REAL is set
NAT is non empty V12() V21() V22() V23() V28() cardinal limit_cardinal Element of K27(REAL)
K27(REAL) is set
NAT is non empty V12() V21() V22() V23() V28() cardinal limit_cardinal set
K27(NAT) is V12() V28() set
K27(NAT) is V12() V28() set
{} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty non pair V21() V22() V23() V25() V26() V27() V28() V29() V32() cardinal {} -element V37() FinSequence-like FinSubsequence-like FinSequence-membered non with_pair nonpair-yielding ext-real non positive non negative V115() V126() set
1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
{{},1} is non empty V28() V32() non with_pair set
K228() is set
K27(K228()) is set
K229() is Element of K27(K228())
K279() is non empty V83() L10()
the carrier of K279() is non empty set
K232( the carrier of K279()) is non empty M19( the carrier of K279())
K278(K279()) is Element of K27(K232( the carrier of K279()))
K27(K232( the carrier of K279())) is set
K28(K278(K279()),NAT) is Relation-like set
K27(K28(K278(K279()),NAT)) is set
K28(NAT,K278(K279())) is Relation-like set
K27(K28(NAT,K278(K279()))) is set
BOOLEAN is non empty set
0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty non pair V21() V22() V23() V25() V26() V27() V28() V29() V32() cardinal {} -element V37() FinSequence-like FinSubsequence-like FinSequence-membered non with_pair nonpair-yielding ext-real non positive non negative V115() V126() Element of NAT
{0,1} is non empty V28() V32() non with_pair set
2 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
2 -tuples_on BOOLEAN is functional non empty FinSequence-membered FinSequenceSet of BOOLEAN
K28((2 -tuples_on BOOLEAN),BOOLEAN) is Relation-like set
K27(K28((2 -tuples_on BOOLEAN),BOOLEAN)) is set
3 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
3 -tuples_on BOOLEAN is functional non empty FinSequence-membered FinSequenceSet of BOOLEAN
K28((3 -tuples_on BOOLEAN),BOOLEAN) is Relation-like set
K27(K28((3 -tuples_on BOOLEAN),BOOLEAN)) is set
'xor' is Relation-like Function-like V18(2 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((2 -tuples_on BOOLEAN),BOOLEAN))
1 -tuples_on BOOLEAN is functional non empty FinSequence-membered FinSequenceSet of BOOLEAN
K28((1 -tuples_on BOOLEAN),BOOLEAN) is Relation-like set
K27(K28((1 -tuples_on BOOLEAN),BOOLEAN)) is set
Seg 1 is non empty V12() V28() 1 -element Element of K27(NAT)
K28(NAT,NAT) is Relation-like V12() V28() set
K27(K28(NAT,NAT)) is V12() V28() set
xor2 is Relation-like Function-like V18(2 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((2 -tuples_on BOOLEAN),BOOLEAN))
and2 is Relation-like Function-like V18(2 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((2 -tuples_on BOOLEAN),BOOLEAN))
xor2c is Relation-like Function-like V18(2 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((2 -tuples_on BOOLEAN),BOOLEAN))
and2c is Relation-like Function-like V18(2 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((2 -tuples_on BOOLEAN),BOOLEAN))
and2a is Relation-like Function-like V18(2 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((2 -tuples_on BOOLEAN),BOOLEAN))
0 -tuples_on BOOLEAN is functional non empty FinSequence-membered FinSequenceSet of BOOLEAN
FALSE is boolean Element of BOOLEAN
(0 -tuples_on BOOLEAN) --> FALSE is Relation-like Function-like V18(0 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((0 -tuples_on BOOLEAN),BOOLEAN))
K28((0 -tuples_on BOOLEAN),BOOLEAN) is Relation-like set
K27(K28((0 -tuples_on BOOLEAN),BOOLEAN)) is set
1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[{},((0 -tuples_on BOOLEAN) --> FALSE)] is non empty pair set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
h0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
N is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
Sn is Relation-like NAT -defined Function-like V14( NAT ) set
Sn . n is set
Sn . 0 is set
An is Relation-like NAT -defined Function-like V14( NAT ) set
An . 0 is set
h is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
o0 is Relation-like NAT -defined Function-like V14( NAT ) set
o0 . n is set
o0 . 0 is set
f1 is Relation-like NAT -defined Function-like V14( NAT ) set
f1 . 0 is set
h0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
N is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . h0 is set
h . 0 is set
Sn is Relation-like NAT -defined Function-like V14( NAT ) set
Sn . 0 is set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE)) is strict non-empty finitely-generated V95( 1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) gate`2=den Boolean MSAlgebra over 1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))
h is non empty V56() ManySortedSign
o0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
o0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (o0 + 1) is set
g . (o0 + 1) is set
An is set
BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (o0 + 1)),(g . (o0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2] is non empty pair set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (o0 + 1)),An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (o0 + 1)),An*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*An,(f . (o0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*An,(f . (o0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2))) +* (1GateCircStr (<*An,(f . (o0 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2] is non empty pair set
[<*(g . (o0 + 1)),An*>,and2] is non empty pair set
[<*An,(f . (o0 + 1))*>,and2] is non empty pair set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
Sn is non-empty MSAlgebra over h
BitGFA0Circ ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),An)
GFA0AdderCirc ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)
2GatesCircuit ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2) is strict non-empty finitely-generated V95( 2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2)
1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)
1GateCircuit (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)
1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2)
1GateCircuit (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2)
(1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),xor2)) +* (1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An,xor2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2))
GFA0CarryCirc ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An)
GFA0CarryICirc ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)
1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)
1GateCircuit (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)
1GateCircuit ((g . (o0 + 1)),An,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (o0 + 1)),An*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (o0 + 1)),An*>,and2)
1GateCircuit (<*(g . (o0 + 1)),An*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (o0 + 1)),An*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (o0 + 1)),An*>,and2)
(1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2)) +* (1GateCircuit ((g . (o0 + 1)),An,and2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2))
1GateCircuit (An,(f . (o0 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)
1GateCircuit (<*An,(f . (o0 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)
((1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2)) +* (1GateCircuit ((g . (o0 + 1)),An,and2))) +* (1GateCircuit (An,(f . (o0 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2))) +* (1GateCircStr (<*An,(f . (o0 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2))) +* (1GateCircStr (<*An,(f . (o0 + 1))*>,and2))
1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3)
(GFA0CarryICirc ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3))
(GFA0AdderCirc ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA0CarryCirc ((f . (o0 + 1)),(g . (o0 + 1)),An)) is strict non-empty finitely-generated V95((GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An))) gate`2=den Boolean MSAlgebra over (GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An))
Sn +* (BitGFA0Circ ((f . (o0 + 1)),(g . (o0 + 1)),An)) is strict non-empty MSAlgebra over h +* (BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),An))
h +* (BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),An)) is non empty non void V56() strict ManySortedSign
An is Relation-like NAT -defined Function-like V14( NAT ) set
An . n is set
h is strict non-empty finitely-generated V95((n,f,g)) gate`2=den Boolean MSAlgebra over (n,f,g)
o0 is Relation-like NAT -defined Function-like V14( NAT ) set
o0 . n is set
An . 0 is set
o0 . 0 is set
f1 is Relation-like NAT -defined Function-like V14( NAT ) set
f1 . 0 is set
g1 is Relation-like NAT -defined Function-like V14( NAT ) set
g1 . n is set
Sn is strict non-empty finitely-generated V95((n,f,g)) gate`2=den Boolean MSAlgebra over (n,f,g)
h1 is Relation-like NAT -defined Function-like V14( NAT ) set
h1 . n is set
g1 . 0 is set
h1 . 0 is set
f1 is Relation-like NAT -defined Function-like V14( NAT ) set
f1 . 0 is set
h is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
An is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
An + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (An + 1) is set
g . (An + 1) is set
Sn is set
BitGFA0Str ((f . (An + 1)),(g . (An + 1)),Sn) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (An + 1)),(g . (An + 1)),Sn) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (An + 1)),(g . (An + 1)),Sn,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (An + 1)),(g . (An + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (An + 1)),(g . (An + 1))*>,xor2] is non empty pair set
<*[<*(f . (An + 1)),(g . (An + 1))*>,xor2],Sn*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,xor2],Sn*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,xor2],Sn*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((f . (An + 1)),(g . (An + 1)),Sn) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (An + 1)),(g . (An + 1)),Sn) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (An + 1)),Sn*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (An + 1)),Sn*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2)) +* (1GateCircStr (<*(g . (An + 1)),Sn*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*Sn,(f . (An + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*Sn,(f . (An + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2)) +* (1GateCircStr (<*(g . (An + 1)),Sn*>,and2))) +* (1GateCircStr (<*Sn,(f . (An + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*(f . (An + 1)),(g . (An + 1))*>,and2] is non empty pair set
[<*(g . (An + 1)),Sn*>,and2] is non empty pair set
[<*Sn,(f . (An + 1))*>,and2] is non empty pair set
<*[<*(f . (An + 1)),(g . (An + 1))*>,and2],[<*(g . (An + 1)),Sn*>,and2],[<*Sn,(f . (An + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,and2],[<*(g . (An + 1)),Sn*>,and2],[<*Sn,(f . (An + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (An + 1)),(g . (An + 1)),Sn)) +* (1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,and2],[<*(g . (An + 1)),Sn*>,and2],[<*Sn,(f . (An + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (An + 1)),(g . (An + 1)),Sn)) +* (GFA0CarryStr ((f . (An + 1)),(g . (An + 1)),Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h +* (BitGFA0Str ((f . (An + 1)),(g . (An + 1)),Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
