₂(),F₃()*> * (Following (S,(F₆(),F₇(),x1))) is Relation-like NAT -defined Function-like finite V95() set
<*x3,f,a*> is non empty Relation-like NAT -defined F₄() -valued Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() FinSequence of F₄()
the_result_sort_of x2 is Element of the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>))
the ResultSort of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) . x2 is Element of the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>))
((F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)),(F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)),S) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
1 + (F₆(),F₇(),x1) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (S,(1 + (F₆(),F₇(),x1))) is non empty Relation-like the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -defined Function-like the Sorts of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -compatible total Element of K246( the Sorts of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)))
(Following (S,(1 + (F₆(),F₇(),x1)))) . ((3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) is set
Following (Following (S,(F₆(),F₇(),x1))) is non empty Relation-like the carrier of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -defined Function-like the Sorts of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)) -compatible total Element of K246( the Sorts of (F₄(),F₆(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>),F₇(),(3,F₄(),F₈(),<*F₁(),F₂(),F₃()*>)))
(Following (Following (S,(F₆(),F₇(),x1)))) . x2 is set
F₈() . (<*F₁(),F₂(),F₃()*> * (Following (S,(F₆(),F₇(),x1)))) is set
F₅() is non empty finite V95() set
F₇() is non empty finite non void V79() Circuit-like unsplit gate`1=arity gate`2=den (F₅())
4 -tuples_on F₅() is non empty functional FinSequence-membered FinSequenceSet of F₅()
[:(4 -tuples_on F₅()),F₅():] is Relation-like set
bool [:(4 -tuples_on F₅()),F₅():] is set
F₉() is Relation-like 4 -tuples_on F₅() -defined F₅() -valued Function-like V30(4 -tuples_on F₅(),F₅()) Element of bool [:(4 -tuples_on F₅()),F₅():]
F₁() is set
F₂() is set
F₃() is set
F₄() is set
<*F₁(),F₂(),F₃(),F₄()*> is non empty Relation-like NAT -defined Function-like finite V42(4) FinSequence-like FinSubsequence-like V95() set
(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (F₅())
((4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) is pair non empty Element of the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)
the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>) is non empty finite V95() set
the carrier' of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>) is non empty set
union the carrier' of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>) is set
InputVertices F₇() is finite V95() Element of bool the carrier of F₇()
the carrier of F₇() is non empty finite V95() set
bool the carrier of F₇() is finite V39() V95() set
the ResultSort of F₇() is Relation-like the carrier' of F₇() -defined the carrier of F₇() -valued Function-like V30( the carrier' of F₇(), the carrier of F₇()) Element of bool [: the carrier' of F₇(), the carrier of F₇():]
the carrier' of F₇() is non empty set
[: the carrier' of F₇(), the carrier of F₇():] is Relation-like set
bool [: the carrier' of F₇(), the carrier of F₇():] is set
K488( the carrier of F₇(), the ResultSort of F₇()) is finite V95() Element of bool the carrier of F₇()
the carrier of F₇() \ K488( the carrier of F₇(), the ResultSort of F₇()) is finite V95() Element of bool the carrier of F₇()
(F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (F₅())
the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) is non empty finite V95() set
F₈() is non-empty finite-yielding gate`2=den (F<sub>7</sub>()) (F<sub>7</sub>()) (F<sub>5</sub>(),F<sub>7</sub>())
(4,F<sub>5</sub>(),F<sub>9</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>) is strict strict non-empty non-empty finite-yielding finite-yielding gate`2=den gate`2=den ( 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>,F<sub>9</sub>())) ((4,F<sub>5</sub>(),F<sub>9</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>)) ( 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>,F<sub>9</sub>())) (F<sub>5</sub>(),(4,F<sub>5</sub>(),F<sub>9</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>))
1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>,F<sub>9</sub>()) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
(F<sub>5</sub>(),F<sub>7</sub>(),(4,F<sub>5</sub>(),F<sub>9</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>),F<sub>8</sub>(),(4,F<sub>5</sub>(),F<sub>9</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>)) is strict non-empty finite-yielding gate`2=den ((F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>))) ((F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>))) (F₅(),(F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)))
the Sorts of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) is non empty Relation-like non-empty non empty-yielding the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -defined Function-like total set
K246( the Sorts of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>))) is non empty functional V93() V94() set
the Sorts of F₈() is non empty Relation-like non-empty non empty-yielding the carrier of F₇() -defined Function-like total set
K246( the Sorts of F₈()) is non empty functional V93() V94() set
InnerVertices F₇() is finite V95() Element of bool the carrier of F₇()
S is non empty Relation-like the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -defined Function-like the Sorts of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -compatible total Element of K246( the Sorts of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)))
S | the carrier of F₇() is Relation-like the carrier of F₇() -defined the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -defined Function-like the Sorts of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -compatible finite V95() set
S . F₁() is set
S . F₂() is set
S . F₃() is set
S . F₄() is set
((F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)),(F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)),S) is non empty Relation-like the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -defined Function-like the Sorts of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -compatible total Element of K246( the Sorts of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)))
((F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)),(F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)),S) . ((4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) is set
x1 is non empty Relation-like the carrier of F₇() -defined Function-like the Sorts of F₈() -compatible total Element of K246( the Sorts of F₈())
(F₇(),F₈(),x1) is non empty Relation-like the carrier of F₇() -defined Function-like the Sorts of F₈() -compatible total Element of K246( the Sorts of F₈())
(F₇(),F₈(),x1) . F₁() is set
(F₇(),F₈(),x1) . F₂() is set
(F₇(),F₈(),x1) . F₃() is set
(F₇(),F₈(),x1) . F₄() is set
InnerVertices (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>) is finite V95() Element of bool the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)
bool the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>) is finite V39() V95() set
the ResultSort of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>) is Relation-like the carrier' of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>) -defined the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>) -valued Function-like V30( the carrier' of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>), the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) Element of bool [: the carrier' of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>), the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>):]
[: the carrier' of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>), the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>):] is Relation-like set
bool [: the carrier' of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>), the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>):] is set