o0 is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
g1 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
g1 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (g1 + 1) is set
g . (g1 + 1) is set
f1 is set
BitGFA0Str ((f . (g1 + 1)),(g . (g1 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (g1 + 1)),(g . (g1 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (g1 + 1)),(g . (g1 + 1)),f1,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (g1 + 1)),(g . (g1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (g1 + 1)),(g . (g1 + 1))*>,xor2] is non empty pair set
<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,xor2],f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,xor2],f1*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,xor2],f1*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((f . (g1 + 1)),(g . (g1 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (g1 + 1)),f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (g1 + 1)),f1*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f1,(f . (g1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f1,(f . (g1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,and2))) +* (1GateCircStr (<*f1,(f . (g1 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2] is non empty pair set
[<*(g . (g1 + 1)),f1*>,and2] is non empty pair set
[<*f1,(f . (g1 + 1))*>,and2] is non empty pair set
<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2],[<*(g . (g1 + 1)),f1*>,and2],[<*f1,(f . (g1 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2],[<*(g . (g1 + 1)),f1*>,and2],[<*f1,(f . (g1 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2],[<*(g . (g1 + 1)),f1*>,and2],[<*f1,(f . (g1 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) +* (GFA0CarryStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
o0 +* (BitGFA0Str ((f . (g1 + 1)),(g . (g1 + 1)),f1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h1 is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f2 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f2 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (f2 + 1) is set
g . (f2 + 1) is set
f1 is set
BitGFA0Str ((f . (f2 + 1)),(g . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (f2 + 1)),(g . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (f2 + 1)),(g . (f2 + 1)),f1,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f2 + 1)),(g . (f2 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (f2 + 1)),(g . (f2 + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f2 + 1)),(g . (f2 + 1))*>,xor2] is non empty pair set
<*[<*(f . (f2 + 1)),(g . (f2 + 1))*>,xor2],f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f2 + 1)),(g . (f2 + 1))*>,xor2],f1*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f2 + 1)),(g . (f2 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (f2 + 1)),(g . (f2 + 1))*>,xor2],f1*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((f . (f2 + 1)),(g . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (f2 + 1)),(g . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (f2 + 1)),(g . (f2 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (f2 + 1)),f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (f2 + 1)),f1*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f2 + 1)),(g . (f2 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f2 + 1)),f1*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f1,(f . (f2 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f1,(f . (f2 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (f2 + 1)),(g . (f2 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f2 + 1)),f1*>,and2))) +* (1GateCircStr (<*f1,(f . (f2 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f2 + 1)),(g . (f2 + 1))*>,and2] is non empty pair set
[<*(g . (f2 + 1)),f1*>,and2] is non empty pair set
[<*f1,(f . (f2 + 1))*>,and2] is non empty pair set
<*[<*(f . (f2 + 1)),(g . (f2 + 1))*>,and2],[<*(g . (f2 + 1)),f1*>,and2],[<*f1,(f . (f2 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f2 + 1)),(g . (f2 + 1))*>,and2],[<*(g . (f2 + 1)),f1*>,and2],[<*f1,(f . (f2 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (f2 + 1)),(g . (f2 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (f2 + 1)),(g . (f2 + 1))*>,and2],[<*(g . (f2 + 1)),f1*>,and2],[<*f1,(f . (f2 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (f2 + 1)),(g . (f2 + 1)),f1)) +* (GFA0CarryStr ((f . (f2 + 1)),(g . (f2 + 1)),f1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h1 +* (BitGFA0Str ((f . (f2 + 1)),(g . (f2 + 1)),f1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f3 is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
n + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (n + 1) is set
g . (n + 1) is set
f0 is set
BitGFA0Str ((f . (n + 1)),(g . (n + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (n + 1)),(g . (n + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (n + 1)),(g . (n + 1)),f0,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),(g . (n + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,xor2] is non empty pair set
<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2],f0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2],f0*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2],f0*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((f . (n + 1)),(g . (n + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (n + 1)),(g . (n + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (n + 1)),f0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (n + 1)),f0*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2)) +* (1GateCircStr (<*(g . (n + 1)),f0*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f0,(f . (n + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f0,(f . (n + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2)) +* (1GateCircStr (<*(g . (n + 1)),f0*>,and2))) +* (1GateCircStr (<*f0,(f . (n + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,and2] is non empty pair set
[<*(g . (n + 1)),f0*>,and2] is non empty pair set
[<*f0,(f . (n + 1))*>,and2] is non empty pair set
<*[<*(f . (n + 1)),(g . (n + 1))*>,and2],[<*(g . (n + 1)),f0*>,and2],[<*f0,(f . (n + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2],[<*(g . (n + 1)),f0*>,and2],[<*f0,(f . (n + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (n + 1)),(g . (n + 1)),f0)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2],[<*(g . (n + 1)),f0*>,and2],[<*f0,(f . (n + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (n + 1)),(g . (n + 1)),f0)) +* (GFA0CarryStr ((f . (n + 1)),(g . (n + 1)),f0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f3 +* (BitGFA0Str ((f . (n + 1)),(g . (n + 1)),f0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
x is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h2 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
h2 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (h2 + 1) is set
g . (h2 + 1) is set
g2 is set
BitGFA0Str ((f . (h2 + 1)),(g . (h2 + 1)),g2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (h2 + 1)),(g . (h2 + 1)),g2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (h2 + 1)),(g . (h2 + 1)),g2,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (h2 + 1)),(g . (h2 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (h2 + 1)),(g . (h2 + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (h2 + 1)),(g . (h2 + 1))*>,xor2] is non empty pair set
<*[<*(f . (h2 + 1)),(g . (h2 + 1))*>,xor2],g2*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (h2 + 1)),(g . (h2 + 1))*>,xor2],g2*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (h2 + 1)),(g . (h2 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (h2 + 1)),(g . (h2 + 1))*>,xor2],g2*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((f . (h2 + 1)),(g . (h2 + 1)),g2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (h2 + 1)),(g . (h2 + 1)),g2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (h2 + 1)),(g . (h2 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (h2 + 1)),g2*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (h2 + 1)),g2*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (h2 + 1)),(g . (h2 + 1))*>,and2)) +* (1GateCircStr (<*(g . (h2 + 1)),g2*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*g2,(f . (h2 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*g2,(f . (h2 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (h2 + 1)),(g . (h2 + 1))*>,and2)) +* (1GateCircStr (<*(g . (h2 + 1)),g2*>,and2))) +* (1GateCircStr (<*g2,(f . (h2 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (h2 + 1)),(g . (h2 + 1))*>,and2] is non empty pair set
[<*(g . (h2 + 1)),g2*>,and2] is non empty pair set
[<*g2,(f . (h2 + 1))*>,and2] is non empty pair set
<*[<*(f . (h2 + 1)),(g . (h2 + 1))*>,and2],[<*(g . (h2 + 1)),g2*>,and2],[<*g2,(f . (h2 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (h2 + 1)),(g . (h2 + 1))*>,and2],[<*(g . (h2 + 1)),g2*>,and2],[<*g2,(f . (h2 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (h2 + 1)),(g . (h2 + 1)),g2)) +* (1GateCircStr (<*[<*(f . (h2 + 1)),(g . (h2 + 1))*>,and2],[<*(g . (h2 + 1)),g2*>,and2],[<*g2,(f . (h2 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (h2 + 1)),(g . (h2 + 1)),g2)) +* (GFA0CarryStr ((f . (h2 + 1)),(g . (h2 + 1)),g2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
x +* (BitGFA0Str ((f . (h2 + 1)),(g . (h2 + 1)),g2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h is non empty V56() ManySortedSign
o0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
o0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (o0 + 1) is set
g . (o0 + 1) is set
An is set
BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (o0 + 1)),(g . (o0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2] is non empty pair set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (o0 + 1)),An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (o0 + 1)),An*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*An,(f . (o0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*An,(f . (o0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2))) +* (1GateCircStr (<*An,(f . (o0 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2] is non empty pair set
[<*(g . (o0 + 1)),An*>,and2] is non empty pair set
[<*An,(f . (o0 + 1))*>,and2] is non empty pair set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
Sn is non-empty MSAlgebra over h
BitGFA0Circ ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),An)
GFA0AdderCirc ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)
2GatesCircuit ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2) is strict non-empty finitely-generated V95( 2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2)
1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)
1GateCircuit (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)
1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2)
1GateCircuit (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2)
(1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),xor2)) +* (1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An,xor2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],An*>,xor2))
GFA0CarryCirc ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An)
GFA0CarryICirc ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)
1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)
1GateCircuit (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)
1GateCircuit ((g . (o0 + 1)),An,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (o0 + 1)),An*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (o0 + 1)),An*>,and2)
1GateCircuit (<*(g . (o0 + 1)),An*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (o0 + 1)),An*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (o0 + 1)),An*>,and2)
(1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2)) +* (1GateCircuit ((g . (o0 + 1)),An,and2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2))
1GateCircuit (An,(f . (o0 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)
1GateCircuit (<*An,(f . (o0 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)
((1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2)) +* (1GateCircuit ((g . (o0 + 1)),An,and2))) +* (1GateCircuit (An,(f . (o0 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2))) +* (1GateCircStr (<*An,(f . (o0 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2))) +* (1GateCircStr (<*An,(f . (o0 + 1))*>,and2))
1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3)
(GFA0CarryICirc ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),An*>,and2],[<*An,(f . (o0 + 1))*>,and2]*>,or3))
(GFA0AdderCirc ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA0CarryCirc ((f . (o0 + 1)),(g . (o0 + 1)),An)) is strict non-empty finitely-generated V95((GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An))) gate`2=den Boolean MSAlgebra over (GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An))
Sn +* (BitGFA0Circ ((f . (o0 + 1)),(g . (o0 + 1)),An)) is strict non-empty MSAlgebra over h +* (BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),An))
h +* (BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),An)) is non empty non void V56() strict ManySortedSign
h is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
Sn is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f1 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f1 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (f1 + 1) is set
g . (f1 + 1) is set
o0 is set
BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f1 + 1)),(g . (f1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2] is non empty pair set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],o0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],o0*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],o0*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (f1 + 1)),o0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (f1 + 1)),o0*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*o0,(f . (f1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*o0,(f . (f1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2))) +* (1GateCircStr (<*o0,(f . (f1 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2] is non empty pair set
[<*(g . (f1 + 1)),o0*>,and2] is non empty pair set
[<*o0,(f . (f1 + 1))*>,and2] is non empty pair set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),o0*>,and2],[<*o0,(f . (f1 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),o0*>,and2],[<*o0,(f . (f1 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),o0*>,and2],[<*o0,(f . (f1 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h +* (BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
An is strict non-empty finitely-generated V95(h) gate`2=den Boolean MSAlgebra over h
BitGFA0Circ ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V95( BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),o0)
GFA0AdderCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V95( GFA0AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over GFA0AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
2GatesCircuit ((f . (f1 + 1)),(g . (f1 + 1)),o0,xor2) is strict non-empty finitely-generated V95( 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,xor2)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,xor2)
1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2)
1GateCircuit (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2)
1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],o0,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],o0*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],o0*>,xor2)
1GateCircuit (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],o0*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],o0*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],o0*>,xor2)
(1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),xor2)) +* (1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],o0,xor2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],o0*>,xor2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],o0*>,xor2))
GFA0CarryCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V95( GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
GFA0CarryICirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V95( GFA0CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over GFA0CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)
1GateCircuit (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)
1GateCircuit ((g . (f1 + 1)),o0,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (f1 + 1)),o0*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (f1 + 1)),o0*>,and2)
1GateCircuit (<*(g . (f1 + 1)),o0*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (f1 + 1)),o0*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (f1 + 1)),o0*>,and2)
(1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2)) +* (1GateCircuit ((g . (f1 + 1)),o0,and2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2))
1GateCircuit (o0,(f . (f1 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*o0,(f . (f1 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*o0,(f . (f1 + 1))*>,and2)
1GateCircuit (<*o0,(f . (f1 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*o0,(f . (f1 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*o0,(f . (f1 + 1))*>,and2)
((1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2)) +* (1GateCircuit ((g . (f1 + 1)),o0,and2))) +* (1GateCircuit (o0,(f . (f1 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2))) +* (1GateCircStr (<*o0,(f . (f1 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2))) +* (1GateCircStr (<*o0,(f . (f1 + 1))*>,and2))
1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),o0*>,and2],[<*o0,(f . (f1 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),o0*>,and2],[<*o0,(f . (f1 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),o0*>,and2],[<*o0,(f . (f1 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),o0*>,and2],[<*o0,(f . (f1 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),o0*>,and2],[<*o0,(f . (f1 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),o0*>,and2],[<*o0,(f . (f1 + 1))*>,and2]*>,or3)
(GFA0CarryICirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),o0*>,and2],[<*o0,(f . (f1 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA0CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),o0*>,and2],[<*o0,(f . (f1 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA0CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),o0*>,and2],[<*o0,(f . (f1 + 1))*>,and2]*>,or3))
(GFA0AdderCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (GFA0CarryCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is strict non-empty finitely-generated V95((GFA0AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))) gate`2=den Boolean MSAlgebra over (GFA0AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))
An +* (BitGFA0Circ ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is strict non-empty finitely-generated V95(h +* (BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),o0))) gate`2=den Boolean MSAlgebra over h +* (BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),o0))
Sn is Relation-like NAT -defined Function-like V14( NAT ) set
Sn . n is set
h is strict non-empty finitely-generated V95((n,f,g)) gate`2=den Boolean MSAlgebra over (n,f,g)
An is Relation-like NAT -defined Function-like V14( NAT ) set
An . n is set
Sn . 0 is set
An . 0 is set
o0 is Relation-like NAT -defined Function-like V14( NAT ) set
o0 . 0 is set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (n,f,g) is non empty set
InnerVertices (n,f,g) is non empty Element of K27( the carrier of (n,f,g))
K27( the carrier of (n,f,g)) is set
A0 is Element of InnerVertices (n,f,g)
h0 is Element of InnerVertices (n,f,g)
N is Relation-like NAT -defined Function-like V14( NAT ) set
N . n is set
N . 0 is set
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . n is set
h . 0 is set
proj1 N is set
proj1 h is set
N is Relation-like NAT -defined Function-like V14( NAT ) set
N . n is set
N . 0 is set
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . 0 is set
InnerVertices (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) is non empty Element of K27( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))))
the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) is non empty set
K27( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)))) is set
{[{},((0 -tuples_on BOOLEAN) --> FALSE)]} is Relation-like Function-like constant non empty V12() V28() 1 -element set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
N . Sn is set
h . Sn is set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
N . (Sn + 1) is set
h . (Sn + 1) is set
An is non empty V56() ManySortedSign
InnerVertices An is Element of K27( the carrier of An)
the carrier of An is non empty set
K27( the carrier of An) is set
An is non empty V56() ManySortedSign
InnerVertices An is Element of K27( the carrier of An)
the carrier of An is non empty set
K27( the carrier of An) is set
f . (Sn + 1) is set
g . (Sn + 1) is set
GFA0CarryOutput ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)) is Element of InnerVertices (GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)))
GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (Sn + 1)),(g . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (Sn + 1)),(h . Sn)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (Sn + 1)),(h . Sn)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(g . (Sn + 1)),(h . Sn)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h . Sn),(f . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h . Sn),(f . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(g . (Sn + 1)),(h . Sn)*>,and2))) +* (1GateCircStr (<*(h . Sn),(f . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2] is non empty pair set
[<*(g . (Sn + 1)),(h . Sn)*>,and2] is non empty pair set
[<*(h . Sn),(f . (Sn + 1))*>,and2] is non empty pair set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),(h . Sn)*>,and2],[<*(h . Sn),(f . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),(h . Sn)*>,and2],[<*(h . Sn),(f . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),(h . Sn)*>,and2],[<*(h . Sn),(f . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) is non empty set
InnerVertices (GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) is non empty Element of K27( the carrier of (GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))))
K27( the carrier of (GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)))) is set
[<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),(h . Sn)*>,and2],[<*(h . Sn),(f . (Sn + 1))*>,and2]*>,or3] is non empty pair set