K488( the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>), the ResultSort of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) is finite V95() Element of bool the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)
{((4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>))} is non empty Relation-like finite V95() set
(F₇(),F₈(),x1) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (S,(F₇(),F₈(),x1)) is non empty Relation-like the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -defined Function-like the Sorts of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -compatible total Element of K246( the Sorts of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)))
(Following (S,(F₇(),F₈(),x1))) | the carrier of F₇() is Relation-like the carrier of F₇() -defined the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -defined Function-like the Sorts of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -compatible finite V95() set
Following (x1,(F₇(),F₈(),x1)) is non empty Relation-like the carrier of F₇() -defined Function-like the Sorts of F₈() -compatible total Element of K246( the Sorts of F₈())
InputVertices (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) is finite V95() Element of bool the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>))
bool the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) is finite V39() V95() set
the ResultSort of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) is Relation-like the carrier' of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -defined the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -valued Function-like V30( the carrier' of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)), the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>))) Element of bool [: the carrier' of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)), the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)):]
the carrier' of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) is non empty set
[: the carrier' of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)), the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)):] is Relation-like set
bool [: the carrier' of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)), the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)):] is set
K488( the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)), the ResultSort of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>))) is finite V95() Element of bool the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>))
the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) \ K488( the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)), the ResultSort of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>))) is finite V95() Element of bool the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>))
InputVertices (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>) is finite V95() Element of bool the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)
the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>) \ K488( the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>), the ResultSort of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) is finite V95() Element of bool the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)
(InputVertices (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) \ (InnerVertices F₇()) is finite V95() Element of bool the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)
(InputVertices F₇()) \/ ((InputVertices (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) \ (InnerVertices F₇())) is finite V95() set
[<*F₁(),F₂(),F₃(),F₄()*>,F₉()] is pair non empty set
{<*F₁(),F₂(),F₃(),F₄()*>,F₉()} is non empty functional finite V95() set
{<*F₁(),F₂(),F₃(),F₄()*>} is non empty functional finite V39() V93() V95() set
{{<*F₁(),F₂(),F₃(),F₄()*>,F₉()},{<*F₁(),F₂(),F₃(),F₄()*>}} is non empty finite V39() V95() set
the carrier of F₇() \/ the carrier of (4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>) is non empty finite V95() set
{[<*F₁(),F₂(),F₃(),F₄()*>,F₉()]} is non empty Relation-like Function-like finite V95() set
the carrier' of F₇() \/ {[<*F₁(),F₂(),F₃(),F₄()*>,F₉()]} is non empty set
x3 is Element of F₅()
f is Element of F₅()
a is Element of F₅()
b is Element of F₅()
F₆(x3,f,a,b) is Element of F₅()
proj2 <*F₁(),F₂(),F₃(),F₄()*> is non empty finite V95() set
{F₁(),F₂(),F₃(),F₄()} is finite V95() set
(Following (S,(F₇(),F₈(),x1))) . F₃() is set
x2 is Element of the carrier' of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>))
the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>))
the Arity of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) is Relation-like the carrier' of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -defined the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) * -valued Function-like V30( the carrier' of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)), the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) * ) Function-yielding V34() Element of bool [: the carrier' of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)),( the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) *):]
[: the carrier' of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)),( the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) *):] is Relation-like set
bool [: the carrier' of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)),( the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) *):] is set
the Arity of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) . x2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V95() Element of the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) *
x2 `2 is Relation-like Function-like set
[( the Arity of (F<sub>5</sub>(),F<sub>7</sub>(),(4,F<sub>5</sub>(),F<sub>9</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>)) . x2),(x2 `2)] is pair non empty set
{( the Arity of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) . x2),(x2 `2)} is non empty functional finite V95() set
{( the Arity of (F<sub>5</sub>(),F<sub>7</sub>(),(4,F<sub>5</sub>(),F<sub>9</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>)) . x2)} is non empty functional finite V39() V93() V95() set
{{( the Arity of (F<sub>5</sub>(),F<sub>7</sub>(),(4,F<sub>5</sub>(),F<sub>9</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>()*>)) . x2),(x2 `2)},{( the Arity of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) . x2)}} is non empty finite V39() V95() set
the_arity_of x2 is Relation-like NAT -defined the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -valued Function-like finite FinSequence-like FinSubsequence-like V95() Element of the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) *
(Following (S,(F₇(),F₈(),x1))) . F₁() is set
(Following (S,(F₇(),F₈(),x1))) . F₄() is set
(Following (S,(F₇(),F₈(),x1))) . F₂() is set
proj1 (Following (S,(F₇(),F₈(),x1))) is non empty set
<*F₁(),F₂(),F₃(),F₄()*> * (Following (S,(F₇(),F₈(),x1))) is Relation-like NAT -defined Function-like finite V95() set
<*x3,f,a,b*> is non empty Relation-like NAT -defined F₅() -valued Function-like finite V42(4) FinSequence-like FinSubsequence-like V95() FinSequence of F₅()
the_result_sort_of x2 is Element of the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>))
the ResultSort of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) . x2 is Element of the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>))
((F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)),(F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)),S) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
1 + (F₇(),F₈(),x1) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (S,(1 + (F₇(),F₈(),x1))) is non empty Relation-like the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -defined Function-like the Sorts of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -compatible total Element of K246( the Sorts of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)))