BitGFA0Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn),xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2] is non empty pair set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2],(h . Sn)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2],(h . Sn)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2],(h . Sn)*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) +* (GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitGFA0Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) is non empty Element of K27( the carrier of (BitGFA0Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))))
the carrier of (BitGFA0Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) is non empty set
K27( the carrier of (BitGFA0Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)))) is set
An +* (BitGFA0Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) is non empty non void V56() strict ManySortedSign
InnerVertices (An +* (BitGFA0Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)))) is non empty Element of K27( the carrier of (An +* (BitGFA0Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)))))
the carrier of (An +* (BitGFA0Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)))) is non empty set
K27( the carrier of (An +* (BitGFA0Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))))) is set
h . n is set
An is non empty V56() ManySortedSign
InnerVertices An is Element of K27( the carrier of An)
the carrier of An is non empty set
K27( the carrier of An) is set
Sn is Element of InnerVertices (n,f,g)
An is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
An + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
h . (An + 1) is set
f . (An + 1) is set
g . (An + 1) is set
h . An is set
GFA0CarryOutput ((f . (An + 1)),(g . (An + 1)),(h . An)) is Element of InnerVertices (GFA0CarryStr ((f . (An + 1)),(g . (An + 1)),(h . An)))
GFA0CarryStr ((f . (An + 1)),(g . (An + 1)),(h . An)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (An + 1)),(g . (An + 1)),(h . An)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (An + 1)),(g . (An + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (An + 1)),(h . An)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (An + 1)),(h . An)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2)) +* (1GateCircStr (<*(g . (An + 1)),(h . An)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h . An),(f . (An + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h . An),(f . (An + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2)) +* (1GateCircStr (<*(g . (An + 1)),(h . An)*>,and2))) +* (1GateCircStr (<*(h . An),(f . (An + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*(f . (An + 1)),(g . (An + 1))*>,and2] is non empty pair set
[<*(g . (An + 1)),(h . An)*>,and2] is non empty pair set
[<*(h . An),(f . (An + 1))*>,and2] is non empty pair set
<*[<*(f . (An + 1)),(g . (An + 1))*>,and2],[<*(g . (An + 1)),(h . An)*>,and2],[<*(h . An),(f . (An + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,and2],[<*(g . (An + 1)),(h . An)*>,and2],[<*(h . An),(f . (An + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (An + 1)),(g . (An + 1)),(h . An))) +* (1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,and2],[<*(g . (An + 1)),(h . An)*>,and2],[<*(h . An),(f . (An + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA0CarryStr ((f . (An + 1)),(g . (An + 1)),(h . An))) is non empty set
InnerVertices (GFA0CarryStr ((f . (An + 1)),(g . (An + 1)),(h . An))) is non empty Element of K27( the carrier of (GFA0CarryStr ((f . (An + 1)),(g . (An + 1)),(h . An))))
K27( the carrier of (GFA0CarryStr ((f . (An + 1)),(g . (An + 1)),(h . An)))) is set
[<*[<*(f . (An + 1)),(g . (An + 1))*>,and2],[<*(g . (An + 1)),(h . An)*>,and2],[<*(h . An),(f . (An + 1))*>,and2]*>,or3] is non empty pair set
f1 is non empty V56() ManySortedSign
o0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
N . o0 is set
g1 is set
h . o0 is set
N . An is set
o0 is non empty V56() ManySortedSign
n is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V14( NAT ) set
g . 0 is set
S0 is Relation-like NAT -defined Function-like V14( NAT ) set
S0 . 0 is set
A0 is Relation-like NAT -defined Function-like V14( NAT ) set
A0 . 0 is set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
(Sn,n,f) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
g . Sn is set
(Sn,n,f) is strict non-empty finitely-generated V95((Sn,n,f)) gate`2=den Boolean MSAlgebra over (Sn,n,f)
S0 . Sn is set
(Sn,n,f) is Element of InnerVertices (Sn,n,f)
the carrier of (Sn,n,f) is non empty set
InnerVertices (Sn,n,f) is non empty Element of K27( the carrier of (Sn,n,f))
K27( the carrier of (Sn,n,f)) is set
A0 . Sn is set
An is Relation-like NAT -defined Function-like V14( NAT ) set
An . Sn is set
o0 is Relation-like NAT -defined Function-like V14( NAT ) set
o0 . Sn is set
An . 0 is set
o0 . 0 is set
f1 is Relation-like NAT -defined Function-like V14( NAT ) set
f1 . 0 is set
g1 is non empty V56() ManySortedSign
f2 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f2 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
n . (f2 + 1) is set
f . (f2 + 1) is set
f1 is set
BitGFA0Str ((n . (f2 + 1)),(f . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((n . (f2 + 1)),(f . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((n . (f2 + 1)),(f . (f2 + 1)),f1,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (f2 + 1)),(f . (f2 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2] is non empty pair set
<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2],f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2],f1*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2],f1*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((n . (f2 + 1)),(f . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((n . (f2 + 1)),(f . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f2 + 1)),f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (f2 + 1)),f1*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2)) +* (1GateCircStr (<*(f . (f2 + 1)),f1*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f1,(n . (f2 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f1,(n . (f2 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2)) +* (1GateCircStr (<*(f . (f2 + 1)),f1*>,and2))) +* (1GateCircStr (<*f1,(n . (f2 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2] is non empty pair set
[<*(f . (f2 + 1)),f1*>,and2] is non empty pair set
[<*f1,(n . (f2 + 1))*>,and2] is non empty pair set
<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2],[<*(f . (f2 + 1)),f1*>,and2],[<*f1,(n . (f2 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2],[<*(f . (f2 + 1)),f1*>,and2],[<*f1,(n . (f2 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2],[<*(f . (f2 + 1)),f1*>,and2],[<*f1,(n . (f2 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (GFA0CarryStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h1 is non-empty MSAlgebra over g1
BitGFA0Circ ((n . (f2 + 1)),(f . (f2 + 1)),f1) is strict non-empty finitely-generated V95( BitGFA0Str ((n . (f2 + 1)),(f . (f2 + 1)),f1)) gate`2=den Boolean MSAlgebra over BitGFA0Str ((n . (f2 + 1)),(f . (f2 + 1)),f1)
GFA0AdderCirc ((n . (f2 + 1)),(f . (f2 + 1)),f1) is strict non-empty finitely-generated V95( GFA0AdderStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) gate`2=den Boolean MSAlgebra over GFA0AdderStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)
2GatesCircuit ((n . (f2 + 1)),(f . (f2 + 1)),f1,xor2) is strict non-empty finitely-generated V95( 2GatesCircStr ((n . (f2 + 1)),(f . (f2 + 1)),f1,xor2)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((n . (f2 + 1)),(f . (f2 + 1)),f1,xor2)
1GateCircuit ((n . (f2 + 1)),(f . (f2 + 1)),xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2)
1GateCircuit (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2)
1GateCircuit ([<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2],f1,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2],f1*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2],f1*>,xor2)
1GateCircuit (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2],f1*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2],f1*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2],f1*>,xor2)
(1GateCircuit ((n . (f2 + 1)),(f . (f2 + 1)),xor2)) +* (1GateCircuit ([<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2],f1,xor2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2],f1*>,xor2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2],f1*>,xor2))
GFA0CarryCirc ((n . (f2 + 1)),(f . (f2 + 1)),f1) is strict non-empty finitely-generated V95( GFA0CarryStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) gate`2=den Boolean MSAlgebra over GFA0CarryStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)
GFA0CarryICirc ((n . (f2 + 1)),(f . (f2 + 1)),f1) is strict non-empty finitely-generated V95( GFA0CarryIStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) gate`2=den Boolean MSAlgebra over GFA0CarryIStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)
1GateCircuit ((n . (f2 + 1)),(f . (f2 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2)
1GateCircuit (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2)
1GateCircuit ((f . (f2 + 1)),f1,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f2 + 1)),f1*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f2 + 1)),f1*>,and2)
1GateCircuit (<*(f . (f2 + 1)),f1*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f2 + 1)),f1*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f2 + 1)),f1*>,and2)
(1GateCircuit ((n . (f2 + 1)),(f . (f2 + 1)),and2)) +* (1GateCircuit ((f . (f2 + 1)),f1,and2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2)) +* (1GateCircStr (<*(f . (f2 + 1)),f1*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2)) +* (1GateCircStr (<*(f . (f2 + 1)),f1*>,and2))
1GateCircuit (f1,(n . (f2 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*f1,(n . (f2 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f1,(n . (f2 + 1))*>,and2)
1GateCircuit (<*f1,(n . (f2 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*f1,(n . (f2 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f1,(n . (f2 + 1))*>,and2)
((1GateCircuit ((n . (f2 + 1)),(f . (f2 + 1)),and2)) +* (1GateCircuit ((f . (f2 + 1)),f1,and2))) +* (1GateCircuit (f1,(n . (f2 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2)) +* (1GateCircStr (<*(f . (f2 + 1)),f1*>,and2))) +* (1GateCircStr (<*f1,(n . (f2 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2)) +* (1GateCircStr (<*(f . (f2 + 1)),f1*>,and2))) +* (1GateCircStr (<*f1,(n . (f2 + 1))*>,and2))
1GateCircuit ([<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2],[<*(f . (f2 + 1)),f1*>,and2],[<*f1,(n . (f2 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2],[<*(f . (f2 + 1)),f1*>,and2],[<*f1,(n . (f2 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2],[<*(f . (f2 + 1)),f1*>,and2],[<*f1,(n . (f2 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2],[<*(f . (f2 + 1)),f1*>,and2],[<*f1,(n . (f2 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2],[<*(f . (f2 + 1)),f1*>,and2],[<*f1,(n . (f2 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2],[<*(f . (f2 + 1)),f1*>,and2],[<*f1,(n . (f2 + 1))*>,and2]*>,or3)
(GFA0CarryICirc ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (1GateCircuit ([<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2],[<*(f . (f2 + 1)),f1*>,and2],[<*f1,(n . (f2 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA0CarryIStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2],[<*(f . (f2 + 1)),f1*>,and2],[<*f1,(n . (f2 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA0CarryIStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2],[<*(f . (f2 + 1)),f1*>,and2],[<*f1,(n . (f2 + 1))*>,and2]*>,or3))