(Following (S,(1 + (F₇(),F₈(),x1)))) . ((4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) is set
Following (Following (S,(F₇(),F₈(),x1))) is non empty Relation-like the carrier of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -defined Function-like the Sorts of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)) -compatible total Element of K246( the Sorts of (F₅(),F₇(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>),F₈(),(4,F₅(),F₉(),<*F₁(),F₂(),F₃(),F₄()*>)))
(Following (Following (S,(F₇(),F₈(),x1)))) . x2 is set
F₉() . (<*F₁(),F₂(),F₃(),F₄()*> * (Following (S,(F₇(),F₈(),x1)))) is set
F₆() is non empty finite V95() set
F₈() is non empty finite non void V79() Circuit-like unsplit gate`1=arity gate`2=den (F₆())
5 -tuples_on F₆() is non empty functional FinSequence-membered FinSequenceSet of F₆()
[:(5 -tuples_on F₆()),F₆():] is Relation-like set
bool [:(5 -tuples_on F₆()),F₆():] is set
F₁₀() is Relation-like 5 -tuples_on F₆() -defined F₆() -valued Function-like V30(5 -tuples_on F₆(),F₆()) Element of bool [:(5 -tuples_on F₆()),F₆():]
F₁() is set
F₂() is set
F₃() is set
F₄() is set
F₅() is set
<*F₁(),F₂(),F₃(),F₄(),F₅()*> is non empty Relation-like NAT -defined Function-like finite V42(5) FinSequence-like FinSubsequence-like V95() set
(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (F₆())
((5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is pair non empty Element of the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)
the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) is non empty finite V95() set
the carrier' of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) is non empty set
union the carrier' of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) is set
InputVertices F₈() is finite V95() Element of bool the carrier of F₈()
the carrier of F₈() is non empty finite V95() set
bool the carrier of F₈() is finite V39() V95() set
the ResultSort of F₈() is Relation-like the carrier' of F₈() -defined the carrier of F₈() -valued Function-like V30( the carrier' of F₈(), the carrier of F₈()) Element of bool [: the carrier' of F₈(), the carrier of F₈():]
the carrier' of F₈() is non empty set
[: the carrier' of F₈(), the carrier of F₈():] is Relation-like set
bool [: the carrier' of F₈(), the carrier of F₈():] is set
K488( the carrier of F₈(), the ResultSort of F₈()) is finite V95() Element of bool the carrier of F₈()
the carrier of F₈() \ K488( the carrier of F₈(), the ResultSort of F₈()) is finite V95() Element of bool the carrier of F₈()
(F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (F₆())
the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is non empty finite V95() set
F₉() is non-empty finite-yielding gate`2=den (F<sub>8</sub>()) (F<sub>8</sub>()) (F<sub>6</sub>(),F<sub>8</sub>())
(5,F<sub>6</sub>(),F<sub>10</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>(),F<sub>5</sub>()*>) is strict strict non-empty non-empty finite-yielding finite-yielding gate`2=den gate`2=den ( 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>(),F<sub>5</sub>()*>,F<sub>10</sub>())) ((5,F<sub>6</sub>(),F<sub>10</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>(),F<sub>5</sub>()*>)) ( 1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>(),F<sub>5</sub>()*>,F<sub>10</sub>())) (F<sub>6</sub>(),(5,F<sub>6</sub>(),F<sub>10</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>(),F<sub>5</sub>()*>))
1GateCircStr (<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>(),F<sub>5</sub>()*>,F<sub>10</sub>()) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () ManySortedSign
(F<sub>6</sub>(),F<sub>8</sub>(),(5,F<sub>6</sub>(),F<sub>10</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>(),F<sub>5</sub>()*>),F<sub>9</sub>(),(5,F<sub>6</sub>(),F<sub>10</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>(),F<sub>5</sub>()*>)) is strict non-empty finite-yielding gate`2=den ((F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))) ((F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))) (F₆(),(F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)))
the Sorts of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is non empty Relation-like non-empty non empty-yielding the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -defined Function-like total set
K246( the Sorts of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))) is non empty functional V93() V94() set
the Sorts of F₉() is non empty Relation-like non-empty non empty-yielding the carrier of F₈() -defined Function-like total set
K246( the Sorts of F₉()) is non empty functional V93() V94() set
InnerVertices F₈() is finite V95() Element of bool the carrier of F₈()
S is non empty Relation-like the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -defined Function-like the Sorts of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -compatible total Element of K246( the Sorts of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)))
S | the carrier of F₈() is Relation-like the carrier of F₈() -defined the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -defined Function-like the Sorts of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -compatible finite V95() set
S . F₁() is set
S . F₂() is set
S . F₃() is set
S . F₄() is set
S . F₅() is set
((F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)),(F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)),S) is non empty Relation-like the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -defined Function-like the Sorts of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -compatible total Element of K246( the Sorts of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)))
((F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)),(F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)),S) . ((5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is set
x1 is non empty Relation-like the carrier of F₈() -defined Function-like the Sorts of F₉() -compatible total Element of K246( the Sorts of F₉())
(F₈(),F₉(),x1) is non empty Relation-like the carrier of F₈() -defined Function-like the Sorts of F₉() -compatible total Element of K246( the Sorts of F₉())
(F₈(),F₉(),x1) . F₁() is set
(F₈(),F₉(),x1) . F₂() is set
(F₈(),F₉(),x1) . F₃() is set
(F₈(),F₉(),x1) . F₄() is set
(F₈(),F₉(),x1) . F₅() is set
InnerVertices (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) is finite V95() Element of bool the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)
bool the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) is finite V39() V95() set
the ResultSort of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) is Relation-like the carrier' of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) -defined the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) -valued Function-like V30( the carrier' of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>), the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) Element of bool [: the carrier' of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>), the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>):]
[: the carrier' of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>), the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>):] is Relation-like set
bool [: the carrier' of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>), the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>):] is set
K488( the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>), the ResultSort of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is finite V95() Element of bool the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)
{((5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))} is non empty Relation-like finite V95() set
(F₈(),F₉(),x1) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (S,(F₈(),F₉(),x1)) is non empty Relation-like the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -defined Function-like the Sorts of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -compatible total Element of K246( the Sorts of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)))