(GFA0AdderCirc ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (GFA0CarryCirc ((n . (f2 + 1)),(f . (f2 + 1)),f1)) is strict non-empty finitely-generated V95((GFA0AdderStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (GFA0CarryStr ((n . (f2 + 1)),(f . (f2 + 1)),f1))) gate`2=den Boolean MSAlgebra over (GFA0AdderStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (GFA0CarryStr ((n . (f2 + 1)),(f . (f2 + 1)),f1))
h1 +* (BitGFA0Circ ((n . (f2 + 1)),(f . (f2 + 1)),f1)) is strict non-empty MSAlgebra over g1 +* (BitGFA0Str ((n . (f2 + 1)),(f . (f2 + 1)),f1))
g1 +* (BitGFA0Str ((n . (f2 + 1)),(f . (f2 + 1)),f1)) is non empty non void V56() strict ManySortedSign
proj1 A0 is set
g1 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
g1 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
A0 . (g1 + 1) is set
n . (g1 + 1) is set
f . (g1 + 1) is set
A0 . g1 is set
GFA0CarryOutput ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1)) is Element of InnerVertices (GFA0CarryStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1)))
GFA0CarryStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (g1 + 1)),(f . (g1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (g1 + 1)),(A0 . g1)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (g1 + 1)),(A0 . g1)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2)) +* (1GateCircStr (<*(f . (g1 + 1)),(A0 . g1)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . g1),(n . (g1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(A0 . g1),(n . (g1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2)) +* (1GateCircStr (<*(f . (g1 + 1)),(A0 . g1)*>,and2))) +* (1GateCircStr (<*(A0 . g1),(n . (g1 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2] is non empty pair set
[<*(f . (g1 + 1)),(A0 . g1)*>,and2] is non empty pair set
[<*(A0 . g1),(n . (g1 + 1))*>,and2] is non empty pair set
<*[<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2],[<*(f . (g1 + 1)),(A0 . g1)*>,and2],[<*(A0 . g1),(n . (g1 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2],[<*(f . (g1 + 1)),(A0 . g1)*>,and2],[<*(A0 . g1),(n . (g1 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1))) +* (1GateCircStr (<*[<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2],[<*(f . (g1 + 1)),(A0 . g1)*>,and2],[<*(A0 . g1),(n . (g1 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA0CarryStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1))) is non empty set
InnerVertices (GFA0CarryStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1))) is non empty Element of K27( the carrier of (GFA0CarryStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1))))
K27( the carrier of (GFA0CarryStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1)))) is set
[<*[<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2],[<*(f . (g1 + 1)),(A0 . g1)*>,and2],[<*(A0 . g1),(n . (g1 + 1))*>,and2]*>,or3] is non empty pair set
g1 is Relation-like NAT -defined Function-like V14( NAT ) set
g1 . Sn is set
g1 . 0 is set
proj1 g1 is set
h1 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
h1 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
g1 . (h1 + 1) is set
n . (h1 + 1) is set
f . (h1 + 1) is set
g1 . h1 is set
GFA0CarryOutput ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1)) is Element of InnerVertices (GFA0CarryStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1)))
GFA0CarryStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (h1 + 1)),(f . (h1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (h1 + 1)),(g1 . h1)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (h1 + 1)),(g1 . h1)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2)) +* (1GateCircStr (<*(f . (h1 + 1)),(g1 . h1)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g1 . h1),(n . (h1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g1 . h1),(n . (h1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2)) +* (1GateCircStr (<*(f . (h1 + 1)),(g1 . h1)*>,and2))) +* (1GateCircStr (<*(g1 . h1),(n . (h1 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2] is non empty pair set
[<*(f . (h1 + 1)),(g1 . h1)*>,and2] is non empty pair set
[<*(g1 . h1),(n . (h1 + 1))*>,and2] is non empty pair set
<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2],[<*(f . (h1 + 1)),(g1 . h1)*>,and2],[<*(g1 . h1),(n . (h1 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2],[<*(f . (h1 + 1)),(g1 . h1)*>,and2],[<*(g1 . h1),(n . (h1 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1))) +* (1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2],[<*(f . (h1 + 1)),(g1 . h1)*>,and2],[<*(g1 . h1),(n . (h1 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA0CarryStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1))) is non empty set
InnerVertices (GFA0CarryStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1))) is non empty Element of K27( the carrier of (GFA0CarryStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1))))
K27( the carrier of (GFA0CarryStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1)))) is set
[<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2],[<*(f . (h1 + 1)),(g1 . h1)*>,and2],[<*(g1 . h1),(n . (h1 + 1))*>,and2]*>,or3] is non empty pair set
n is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(0,n,f) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(0,n,f) is strict non-empty finitely-generated V95((0,n,f)) gate`2=den Boolean MSAlgebra over (0,n,f)
(0,n,f) is Element of InnerVertices (0,n,f)
the carrier of (0,n,f) is non empty set
InnerVertices (0,n,f) is non empty Element of K27( the carrier of (0,n,f))
K27( the carrier of (0,n,f)) is set
h0 is Relation-like NAT -defined Function-like V14( NAT ) set
h0 . 0 is set
N is Relation-like NAT -defined Function-like V14( NAT ) set
N . 0 is set
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . 0 is set
h0 is Relation-like NAT -defined Function-like V14( NAT ) set
h0 . 0 is set
N is Relation-like NAT -defined Function-like V14( NAT ) set
N . 0 is set
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . 0 is set
{[{},((0 -tuples_on BOOLEAN) --> FALSE)]} is Relation-like Function-like constant non empty V12() V28() 1 -element set
h0 is Relation-like NAT -defined Function-like V14( NAT ) set
h0 . 0 is set
N is Relation-like NAT -defined Function-like V14( NAT ) set
N . 0 is set
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . 0 is set
S0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
A0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(1,S0,A0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
S0 . 1 is set
A0 . 1 is set
(1,S0,A0) is strict non-empty finitely-generated V95((1,S0,A0)) gate`2=den Boolean MSAlgebra over (1,S0,A0)
(1,S0,A0) is Element of InnerVertices (1,S0,A0)
the carrier of (1,S0,A0) is non empty set
InnerVertices (1,S0,A0) is non empty Element of K27( the carrier of (1,S0,A0))
K27( the carrier of (1,S0,A0)) is set
h0 is set
BitGFA0Str ((S0 . 1),(A0 . 1),h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((S0 . 1),(A0 . 1),h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((S0 . 1),(A0 . 1),h0,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(S0 . 1),(A0 . 1)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(S0 . 1),(A0 . 1)*>,xor2] is non empty pair set
<*[<*(S0 . 1),(A0 . 1)*>,xor2],h0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2],h0*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2)) +* (1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2],h0*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((S0 . 1),(A0 . 1),h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((S0 . 1),(A0 . 1),h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . 1),h0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(A0 . 1),h0*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2)) +* (1GateCircStr (<*(A0 . 1),h0*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*h0,(S0 . 1)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*h0,(S0 . 1)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2)) +* (1GateCircStr (<*(A0 . 1),h0*>,and2))) +* (1GateCircStr (<*h0,(S0 . 1)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*(S0 . 1),(A0 . 1)*>,and2] is non empty pair set
[<*(A0 . 1),h0*>,and2] is non empty pair set
[<*h0,(S0 . 1)*>,and2] is non empty pair set
<*[<*(S0 . 1),(A0 . 1)*>,and2],[<*(A0 . 1),h0*>,and2],[<*h0,(S0 . 1)*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2],[<*(A0 . 1),h0*>,and2],[<*h0,(S0 . 1)*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((S0 . 1),(A0 . 1),h0)) +* (1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2],[<*(A0 . 1),h0*>,and2],[<*h0,(S0 . 1)*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((S0 . 1),(A0 . 1),h0)) +* (GFA0CarryStr ((S0 . 1),(A0 . 1),h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitGFA0Str ((S0 . 1),(A0 . 1),h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitGFA0Circ ((S0 . 1),(A0 . 1),h0) is strict non-empty finitely-generated V95( BitGFA0Str ((S0 . 1),(A0 . 1),h0)) gate`2=den Boolean MSAlgebra over BitGFA0Str ((S0 . 1),(A0 . 1),h0)
GFA0AdderCirc ((S0 . 1),(A0 . 1),h0) is strict non-empty finitely-generated V95( GFA0AdderStr ((S0 . 1),(A0 . 1),h0)) gate`2=den Boolean MSAlgebra over GFA0AdderStr ((S0 . 1),(A0 . 1),h0)
2GatesCircuit ((S0 . 1),(A0 . 1),h0,xor2) is strict non-empty finitely-generated V95( 2GatesCircStr ((S0 . 1),(A0 . 1),h0,xor2)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((S0 . 1),(A0 . 1),h0,xor2)
1GateCircuit ((S0 . 1),(A0 . 1),xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2)
1GateCircuit (<*(S0 . 1),(A0 . 1)*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2)
1GateCircuit ([<*(S0 . 1),(A0 . 1)*>,xor2],h0,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2],h0*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2],h0*>,xor2)
1GateCircuit (<*[<*(S0 . 1),(A0 . 1)*>,xor2],h0*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2],h0*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2],h0*>,xor2)
(1GateCircuit ((S0 . 1),(A0 . 1),xor2)) +* (1GateCircuit ([<*(S0 . 1),(A0 . 1)*>,xor2],h0,xor2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2)) +* (1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2],h0*>,xor2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2)) +* (1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2],h0*>,xor2))
GFA0CarryCirc ((S0 . 1),(A0 . 1),h0) is strict non-empty finitely-generated V95( GFA0CarryStr ((S0 . 1),(A0 . 1),h0)) gate`2=den Boolean MSAlgebra over GFA0CarryStr ((S0 . 1),(A0 . 1),h0)
GFA0CarryICirc ((S0 . 1),(A0 . 1),h0) is strict non-empty finitely-generated V95( GFA0CarryIStr ((S0 . 1),(A0 . 1),h0)) gate`2=den Boolean MSAlgebra over GFA0CarryIStr ((S0 . 1),(A0 . 1),h0)
1GateCircuit ((S0 . 1),(A0 . 1),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2)
1GateCircuit (<*(S0 . 1),(A0 . 1)*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2)
1GateCircuit ((A0 . 1),h0,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(A0 . 1),h0*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(A0 . 1),h0*>,and2)
1GateCircuit (<*(A0 . 1),h0*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(A0 . 1),h0*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(A0 . 1),h0*>,and2)