(Following (S,(F₈(),F₉(),x1))) | the carrier of F₈() is Relation-like the carrier of F₈() -defined the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -defined Function-like the Sorts of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -compatible finite V95() set
Following (x1,(F₈(),F₉(),x1)) is non empty Relation-like the carrier of F₈() -defined Function-like the Sorts of F₉() -compatible total Element of K246( the Sorts of F₉())
InputVertices (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is finite V95() Element of bool the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))
bool the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is finite V39() V95() set
the ResultSort of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is Relation-like the carrier' of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -defined the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -valued Function-like V30( the carrier' of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)), the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))) Element of bool [: the carrier' of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)), the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)):]
the carrier' of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is non empty set
[: the carrier' of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)), the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)):] is Relation-like set
bool [: the carrier' of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)), the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)):] is set
K488( the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)), the ResultSort of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))) is finite V95() Element of bool the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))
the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) \ K488( the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)), the ResultSort of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))) is finite V95() Element of bool the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))
InputVertices (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) is finite V95() Element of bool the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)
the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) \ K488( the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>), the ResultSort of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is finite V95() Element of bool the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)
(InputVertices (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) \ (InnerVertices F₈()) is finite V95() Element of bool the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)
(InputVertices F₈()) \/ ((InputVertices (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) \ (InnerVertices F₈())) is finite V95() set
[<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₁₀()] is pair non empty set
{<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₁₀()} is non empty functional finite V95() set
{<*F₁(),F₂(),F₃(),F₄(),F₅()*>} is non empty functional finite V39() V93() V95() set
{{<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₁₀()},{<*F₁(),F₂(),F₃(),F₄(),F₅()*>}} is non empty finite V39() V95() set
the carrier of F₈() \/ the carrier of (5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>) is non empty finite V95() set
{[<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₁₀()]} is non empty Relation-like Function-like finite V95() set
the carrier' of F₈() \/ {[<*F₁(),F₂(),F₃(),F₄(),F₅()*>,F₁₀()]} is non empty set
x3 is Element of F₆()
f is Element of F₆()
a is Element of F₆()
b is Element of F₆()
c is Element of F₆()
F₇(x3,f,a,b,c) is Element of F₆()
proj2 <*F₁(),F₂(),F₃(),F₄(),F₅()*> is non empty finite V95() set
{F₁(),F₂(),F₃(),F₄(),F₅()} is finite V95() set
(Following (S,(F₈(),F₉(),x1))) . F₅() is set
(Following (S,(F₈(),F₉(),x1))) . F₃() is set
(Following (S,(F₈(),F₉(),x1))) . F₁() is set
x2 is Element of the carrier' of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))
the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))
the Arity of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is Relation-like the carrier' of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -defined the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) * -valued Function-like V30( the carrier' of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)), the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) * ) Function-yielding V34() Element of bool [: the carrier' of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)),( the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) *):]
[: the carrier' of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)),( the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) *):] is Relation-like set
bool [: the carrier' of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)),( the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) *):] is set
the Arity of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) . x2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V95() Element of the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) *
x2 `2 is Relation-like Function-like set
[( the Arity of (F<sub>6</sub>(),F<sub>8</sub>(),(5,F<sub>6</sub>(),F<sub>10</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>(),F<sub>5</sub>()*>)) . x2),(x2 `2)] is pair non empty set
{( the Arity of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) . x2),(x2 `2)} is non empty functional finite V95() set
{( the Arity of (F<sub>6</sub>(),F<sub>8</sub>(),(5,F<sub>6</sub>(),F<sub>10</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>(),F<sub>5</sub>()*>)) . x2)} is non empty functional finite V39() V93() V95() set
{{( the Arity of (F<sub>6</sub>(),F<sub>8</sub>(),(5,F<sub>6</sub>(),F<sub>10</sub>(),<*F<sub>1</sub>(),F<sub>2</sub>(),F<sub>3</sub>(),F<sub>4</sub>(),F<sub>5</sub>()*>)) . x2),(x2 `2)},{( the Arity of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) . x2)}} is non empty finite V39() V95() set
the_arity_of x2 is Relation-like NAT -defined the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -valued Function-like finite FinSequence-like FinSubsequence-like V95() Element of the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) *
(Following (S,(F₈(),F₉(),x1))) . F₄() is set
(Following (S,(F₈(),F₉(),x1))) . F₂() is set
proj1 (Following (S,(F₈(),F₉(),x1))) is non empty set
<*F₁(),F₂(),F₃(),F₄(),F₅()*> * (Following (S,(F₈(),F₉(),x1))) is Relation-like NAT -defined Function-like finite V95() set
<*x3,f,a,b,c*> is non empty Relation-like NAT -defined F₆() -valued Function-like finite V42(5) FinSequence-like FinSubsequence-like V95() FinSequence of F₆()
the_result_sort_of x2 is Element of the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))
the ResultSort of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) . x2 is Element of the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>))
((F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)),(F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)),S) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
1 + (F₈(),F₉(),x1) is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Following (S,(1 + (F₈(),F₉(),x1))) is non empty Relation-like the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -defined Function-like the Sorts of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -compatible total Element of K246( the Sorts of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)))
(Following (S,(1 + (F₈(),F₉(),x1)))) . ((5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) is set
Following (Following (S,(F₈(),F₉(),x1))) is non empty Relation-like the carrier of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -defined Function-like the Sorts of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)) -compatible total Element of K246( the Sorts of (F₆(),F₈(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>),F₉(),(5,F₆(),F₁₀(),<*F₁(),F₂(),F₃(),F₄(),F₅()*>)))
(Following (Following (S,(F₈(),F₉(),x1)))) . x2 is set
F₁₀() . (<*F₁(),F₂(),F₃(),F₄(),F₅()*> * (Following (S,(F₈(),F₉(),x1)))) is set
X is pair non empty set
X is non with_pair set
bool X is set
S is Element of bool X
x1 is pair non empty set
X is Relation-like Function-like set
proj2 X is set
S is set
proj1 X is set
X . S is set
the Relation-like NAT -defined NAT -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like V95() nonpair-yielding natural-valued FinSequence of NAT is Relation-like NAT -defined NAT -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like V95() nonpair-yielding natural-valued FinSequence of NAT
X is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
Seg X is finite V42(X) V95() non with_pair V140() V141() V142() V143() V144() V145() V149() V150() V151() Element of bool NAT
id (Seg X) is Relation-like Seg X -defined Seg X -valued Function-like one-to-one total finite V95() Element of bool [:(Seg X),(Seg X):]
[:(Seg X),(Seg X):] is Relation-like finite V95() set
bool [:(Seg X),(Seg X):] is finite V39() V95() set
proj1 (id (Seg X)) is finite V95() set
proj2 (id (Seg X)) is finite V95() set
x1 is Relation-like NAT -defined NAT -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like V95() nonpair-yielding natural-valued FinSequence of NAT
len x1 is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
x2 is Relation-like NAT -defined Function-like finite V42(X) FinSequence-like FinSubsequence-like V95() set
S is set
X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V95() nonpair-yielding set
1GateCircStr (X,S) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity ManySortedSign
InputVertices (1GateCircStr (X,S)) is finite V95() Element of bool the carrier of (1GateCircStr (X,S))
the carrier of (1GateCircStr (X,S)) is non empty finite V95() set
bool the carrier of (1GateCircStr (X,S)) is finite V39() V95() set
the ResultSort of (1GateCircStr (X,S)) is Relation-like the carrier' of (1GateCircStr (X,S)) -defined the carrier of (1GateCircStr (X,S)) -valued Function-like V30( the carrier' of (1GateCircStr (X,S)), the carrier of (1GateCircStr (X,S))) Element of bool [: the carrier' of (1GateCircStr (X,S)), the carrier of (1GateCircStr (X,S)):]
the carrier' of (1GateCircStr (X,S)) is non empty set
[: the carrier' of (1GateCircStr (X,S)), the carrier of (1GateCircStr (X,S)):] is Relation-like set
bool [: the carrier' of (1GateCircStr (X,S)), the carrier of (1GateCircStr (X,S)):] is set
K488( the carrier of (1GateCircStr (X,S)), the ResultSort of (1GateCircStr (X,S))) is finite V95() Element of bool the carrier of (1GateCircStr (X,S))
the carrier of (1GateCircStr (X,S)) \ K488( the carrier of (1GateCircStr (X,S)), the ResultSort of (1GateCircStr (X,S))) is finite V95() Element of bool the carrier of (1GateCircStr (X,S))
proj2 X is finite V95() non with_pair set
the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT is non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT
the non empty finite V95() set is non empty finite V95() set
the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set is non empty functional FinSequence-membered FinSequenceSet of the non empty finite V95() set
[:( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set ), the non empty finite V95() set :] is Relation-like set
bool [:( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set ), the non empty finite V95() set :] is set
the Relation-like the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set -defined the non empty finite V95() set -valued Function-like V30( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set , the non empty finite V95() set ) Element of bool [:( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set ), the non empty finite V95() set :] is Relation-like the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set -defined the non empty finite V95() set -valued Function-like V30( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set , the non empty finite V95() set ) Element of bool [:( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set ), the non empty finite V95() set :]
the Relation-like NAT -defined Function-like finite V42( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT ) FinSequence-like FinSubsequence-like V95() nonpair-yielding natural-valued set is Relation-like NAT -defined Function-like finite V42( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT ) FinSequence-like FinSubsequence-like V95() nonpair-yielding natural-valued set
( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT , the non empty finite V95() set , the Relation-like the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set -defined the non empty finite V95() set -valued Function-like V30( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set , the non empty finite V95() set ) Element of bool [:( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT -tuples_on the non empty finite V95() set ), the non empty finite V95() set :], the Relation-like NAT -defined Function-like finite V42( the non pair V17() V18() V19() V23() V47() ext-real V140() V141() V142() V143() V144() V145() V149() V153() Element of NAT ) FinSequence-like FinSubsequence-like V95() nonpair-yielding natural-valued set ) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () () ( the non empty finite V95() set )
X is non empty finite V95() set
the Relation-like NAT -defined Function-like finite V42( 0 ) FinSequence-like FinSubsequence-like V95() nonpair-yielding natural-valued set is Relation-like NAT -defined Function-like finite V42( 0 ) FinSequence-like FinSubsequence-like V95() nonpair-yielding natural-valued set
0 -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
[:(0 -tuples_on X),X:] is Relation-like set
bool [:(0 -tuples_on X),X:] is set
the Relation-like 0 -tuples_on X -defined X -valued Function-like V30(0 -tuples_on X,X) Element of bool [:(0 -tuples_on X),X:] is Relation-like 0 -tuples_on X -defined X -valued Function-like V30(0 -tuples_on X,X) Element of bool [:(0 -tuples_on X),X:]
(0,X, the Relation-like 0 -tuples_on X -defined X -valued Function-like V30(0 -tuples_on X,X) Element of bool [:(0 -tuples_on X),X:], the Relation-like NAT -defined Function-like finite V42( 0 ) FinSequence-like FinSubsequence-like V95() nonpair-yielding natural-valued set ) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () () (X)
X is non empty V79() () ManySortedSign
InputVertices X is Element of bool the carrier of X
the carrier of X is non empty set
bool the carrier of X is set
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
the carrier' of X is set
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
the carrier of X \ K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
X is non empty V79() () ManySortedSign
the carrier of X is non empty set
InnerVertices X is Element of bool the carrier of X
bool the carrier of X is set
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
the carrier' of X is set
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
S is Element of the carrier of X
InputVertices X is non with_pair Element of bool the carrier of X
the carrier of X \ K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
(InputVertices X) \/ (InnerVertices X) is Element of bool the carrier of X
X is non empty V79() Circuit-like unsplit gate`1=arity ManySortedSign
InnerVertices X is Element of bool the carrier of X
the carrier of X is non empty set
bool the carrier of X is set
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
the carrier' of X is set
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
S is set
the Arity of X is Relation-like the carrier' of X -defined the carrier of X * -valued Function-like V30( the carrier' of X, the carrier of X * ) Function-yielding V34() Element of bool [: the carrier' of X,( the carrier of X *):]
the carrier of X * is non empty functional FinSequence-membered FinSequenceSet of the carrier of X
[: the carrier' of X,( the carrier of X *):] is Relation-like set
bool [: the carrier' of X,( the carrier of X *):] is set
the Arity of X . S is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V95() set
S `2 is set