(1GateCircuit ((S0 . 1),(A0 . 1),and2)) +* (1GateCircuit ((A0 . 1),h0,and2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2)) +* (1GateCircStr (<*(A0 . 1),h0*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2)) +* (1GateCircStr (<*(A0 . 1),h0*>,and2))
1GateCircuit (h0,(S0 . 1),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*h0,(S0 . 1)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*h0,(S0 . 1)*>,and2)
1GateCircuit (<*h0,(S0 . 1)*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*h0,(S0 . 1)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*h0,(S0 . 1)*>,and2)
((1GateCircuit ((S0 . 1),(A0 . 1),and2)) +* (1GateCircuit ((A0 . 1),h0,and2))) +* (1GateCircuit (h0,(S0 . 1),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2)) +* (1GateCircStr (<*(A0 . 1),h0*>,and2))) +* (1GateCircStr (<*h0,(S0 . 1)*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2)) +* (1GateCircStr (<*(A0 . 1),h0*>,and2))) +* (1GateCircStr (<*h0,(S0 . 1)*>,and2))
1GateCircuit ([<*(S0 . 1),(A0 . 1)*>,and2],[<*(A0 . 1),h0*>,and2],[<*h0,(S0 . 1)*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2],[<*(A0 . 1),h0*>,and2],[<*h0,(S0 . 1)*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2],[<*(A0 . 1),h0*>,and2],[<*h0,(S0 . 1)*>,and2]*>,or3)
1GateCircuit (<*[<*(S0 . 1),(A0 . 1)*>,and2],[<*(A0 . 1),h0*>,and2],[<*h0,(S0 . 1)*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2],[<*(A0 . 1),h0*>,and2],[<*h0,(S0 . 1)*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2],[<*(A0 . 1),h0*>,and2],[<*h0,(S0 . 1)*>,and2]*>,or3)
(GFA0CarryICirc ((S0 . 1),(A0 . 1),h0)) +* (1GateCircuit ([<*(S0 . 1),(A0 . 1)*>,and2],[<*(A0 . 1),h0*>,and2],[<*h0,(S0 . 1)*>,and2],or3)) is strict non-empty finitely-generated V95((GFA0CarryIStr ((S0 . 1),(A0 . 1),h0)) +* (1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2],[<*(A0 . 1),h0*>,and2],[<*h0,(S0 . 1)*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA0CarryIStr ((S0 . 1),(A0 . 1),h0)) +* (1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2],[<*(A0 . 1),h0*>,and2],[<*h0,(S0 . 1)*>,and2]*>,or3))
(GFA0AdderCirc ((S0 . 1),(A0 . 1),h0)) +* (GFA0CarryCirc ((S0 . 1),(A0 . 1),h0)) is strict non-empty finitely-generated V95((GFA0AdderStr ((S0 . 1),(A0 . 1),h0)) +* (GFA0CarryStr ((S0 . 1),(A0 . 1),h0))) gate`2=den Boolean MSAlgebra over (GFA0AdderStr ((S0 . 1),(A0 . 1),h0)) +* (GFA0CarryStr ((S0 . 1),(A0 . 1),h0))
(1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitGFA0Circ ((S0 . 1),(A0 . 1),h0)) is strict non-empty finitely-generated V95((1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitGFA0Str ((S0 . 1),(A0 . 1),h0))) gate`2=den Boolean MSAlgebra over (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitGFA0Str ((S0 . 1),(A0 . 1),h0))
GFA0CarryOutput ((S0 . 1),(A0 . 1),h0) is Element of InnerVertices (GFA0CarryStr ((S0 . 1),(A0 . 1),h0))
the carrier of (GFA0CarryStr ((S0 . 1),(A0 . 1),h0)) is non empty set
InnerVertices (GFA0CarryStr ((S0 . 1),(A0 . 1),h0)) is non empty Element of K27( the carrier of (GFA0CarryStr ((S0 . 1),(A0 . 1),h0)))
K27( the carrier of (GFA0CarryStr ((S0 . 1),(A0 . 1),h0))) is set
[<*[<*(S0 . 1),(A0 . 1)*>,and2],[<*(A0 . 1),h0*>,and2],[<*h0,(S0 . 1)*>,and2]*>,or3] is non empty pair set
N is Relation-like NAT -defined Function-like V14( NAT ) set
N . 1 is set
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . 1 is set
N . 0 is set
h . 0 is set
Sn is Relation-like NAT -defined Function-like V14( NAT ) set
Sn . 0 is set
0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
Sn . (0 + 1) is set
n is set
<*n*> is Relation-like NAT -defined Function-like constant non empty V12() V28() 1 -element FinSequence-like FinSubsequence-like set
f is set
<*f*> is Relation-like NAT -defined Function-like constant non empty V12() V28() 1 -element FinSequence-like FinSubsequence-like set
(1,<*n*>,<*f*>) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1,<*n*>,<*f*>) is strict non-empty finitely-generated V95((1,<*n*>,<*f*>)) gate`2=den Boolean MSAlgebra over (1,<*n*>,<*f*>)
(1,<*n*>,<*f*>) is Element of InnerVertices (1,<*n*>,<*f*>)
the carrier of (1,<*n*>,<*f*>) is non empty set
InnerVertices (1,<*n*>,<*f*>) is non empty Element of K27( the carrier of (1,<*n*>,<*f*>))
K27( the carrier of (1,<*n*>,<*f*>)) is set
<*n*> . 1 is set
<*f*> . 1 is set
g is set
BitGFA0Str (n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr (n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (n,f,g,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,f*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*n,f*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*n,f*>,xor2] is non empty pair set
<*[<*n,f*>,xor2],g*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*n,f*>,xor2],g*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,xor2)) +* (1GateCircStr (<*[<*n,f*>,xor2],g*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr (n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr (n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f,g*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f,g*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,and2)) +* (1GateCircStr (<*f,g*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*g,n*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*g,n*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*g,n*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*n,f*>,and2] is non empty pair set
[<*f,g*>,and2] is non empty pair set
[<*g,n*>,and2] is non empty pair set
<*[<*n,f*>,and2],[<*f,g*>,and2],[<*g,n*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*n,f*>,and2],[<*f,g*>,and2],[<*g,n*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2],[<*f,g*>,and2],[<*g,n*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr (n,f,g)) +* (GFA0CarryStr (n,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitGFA0Str (n,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitGFA0Circ (n,f,g) is strict non-empty finitely-generated V95( BitGFA0Str (n,f,g)) gate`2=den Boolean MSAlgebra over BitGFA0Str (n,f,g)
GFA0AdderCirc (n,f,g) is strict non-empty finitely-generated V95( GFA0AdderStr (n,f,g)) gate`2=den Boolean MSAlgebra over GFA0AdderStr (n,f,g)
2GatesCircuit (n,f,g,xor2) is strict non-empty finitely-generated V95( 2GatesCircStr (n,f,g,xor2)) gate`2=den Boolean MSAlgebra over 2GatesCircStr (n,f,g,xor2)
1GateCircuit (n,f,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*n,f*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,xor2)
1GateCircuit (<*n,f*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*n,f*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,xor2)
1GateCircuit ([<*n,f*>,xor2],g,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*n,f*>,xor2],g*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,xor2],g*>,xor2)
1GateCircuit (<*[<*n,f*>,xor2],g*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*n,f*>,xor2],g*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,xor2],g*>,xor2)
(1GateCircuit (n,f,xor2)) +* (1GateCircuit ([<*n,f*>,xor2],g,xor2)) is strict non-empty finitely-generated V95((1GateCircStr (<*n,f*>,xor2)) +* (1GateCircStr (<*[<*n,f*>,xor2],g*>,xor2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,xor2)) +* (1GateCircStr (<*[<*n,f*>,xor2],g*>,xor2))
GFA0CarryCirc (n,f,g) is strict non-empty finitely-generated V95( GFA0CarryStr (n,f,g)) gate`2=den Boolean MSAlgebra over GFA0CarryStr (n,f,g)
GFA0CarryICirc (n,f,g) is strict non-empty finitely-generated V95( GFA0CarryIStr (n,f,g)) gate`2=den Boolean MSAlgebra over GFA0CarryIStr (n,f,g)
1GateCircuit (n,f,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*n,f*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2)
1GateCircuit (<*n,f*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*n,f*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2)
1GateCircuit (f,g,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
1GateCircuit (<*f,g*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
(1GateCircuit (n,f,and2)) +* (1GateCircuit (f,g,and2)) is strict non-empty finitely-generated V95((1GateCircStr (<*n,f*>,and2)) +* (1GateCircStr (<*f,g*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,and2)) +* (1GateCircStr (<*f,g*>,and2))
1GateCircuit (g,n,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*g,n*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,and2)
1GateCircuit (<*g,n*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*g,n*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,and2)
((1GateCircuit (n,f,and2)) +* (1GateCircuit (f,g,and2))) +* (1GateCircuit (g,n,and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*n,f*>,and2)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*g,n*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,and2)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*g,n*>,and2))
1GateCircuit ([<*n,f*>,and2],[<*f,g*>,and2],[<*g,n*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*n,f*>,and2],[<*f,g*>,and2],[<*g,n*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2],[<*f,g*>,and2],[<*g,n*>,and2]*>,or3)
1GateCircuit (<*[<*n,f*>,and2],[<*f,g*>,and2],[<*g,n*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*n,f*>,and2],[<*f,g*>,and2],[<*g,n*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2],[<*f,g*>,and2],[<*g,n*>,and2]*>,or3)
(GFA0CarryICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,and2],[<*f,g*>,and2],[<*g,n*>,and2],or3)) is strict non-empty finitely-generated V95((GFA0CarryIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2],[<*f,g*>,and2],[<*g,n*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA0CarryIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2],[<*f,g*>,and2],[<*g,n*>,and2]*>,or3))
(GFA0AdderCirc (n,f,g)) +* (GFA0CarryCirc (n,f,g)) is strict non-empty finitely-generated V95((GFA0AdderStr (n,f,g)) +* (GFA0CarryStr (n,f,g))) gate`2=den Boolean MSAlgebra over (GFA0AdderStr (n,f,g)) +* (GFA0CarryStr (n,f,g))
(1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitGFA0Circ (n,f,g)) is strict non-empty finitely-generated V95((1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitGFA0Str (n,f,g))) gate`2=den Boolean MSAlgebra over (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitGFA0Str (n,f,g))
GFA0CarryOutput (n,f,g) is Element of InnerVertices (GFA0CarryStr (n,f,g))
the carrier of (GFA0CarryStr (n,f,g)) is non empty set
InnerVertices (GFA0CarryStr (n,f,g)) is non empty Element of K27( the carrier of (GFA0CarryStr (n,f,g)))
K27( the carrier of (GFA0CarryStr (n,f,g))) is set
[<*[<*n,f*>,and2],[<*f,g*>,and2],[<*g,n*>,and2]*>,or3] is non empty pair set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is Relation-like NAT -defined Function-like V28() n -element FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() n -element FinSequence-like FinSubsequence-like set
S0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
f ^ S0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
h0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g ^ h0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,(f ^ S0),(g ^ h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
A0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
f ^ A0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
N is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g ^ N is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,(f ^ A0),(g ^ N)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,(f ^ S0),(g ^ h0)) is strict non-empty finitely-generated V95((n,(f ^ S0),(g ^ h0))) gate`2=den Boolean MSAlgebra over (n,(f ^ S0),(g ^ h0))