[( the Arity of X . S),(S `2)] is pair non empty set
{( the Arity of X . S),(S `2)} is non empty finite V95() set
{( the Arity of X . S)} is non empty functional finite V39() V93() V95() set
{{( the Arity of X . S),(S `2)},{( the Arity of X . S)}} is non empty finite V39() V95() set
X is non empty non void V79() Circuit-like unsplit gate`2=den ManySortedSign
InnerVertices X is Element of bool the carrier of X
the carrier of X is non empty set
bool the carrier of X is set
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
the carrier' of X is non empty set
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
S is set
x1 is MSAlgebra over X
x2 is Element of the carrier' of X
x2 `1 is set
the Charact of x1 is non empty Relation-like the carrier' of X -defined Function-like total Function-yielding V34() ManySortedFunction of the Arity of X * ( the Sorts of x1 #), the ResultSort of X * the Sorts of x1
the Arity of X is Relation-like the carrier' of X -defined the carrier of X * -valued Function-like V30( the carrier' of X, the carrier of X * ) Function-yielding V34() Element of bool [: the carrier' of X,( the carrier of X *):]
the carrier of X * is non empty functional FinSequence-membered FinSequenceSet of the carrier of X
[: the carrier' of X,( the carrier of X *):] is Relation-like set
bool [: the carrier' of X,( the carrier of X *):] is set
the Sorts of x1 is non empty Relation-like the carrier of X -defined Function-like total set
the Sorts of x1 # is non empty Relation-like the carrier of X * -defined Function-like total set
the Arity of X * ( the Sorts of x1 #) is non empty Relation-like the carrier' of X -defined Function-like total set
the ResultSort of X * the Sorts of x1 is non empty Relation-like the carrier' of X -defined Function-like total set
the Charact of x1 . x2 is Relation-like Function-like set
[(x2 `1),( the Charact of x1 . x2)] is pair non empty set
{(x2 `1),( the Charact of x1 . x2)} is non empty finite V95() set
{(x2 `1)} is non empty finite V95() set
{{(x2 `1),( the Charact of x1 . x2)},{(x2 `1)}} is non empty finite V39() V95() set
X is non empty V79() Circuit-like unsplit gate`1=arity () ManySortedSign
S is non empty V79() Circuit-like unsplit gate`1=arity () ManySortedSign
X +* S is non empty V79() strict Circuit-like unsplit gate`1=arity ManySortedSign
InputVertices (X +* S) is Element of bool the carrier of (X +* S)
the carrier of (X +* S) is non empty set
bool the carrier of (X +* S) is set
the ResultSort of (X +* S) is Relation-like the carrier' of (X +* S) -defined the carrier of (X +* S) -valued Function-like V30( the carrier' of (X +* S), the carrier of (X +* S)) Element of bool [: the carrier' of (X +* S), the carrier of (X +* S):]
the carrier' of (X +* S) is set
[: the carrier' of (X +* S), the carrier of (X +* S):] is Relation-like set
bool [: the carrier' of (X +* S), the carrier of (X +* S):] is set
K488( the carrier of (X +* S), the ResultSort of (X +* S)) is Element of bool the carrier of (X +* S)
the carrier of (X +* S) \ K488( the carrier of (X +* S), the ResultSort of (X +* S)) is Element of bool the carrier of (X +* S)
InputVertices X is non with_pair Element of bool the carrier of X
the carrier of X is non empty set
bool the carrier of X is set
the ResultSort of X is Relation-like the carrier' of X -defined the carrier of X -valued Function-like V30( the carrier' of X, the carrier of X) Element of bool [: the carrier' of X, the carrier of X:]
the carrier' of X is set
[: the carrier' of X, the carrier of X:] is Relation-like set
bool [: the carrier' of X, the carrier of X:] is set
K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
the carrier of X \ K488( the carrier of X, the ResultSort of X) is Element of bool the carrier of X
InputVertices S is non with_pair Element of bool the carrier of S
the carrier of S is non empty set
bool the carrier of S is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K488( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
the carrier of S \ K488( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
(InputVertices X) \/ (InputVertices S) is non with_pair set
bool ((InputVertices X) \/ (InputVertices S)) is set
X is non pair set
S is set
x1 is set
[S,x1] is pair non empty set
{S,x1} is non empty finite V95() set
{S} is non empty finite V95() set
{{S,x1},{S}} is non empty finite V39() V95() set
S is Relation-like set
X is set
<*X*> is non empty Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() set
S is non empty finite V95() set
1 -tuples_on S is non empty functional FinSequence-membered FinSequenceSet of S
[:(1 -tuples_on S),S:] is Relation-like set
bool [:(1 -tuples_on S),S:] is set
x1 is Relation-like 1 -tuples_on S -defined S -valued Function-like V30(1 -tuples_on S,S) Element of bool [:(1 -tuples_on S),S:]
(1,S,x1,<*X*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (S)
x2 is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den () (S)
the carrier of x2 is non empty set
(S,x2,(1,S,x1,<*X*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (S)
((1,S,x1,<*X*>)) is pair non empty Element of the carrier of (1,S,x1,<*X*>)
the carrier of (1,S,x1,<*X*>) is non empty finite V95() set
the carrier' of (1,S,x1,<*X*>) is non empty set
union the carrier' of (1,S,x1,<*X*>) is set
InputVertices x2 is non with_pair Element of bool the carrier of x2
bool the carrier of x2 is set
the ResultSort of x2 is Relation-like the carrier' of x2 -defined the carrier of x2 -valued Function-like V30( the carrier' of x2, the carrier of x2) Element of bool [: the carrier' of x2, the carrier of x2:]
the carrier' of x2 is non empty set
[: the carrier' of x2, the carrier of x2:] is Relation-like set
bool [: the carrier' of x2, the carrier of x2:] is set
K488( the carrier of x2, the ResultSort of x2) is Element of bool the carrier of x2
the carrier of x2 \ K488( the carrier of x2, the ResultSort of x2) is Element of bool the carrier of x2
InputVertices (S,x2,(1,S,x1,<*X*>)) is Element of bool the carrier of (S,x2,(1,S,x1,<*X*>))
the carrier of (S,x2,(1,S,x1,<*X*>)) is non empty set
bool the carrier of (S,x2,(1,S,x1,<*X*>)) is set
the ResultSort of (S,x2,(1,S,x1,<*X*>)) is Relation-like the carrier' of (S,x2,(1,S,x1,<*X*>)) -defined the carrier of (S,x2,(1,S,x1,<*X*>)) -valued Function-like V30( the carrier' of (S,x2,(1,S,x1,<*X*>)), the carrier of (S,x2,(1,S,x1,<*X*>))) Element of bool [: the carrier' of (S,x2,(1,S,x1,<*X*>)), the carrier of (S,x2,(1,S,x1,<*X*>)):]
the carrier' of (S,x2,(1,S,x1,<*X*>)) is non empty set
[: the carrier' of (S,x2,(1,S,x1,<*X*>)), the carrier of (S,x2,(1,S,x1,<*X*>)):] is Relation-like set
bool [: the carrier' of (S,x2,(1,S,x1,<*X*>)), the carrier of (S,x2,(1,S,x1,<*X*>)):] is set
K488( the carrier of (S,x2,(1,S,x1,<*X*>)), the ResultSort of (S,x2,(1,S,x1,<*X*>))) is Element of bool the carrier of (S,x2,(1,S,x1,<*X*>))
the carrier of (S,x2,(1,S,x1,<*X*>)) \ K488( the carrier of (S,x2,(1,S,x1,<*X*>)), the ResultSort of (S,x2,(1,S,x1,<*X*>))) is Element of bool the carrier of (S,x2,(1,S,x1,<*X*>))
proj2 <*X*> is non empty finite V95() set
x3 is non pair set
{x3} is non empty finite V95() non with_pair set
InputVertices (S,x2,(1,S,x1,<*X*>)) is Element of bool the carrier of (S,x2,(1,S,x1,<*X*>))
the carrier of (S,x2,(1,S,x1,<*X*>)) is non empty set
bool the carrier of (S,x2,(1,S,x1,<*X*>)) is set
the ResultSort of (S,x2,(1,S,x1,<*X*>)) is Relation-like the carrier' of (S,x2,(1,S,x1,<*X*>)) -defined the carrier of (S,x2,(1,S,x1,<*X*>)) -valued Function-like V30( the carrier' of (S,x2,(1,S,x1,<*X*>)), the carrier of (S,x2,(1,S,x1,<*X*>))) Element of bool [: the carrier' of (S,x2,(1,S,x1,<*X*>)), the carrier of (S,x2,(1,S,x1,<*X*>)):]
the carrier' of (S,x2,(1,S,x1,<*X*>)) is non empty set
[: the carrier' of (S,x2,(1,S,x1,<*X*>)), the carrier of (S,x2,(1,S,x1,<*X*>)):] is Relation-like set
bool [: the carrier' of (S,x2,(1,S,x1,<*X*>)), the carrier of (S,x2,(1,S,x1,<*X*>)):] is set
K488( the carrier of (S,x2,(1,S,x1,<*X*>)), the ResultSort of (S,x2,(1,S,x1,<*X*>))) is Element of bool the carrier of (S,x2,(1,S,x1,<*X*>))