(n,(f ^ A0),(g ^ N)) is strict non-empty finitely-generated V95((n,(f ^ A0),(g ^ N))) gate`2=den Boolean MSAlgebra over (n,(f ^ A0),(g ^ N))
(n,(f ^ S0),(g ^ h0)) is Element of InnerVertices (n,(f ^ S0),(g ^ h0))
the carrier of (n,(f ^ S0),(g ^ h0)) is non empty set
InnerVertices (n,(f ^ S0),(g ^ h0)) is non empty Element of K27( the carrier of (n,(f ^ S0),(g ^ h0)))
K27( the carrier of (n,(f ^ S0),(g ^ h0))) is set
(n,(f ^ A0),(g ^ N)) is Element of InnerVertices (n,(f ^ A0),(g ^ N))
the carrier of (n,(f ^ A0),(g ^ N)) is non empty set
InnerVertices (n,(f ^ A0),(g ^ N)) is non empty Element of K27( the carrier of (n,(f ^ A0),(g ^ N)))
K27( the carrier of (n,(f ^ A0),(g ^ N))) is set
h1 is Relation-like NAT -defined Function-like V14( NAT ) set
h1 . n is set
f1 is Relation-like NAT -defined Function-like V14( NAT ) set
f1 . n is set
h1 . 0 is set
f1 . 0 is set
f2 is Relation-like NAT -defined Function-like V14( NAT ) set
f2 . 0 is set
x is Relation-like NAT -defined Function-like V14( NAT ) set
x . n is set
g2 is Relation-like NAT -defined Function-like V14( NAT ) set
g2 . n is set
x . 0 is set
g2 . 0 is set
h2 is Relation-like NAT -defined Function-like V14( NAT ) set
h2 . 0 is set
i is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f2 . i is set
h2 . i is set
h1 . i is set
x . i is set
f1 . i is set
g2 . i is set
i + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f2 . (i + 1) is set
h2 . (i + 1) is set
h1 . (i + 1) is set
x . (i + 1) is set
f1 . (i + 1) is set
g2 . (i + 1) is set
len f is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
len g is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
dom f is V28() n -element Element of K27(NAT)
Seg n is V28() n -element Element of K27(NAT)
dom g is V28() n -element Element of K27(NAT)
0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
(f ^ S0) . (i + 1) is set
f . (i + 1) is set
(f ^ A0) . (i + 1) is set
(g ^ h0) . (i + 1) is set
g . (i + 1) is set
(g ^ N) . (i + 1) is set
A is non empty V56() ManySortedSign
S is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
h1 . S is set
c26 is non-empty MSAlgebra over A
f1 . S is set
c27 is set
f2 . S is set
S is non empty V56() ManySortedSign
c27 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
c27 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
(f ^ S0) . (c27 + 1) is set
(g ^ h0) . (c27 + 1) is set
c26 is set
BitGFA0Str (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2] is non empty pair set
<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2],c26*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2],c26*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2)) +* (1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2],c26*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((g ^ h0) . (c27 + 1)),c26*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2)) +* (1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*c26,((f ^ S0) . (c27 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2)) +* (1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2))) +* (1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2] is non empty pair set
[<*((g ^ h0) . (c27 + 1)),c26*>,and2] is non empty pair set
[<*c26,((f ^ S0) . (c27 + 1))*>,and2] is non empty pair set
<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2],[<*((g ^ h0) . (c27 + 1)),c26*>,and2],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2],[<*((g ^ h0) . (c27 + 1)),c26*>,and2],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2],[<*((g ^ h0) . (c27 + 1)),c26*>,and2],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (GFA0CarryStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
A is non-empty MSAlgebra over S
BitGFA0Circ (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is strict non-empty finitely-generated V95( BitGFA0Str (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) gate`2=den Boolean MSAlgebra over BitGFA0Str (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)
GFA0AdderCirc (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is strict non-empty finitely-generated V95( GFA0AdderStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) gate`2=den Boolean MSAlgebra over GFA0AdderStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)
2GatesCircuit (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26,xor2) is strict non-empty finitely-generated V95( 2GatesCircStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26,xor2)) gate`2=den Boolean MSAlgebra over 2GatesCircStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26,xor2)
1GateCircuit (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2)
1GateCircuit (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2)
1GateCircuit ([<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2],c26,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2],c26*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2],c26*>,xor2)
1GateCircuit (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2],c26*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2],c26*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2],c26*>,xor2)
(1GateCircuit (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),xor2)) +* (1GateCircuit ([<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2],c26,xor2)) is strict non-empty finitely-generated V95((1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2)) +* (1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2],c26*>,xor2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2)) +* (1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2],c26*>,xor2))
GFA0CarryCirc (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is strict non-empty finitely-generated V95( GFA0CarryStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) gate`2=den Boolean MSAlgebra over GFA0CarryStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)
GFA0CarryICirc (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is strict non-empty finitely-generated V95( GFA0CarryIStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) gate`2=den Boolean MSAlgebra over GFA0CarryIStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)
1GateCircuit (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2)
1GateCircuit (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2)
1GateCircuit (((g ^ h0) . (c27 + 1)),c26,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2)
1GateCircuit (<*((g ^ h0) . (c27 + 1)),c26*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2)
(1GateCircuit (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),and2)) +* (1GateCircuit (((g ^ h0) . (c27 + 1)),c26,and2)) is strict non-empty finitely-generated V95((1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2)) +* (1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2)) +* (1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2))
1GateCircuit (c26,((f ^ S0) . (c27 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2)
1GateCircuit (<*c26,((f ^ S0) . (c27 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2)
((1GateCircuit (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),and2)) +* (1GateCircuit (((g ^ h0) . (c27 + 1)),c26,and2))) +* (1GateCircuit (c26,((f ^ S0) . (c27 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2)) +* (1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2))) +* (1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2)) +* (1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2))) +* (1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2))
1GateCircuit ([<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2],[<*((g ^ h0) . (c27 + 1)),c26*>,and2],[<*c26,((f ^ S0) . (c27 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2],[<*((g ^ h0) . (c27 + 1)),c26*>,and2],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2],[<*((g ^ h0) . (c27 + 1)),c26*>,and2],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2],[<*((g ^ h0) . (c27 + 1)),c26*>,and2],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2],[<*((g ^ h0) . (c27 + 1)),c26*>,and2],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2],[<*((g ^ h0) . (c27 + 1)),c26*>,and2],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3)
(GFA0CarryICirc (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (1GateCircuit ([<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2],[<*((g ^ h0) . (c27 + 1)),c26*>,and2],[<*c26,((f ^ S0) . (c27 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA0CarryIStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2],[<*((g ^ h0) . (c27 + 1)),c26*>,and2],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA0CarryIStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2],[<*((g ^ h0) . (c27 + 1)),c26*>,and2],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3))
(GFA0AdderCirc (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (GFA0CarryCirc (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) is strict non-empty finitely-generated V95((GFA0AdderStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (GFA0CarryStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26))) gate`2=den Boolean MSAlgebra over (GFA0AdderStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (GFA0CarryStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26))
A +* (BitGFA0Circ (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) is strict non-empty MSAlgebra over S +* (BitGFA0Str (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26))
S +* (BitGFA0Str (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) is non empty non void V56() strict ManySortedSign
S is non empty V56() ManySortedSign
A is non-empty MSAlgebra over S
GFA0CarryOutput (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is Element of InnerVertices (GFA0CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)))
GFA0CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((g ^ N) . (i + 1)),(h2 . i)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2)) +* (1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h2 . i),((f ^ A0) . (i + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2)) +* (1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2))) +* (1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2] is non empty pair set
[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2] is non empty pair set
[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2] is non empty pair set
<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA0CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) is non empty set
InnerVertices (GFA0CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) is non empty Element of K27( the carrier of (GFA0CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))))
K27( the carrier of (GFA0CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)))) is set
[<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3] is non empty pair set
BitGFA0Str (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i),xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2] is non empty pair set
<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2],(h2 . i)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2],(h2 . i)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2)) +* (1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2],(h2 . i)*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (GFA0CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
S +* (BitGFA0Str (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) is non empty non void V56() strict ManySortedSign