the carrier of (S,x2,(1,S,x1,<*X*>)) \ K488( the carrier of (S,x2,(1,S,x1,<*X*>)), the ResultSort of (S,x2,(1,S,x1,<*X*>))) is Element of bool the carrier of (S,x2,(1,S,x1,<*X*>))
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den () (X)
the carrier of S is non empty set
1 -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
[:(1 -tuples_on X),X:] is Relation-like set
bool [:(1 -tuples_on X),X:] is set
x2 is Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:]
x1 is Element of the carrier of S
<*x1*> is non empty Relation-like NAT -defined the carrier of S -valued Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() FinSequence of the carrier of S
(1,X,x2,<*x1*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (X)
(X,S,(1,X,x2,<*x1*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (X)
X is non empty finite V95() set
1 -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
[:(1 -tuples_on X),X:] is Relation-like set
bool [:(1 -tuples_on X),X:] is set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den () (X)
x2 is Relation-like 1 -tuples_on X -defined X -valued Function-like V30(1 -tuples_on X,X) Element of bool [:(1 -tuples_on X),X:]
x1 is non pair set
<*x1*> is non empty Relation-like NAT -defined Function-like finite V42(1) FinSequence-like FinSubsequence-like V95() nonpair-yielding set
(1,X,x2,<*x1*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () () (X)
(X,S,(1,X,x2,<*x1*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (X)
X is set
S is set
<*X,S*> is non empty Relation-like NAT -defined Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() set
x1 is non empty finite V95() set
2 -tuples_on x1 is non empty functional FinSequence-membered FinSequenceSet of x1
[:(2 -tuples_on x1),x1:] is Relation-like set
bool [:(2 -tuples_on x1),x1:] is set
x2 is Relation-like 2 -tuples_on x1 -defined x1 -valued Function-like V30(2 -tuples_on x1,x1) Element of bool [:(2 -tuples_on x1),x1:]
(2,x1,x2,<*X,S*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (x1)
x3 is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den () (x1)
the carrier of x3 is non empty set
(x1,x3,(2,x1,x2,<*X,S*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (x1)
((2,x1,x2,<*X,S*>)) is pair non empty Element of the carrier of (2,x1,x2,<*X,S*>)
the carrier of (2,x1,x2,<*X,S*>) is non empty finite V95() set
the carrier' of (2,x1,x2,<*X,S*>) is non empty set
union the carrier' of (2,x1,x2,<*X,S*>) is set
InputVertices x3 is non with_pair Element of bool the carrier of x3
bool the carrier of x3 is set
the ResultSort of x3 is Relation-like the carrier' of x3 -defined the carrier of x3 -valued Function-like V30( the carrier' of x3, the carrier of x3) Element of bool [: the carrier' of x3, the carrier of x3:]
the carrier' of x3 is non empty set
[: the carrier' of x3, the carrier of x3:] is Relation-like set
bool [: the carrier' of x3, the carrier of x3:] is set
K488( the carrier of x3, the ResultSort of x3) is Element of bool the carrier of x3
the carrier of x3 \ K488( the carrier of x3, the ResultSort of x3) is Element of bool the carrier of x3
InnerVertices x3 is Relation-like Element of bool the carrier of x3
InputVertices (x1,x3,(2,x1,x2,<*X,S*>)) is Element of bool the carrier of (x1,x3,(2,x1,x2,<*X,S*>))
the carrier of (x1,x3,(2,x1,x2,<*X,S*>)) is non empty set
bool the carrier of (x1,x3,(2,x1,x2,<*X,S*>)) is set
the ResultSort of (x1,x3,(2,x1,x2,<*X,S*>)) is Relation-like the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)) -defined the carrier of (x1,x3,(2,x1,x2,<*X,S*>)) -valued Function-like V30( the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)), the carrier of (x1,x3,(2,x1,x2,<*X,S*>))) Element of bool [: the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)), the carrier of (x1,x3,(2,x1,x2,<*X,S*>)):]
the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)) is non empty set
[: the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)), the carrier of (x1,x3,(2,x1,x2,<*X,S*>)):] is Relation-like set
bool [: the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)), the carrier of (x1,x3,(2,x1,x2,<*X,S*>)):] is set
K488( the carrier of (x1,x3,(2,x1,x2,<*X,S*>)), the ResultSort of (x1,x3,(2,x1,x2,<*X,S*>))) is Element of bool the carrier of (x1,x3,(2,x1,x2,<*X,S*>))
the carrier of (x1,x3,(2,x1,x2,<*X,S*>)) \ K488( the carrier of (x1,x3,(2,x1,x2,<*X,S*>)), the ResultSort of (x1,x3,(2,x1,x2,<*X,S*>))) is Element of bool the carrier of (x1,x3,(2,x1,x2,<*X,S*>))
{S} is non empty finite V95() set
{S} \/ (InputVertices x3) is non empty set
{X} is non empty finite V95() set
{X} \/ (InputVertices x3) is non empty set
proj2 <*X,S*> is non empty finite V95() set
f is non pair set
a is non pair set
{f,a} is non empty finite V95() non with_pair set
InputVertices (x1,x3,(2,x1,x2,<*X,S*>)) is Element of bool the carrier of (x1,x3,(2,x1,x2,<*X,S*>))
the carrier of (x1,x3,(2,x1,x2,<*X,S*>)) is non empty set
bool the carrier of (x1,x3,(2,x1,x2,<*X,S*>)) is set
the ResultSort of (x1,x3,(2,x1,x2,<*X,S*>)) is Relation-like the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)) -defined the carrier of (x1,x3,(2,x1,x2,<*X,S*>)) -valued Function-like V30( the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)), the carrier of (x1,x3,(2,x1,x2,<*X,S*>))) Element of bool [: the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)), the carrier of (x1,x3,(2,x1,x2,<*X,S*>)):]
the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)) is non empty set
[: the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)), the carrier of (x1,x3,(2,x1,x2,<*X,S*>)):] is Relation-like set
bool [: the carrier' of (x1,x3,(2,x1,x2,<*X,S*>)), the carrier of (x1,x3,(2,x1,x2,<*X,S*>)):] is set
K488( the carrier of (x1,x3,(2,x1,x2,<*X,S*>)), the ResultSort of (x1,x3,(2,x1,x2,<*X,S*>))) is Element of bool the carrier of (x1,x3,(2,x1,x2,<*X,S*>))
the carrier of (x1,x3,(2,x1,x2,<*X,S*>)) \ K488( the carrier of (x1,x3,(2,x1,x2,<*X,S*>)), the ResultSort of (x1,x3,(2,x1,x2,<*X,S*>))) is Element of bool the carrier of (x1,x3,(2,x1,x2,<*X,S*>))
InnerVertices x3 is Relation-like Element of bool the carrier of x3
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den () (X)
the carrier of S is non empty set
2 -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
[:(2 -tuples_on X),X:] is Relation-like set
bool [:(2 -tuples_on X),X:] is set
x3 is Relation-like 2 -tuples_on X -defined X -valued Function-like V30(2 -tuples_on X,X) Element of bool [:(2 -tuples_on X),X:]
x1 is Element of the carrier of S
x2 is non pair set
<*x1,x2*> is non empty Relation-like NAT -defined Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() set
(2,X,x3,<*x1,x2*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (X)
(X,S,(2,X,x3,<*x1,x2*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (X)
<*x2,x1*> is non empty Relation-like NAT -defined Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() set
(2,X,x3,<*x2,x1*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (X)
(X,S,(2,X,x3,<*x2,x1*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (X)
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den () (X)
the carrier of S is non empty set
2 -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
[:(2 -tuples_on X),X:] is Relation-like set
bool [:(2 -tuples_on X),X:] is set
x3 is Relation-like 2 -tuples_on X -defined X -valued Function-like V30(2 -tuples_on X,X) Element of bool [:(2 -tuples_on X),X:]
x1 is Element of the carrier of S
x2 is Element of the carrier of S
<*x1,x2*> is non empty Relation-like NAT -defined the carrier of S -valued Function-like finite V42(2) FinSequence-like FinSubsequence-like V95() FinSequence of the carrier of S
(2,X,x3,<*x1,x2*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (X)
(X,S,(2,X,x3,<*x1,x2*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (X)
X is set
S is set
x1 is set
<*X,S,x1*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
x2 is non empty finite V95() set
3 -tuples_on x2 is non empty functional FinSequence-membered FinSequenceSet of x2
[:(3 -tuples_on x2),x2:] is Relation-like set
bool [:(3 -tuples_on x2),x2:] is set
x3 is Relation-like 3 -tuples_on x2 -defined x2 -valued Function-like V30(3 -tuples_on x2,x2) Element of bool [:(3 -tuples_on x2),x2:]
(3,x2,x3,<*X,S,x1*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (x2)
f is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den () (x2)
the carrier of f is non empty set
(x2,f,(3,x2,x3,<*X,S,x1*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (x2)
((3,x2,x3,<*X,S,x1*>)) is pair non empty Element of the carrier of (3,x2,x3,<*X,S,x1*>)
the carrier of (3,x2,x3,<*X,S,x1*>) is non empty finite V95() set
the carrier' of (3,x2,x3,<*X,S,x1*>) is non empty set
union the carrier' of (3,x2,x3,<*X,S,x1*>) is set
InputVertices f is non with_pair Element of bool the carrier of f
bool the carrier of f is set
the ResultSort of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V30( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the carrier' of f is non empty set
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
K488( the carrier of f, the ResultSort of f) is Element of bool the carrier of f
the carrier of f \ K488( the carrier of f, the ResultSort of f) is Element of bool the carrier of f
InnerVertices f is Relation-like Element of bool the carrier of f
InputVertices (x2,f,(3,x2,x3,<*X,S,x1*>)) is Element of bool the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>))
the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)) is non empty set
bool the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)) is set
the ResultSort of (x2,f,(3,x2,x3,<*X,S,x1*>)) is Relation-like the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)) -defined the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)) -valued Function-like V30( the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)), the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>))) Element of bool [: the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)), the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)):]
the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)) is non empty set
[: the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)), the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)):] is Relation-like set
bool [: the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)), the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)):] is set
K488( the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)), the ResultSort of (x2,f,(3,x2,x3,<*X,S,x1*>))) is Element of bool the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>))
the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)) \ K488( the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)), the ResultSort of (x2,f,(3,x2,x3,<*X,S,x1*>))) is Element of bool the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>))
{S} is non empty finite V95() set
{S} \/ (InputVertices f) is non empty set
{X} is non empty finite V95() set
{X} \/ (InputVertices f) is non empty set
{x1} is non empty finite V95() set
{x1} \/ (InputVertices f) is non empty set
{X,S} is non empty finite V95() set
{X,S} \/ (InputVertices f) is non empty set
{S,x1} is non empty finite V95() set
{S,x1} \/ (InputVertices f) is non empty set
{X,x1} is non empty finite V95() set
{X,x1} \/ (InputVertices f) is non empty set
proj2 <*X,S,x1*> is non empty finite V95() set
a is non pair set
b is non pair set
c is non pair set
{a,b,c} is finite V95() non with_pair set
InputVertices (x2,f,(3,x2,x3,<*X,S,x1*>)) is Element of bool the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>))
the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)) is non empty set
bool the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)) is set
the ResultSort of (x2,f,(3,x2,x3,<*X,S,x1*>)) is Relation-like the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)) -defined the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)) -valued Function-like V30( the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)), the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>))) Element of bool [: the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)), the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)):]
the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)) is non empty set
[: the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)), the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)):] is Relation-like set
bool [: the carrier' of (x2,f,(3,x2,x3,<*X,S,x1*>)), the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)):] is set
K488( the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)), the ResultSort of (x2,f,(3,x2,x3,<*X,S,x1*>))) is Element of bool the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>))
the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)) \ K488( the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>)), the ResultSort of (x2,f,(3,x2,x3,<*X,S,x1*>))) is Element of bool the carrier of (x2,f,(3,x2,x3,<*X,S,x1*>))
InnerVertices f is Relation-like Element of bool the carrier of f
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den () (X)
the carrier of S is non empty set
3 -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
[:(3 -tuples_on X),X:] is Relation-like set
bool [:(3 -tuples_on X),X:] is set
f is Relation-like 3 -tuples_on X -defined X -valued Function-like V30(3 -tuples_on X,X) Element of bool [:(3 -tuples_on X),X:]
x1 is Element of the carrier of S
x2 is Element of the carrier of S
x3 is non pair set
<*x1,x2,x3*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
(3,X,f,<*x1,x2,x3*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (X)
(X,S,(3,X,f,<*x1,x2,x3*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (X)
<*x1,x3,x2*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
(3,X,f,<*x1,x3,x2*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (X)
(X,S,(3,X,f,<*x1,x3,x2*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (X)
<*x3,x1,x2*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
(3,X,f,<*x3,x1,x2*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (X)
(X,S,(3,X,f,<*x3,x1,x2*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (X)
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den () (X)
the carrier of S is non empty set
3 -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
[:(3 -tuples_on X),X:] is Relation-like set
bool [:(3 -tuples_on X),X:] is set
f is Relation-like 3 -tuples_on X -defined X -valued Function-like V30(3 -tuples_on X,X) Element of bool [:(3 -tuples_on X),X:]
x1 is Element of the carrier of S
x2 is non pair set
x3 is non pair set
<*x1,x2,x3*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
(3,X,f,<*x1,x2,x3*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (X)
(X,S,(3,X,f,<*x1,x2,x3*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (X)
<*x2,x1,x3*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
(3,X,f,<*x2,x1,x3*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (X)
(X,S,(3,X,f,<*x2,x1,x3*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (X)
<*x2,x3,x1*> is non empty Relation-like NAT -defined Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() set
(3,X,f,<*x2,x3,x1*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (X)
(X,S,(3,X,f,<*x2,x3,x1*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (X)
X is non empty finite V95() set
S is non empty non void V79() Circuit-like unsplit gate`1=arity gate`2=den () (X)
the carrier of S is non empty set
3 -tuples_on X is non empty functional FinSequence-membered FinSequenceSet of X
[:(3 -tuples_on X),X:] is Relation-like set
bool [:(3 -tuples_on X),X:] is set
f is Relation-like 3 -tuples_on X -defined X -valued Function-like V30(3 -tuples_on X,X) Element of bool [:(3 -tuples_on X),X:]
x1 is Element of the carrier of S
x2 is Element of the carrier of S
x3 is Element of the carrier of S
<*x1,x2,x3*> is non empty Relation-like NAT -defined the carrier of S -valued Function-like finite V42(3) FinSequence-like FinSubsequence-like V95() FinSequence of the carrier of S
(3,X,f,<*x1,x2,x3*>) is non empty finite non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den () (X)
(X,S,(3,X,f,<*x1,x2,x3*>)) is non empty non void V79() strict Circuit-like unsplit gate`1=arity gate`2=den (X)