BitGFA0Circ (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is strict non-empty finitely-generated V95( BitGFA0Str (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) gate`2=den Boolean MSAlgebra over BitGFA0Str (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))
GFA0AdderCirc (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is strict non-empty finitely-generated V95( GFA0AdderStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) gate`2=den Boolean MSAlgebra over GFA0AdderStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))
2GatesCircuit (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i),xor2) is strict non-empty finitely-generated V95( 2GatesCircStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i),xor2)) gate`2=den Boolean MSAlgebra over 2GatesCircStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i),xor2)
1GateCircuit (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2)
1GateCircuit (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2)
1GateCircuit ([<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2],(h2 . i),xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2],(h2 . i)*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2],(h2 . i)*>,xor2)
1GateCircuit (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2],(h2 . i)*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2],(h2 . i)*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2],(h2 . i)*>,xor2)
(1GateCircuit (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),xor2)) +* (1GateCircuit ([<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2],(h2 . i),xor2)) is strict non-empty finitely-generated V95((1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2)) +* (1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2],(h2 . i)*>,xor2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2)) +* (1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2],(h2 . i)*>,xor2))
GFA0CarryCirc (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is strict non-empty finitely-generated V95( GFA0CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) gate`2=den Boolean MSAlgebra over GFA0CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))
GFA0CarryICirc (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is strict non-empty finitely-generated V95( GFA0CarryIStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) gate`2=den Boolean MSAlgebra over GFA0CarryIStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))
1GateCircuit (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2)
1GateCircuit (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2)
1GateCircuit (((g ^ N) . (i + 1)),(h2 . i),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2)
1GateCircuit (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2)
(1GateCircuit (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),and2)) +* (1GateCircuit (((g ^ N) . (i + 1)),(h2 . i),and2)) is strict non-empty finitely-generated V95((1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2)) +* (1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2)) +* (1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2))
1GateCircuit ((h2 . i),((f ^ A0) . (i + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2)
1GateCircuit (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2)
((1GateCircuit (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),and2)) +* (1GateCircuit (((g ^ N) . (i + 1)),(h2 . i),and2))) +* (1GateCircuit ((h2 . i),((f ^ A0) . (i + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2)) +* (1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2))) +* (1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2)) +* (1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2))) +* (1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2))
1GateCircuit ([<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3)
(GFA0CarryICirc (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (1GateCircuit ([<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA0CarryIStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA0CarryIStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3))
(GFA0AdderCirc (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (GFA0CarryCirc (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) is strict non-empty finitely-generated V95((GFA0AdderStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (GFA0CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)))) gate`2=den Boolean MSAlgebra over (GFA0AdderStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (GFA0CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)))
A +* (BitGFA0Circ (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) is strict non-empty MSAlgebra over S +* (BitGFA0Str (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)))
f2 . n is set
h2 . n is set
S0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
S0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
A0 is Relation-like NAT -defined Function-like V28() S0 -element FinSequence-like FinSubsequence-like set
h0 is Relation-like NAT -defined Function-like V28() S0 -element FinSequence-like FinSubsequence-like set
(S0,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(S0,A0,h0) is Element of InnerVertices (S0,A0,h0)
the carrier of (S0,A0,h0) is non empty set
InnerVertices (S0,A0,h0) is non empty Element of K27( the carrier of (S0,A0,h0))
K27( the carrier of (S0,A0,h0)) is set
(S0,A0,h0) is strict non-empty finitely-generated V95((S0,A0,h0)) gate`2=den Boolean MSAlgebra over (S0,A0,h0)
N is set
<*N*> is Relation-like NAT -defined Function-like constant non empty V12() V28() 1 -element FinSequence-like FinSubsequence-like set
A0 ^ <*N*> is Relation-like NAT -defined Function-like non empty V28() S0 + 1 -element FinSequence-like FinSubsequence-like set
h is set
<*h*> is Relation-like NAT -defined Function-like constant non empty V12() V28() 1 -element FinSequence-like FinSubsequence-like set
h0 ^ <*h*> is Relation-like NAT -defined Function-like non empty V28() S0 + 1 -element FinSequence-like FinSubsequence-like set
((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitGFA0Str (N,h,(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr (N,h,(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (N,h,(S0,A0,h0),xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*N,h*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*N,h*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*N,h*>,xor2] is non empty pair set
<*[<*N,h*>,xor2],(S0,A0,h0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*N,h*>,xor2],(S0,A0,h0)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*N,h*>,xor2)) +* (1GateCircStr (<*[<*N,h*>,xor2],(S0,A0,h0)*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr (N,h,(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr (N,h,(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*N,h*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*h,(S0,A0,h0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*h,(S0,A0,h0)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*N,h*>,and2)) +* (1GateCircStr (<*h,(S0,A0,h0)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(S0,A0,h0),N*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(S0,A0,h0),N*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*N,h*>,and2)) +* (1GateCircStr (<*h,(S0,A0,h0)*>,and2))) +* (1GateCircStr (<*(S0,A0,h0),N*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*N,h*>,and2] is non empty pair set
[<*h,(S0,A0,h0)*>,and2] is non empty pair set
[<*(S0,A0,h0),N*>,and2] is non empty pair set
<*[<*N,h*>,and2],[<*h,(S0,A0,h0)*>,and2],[<*(S0,A0,h0),N*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*N,h*>,and2],[<*h,(S0,A0,h0)*>,and2],[<*(S0,A0,h0),N*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr (N,h,(S0,A0,h0))) +* (1GateCircStr (<*[<*N,h*>,and2],[<*h,(S0,A0,h0)*>,and2],[<*(S0,A0,h0),N*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr (N,h,(S0,A0,h0))) +* (GFA0CarryStr (N,h,(S0,A0,h0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(S0,A0,h0) +* (BitGFA0Str (N,h,(S0,A0,h0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>)) is strict non-empty finitely-generated V95(((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>))) gate`2=den Boolean MSAlgebra over ((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>))
BitGFA0Circ (N,h,(S0,A0,h0)) is strict non-empty finitely-generated V95( BitGFA0Str (N,h,(S0,A0,h0))) gate`2=den Boolean MSAlgebra over BitGFA0Str (N,h,(S0,A0,h0))
GFA0AdderCirc (N,h,(S0,A0,h0)) is strict non-empty finitely-generated V95( GFA0AdderStr (N,h,(S0,A0,h0))) gate`2=den Boolean MSAlgebra over GFA0AdderStr (N,h,(S0,A0,h0))
2GatesCircuit (N,h,(S0,A0,h0),xor2) is strict non-empty finitely-generated V95( 2GatesCircStr (N,h,(S0,A0,h0),xor2)) gate`2=den Boolean MSAlgebra over 2GatesCircStr (N,h,(S0,A0,h0),xor2)
1GateCircuit (N,h,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*N,h*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*N,h*>,xor2)
1GateCircuit (<*N,h*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*N,h*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*N,h*>,xor2)
1GateCircuit ([<*N,h*>,xor2],(S0,A0,h0),xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*N,h*>,xor2],(S0,A0,h0)*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*N,h*>,xor2],(S0,A0,h0)*>,xor2)
1GateCircuit (<*[<*N,h*>,xor2],(S0,A0,h0)*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*N,h*>,xor2],(S0,A0,h0)*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*N,h*>,xor2],(S0,A0,h0)*>,xor2)
(1GateCircuit (N,h,xor2)) +* (1GateCircuit ([<*N,h*>,xor2],(S0,A0,h0),xor2)) is strict non-empty finitely-generated V95((1GateCircStr (<*N,h*>,xor2)) +* (1GateCircStr (<*[<*N,h*>,xor2],(S0,A0,h0)*>,xor2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*N,h*>,xor2)) +* (1GateCircStr (<*[<*N,h*>,xor2],(S0,A0,h0)*>,xor2))
GFA0CarryCirc (N,h,(S0,A0,h0)) is strict non-empty finitely-generated V95( GFA0CarryStr (N,h,(S0,A0,h0))) gate`2=den Boolean MSAlgebra over GFA0CarryStr (N,h,(S0,A0,h0))
GFA0CarryICirc (N,h,(S0,A0,h0)) is strict non-empty finitely-generated V95( GFA0CarryIStr (N,h,(S0,A0,h0))) gate`2=den Boolean MSAlgebra over GFA0CarryIStr (N,h,(S0,A0,h0))
1GateCircuit (N,h,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*N,h*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*N,h*>,and2)
1GateCircuit (<*N,h*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*N,h*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*N,h*>,and2)
1GateCircuit (h,(S0,A0,h0),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*h,(S0,A0,h0)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*h,(S0,A0,h0)*>,and2)
1GateCircuit (<*h,(S0,A0,h0)*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*h,(S0,A0,h0)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*h,(S0,A0,h0)*>,and2)
(1GateCircuit (N,h,and2)) +* (1GateCircuit (h,(S0,A0,h0),and2)) is strict non-empty finitely-generated V95((1GateCircStr (<*N,h*>,and2)) +* (1GateCircStr (<*h,(S0,A0,h0)*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*N,h*>,and2)) +* (1GateCircStr (<*h,(S0,A0,h0)*>,and2))
1GateCircuit ((S0,A0,h0),N,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0,A0,h0),N*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0,A0,h0),N*>,and2)
1GateCircuit (<*(S0,A0,h0),N*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0,A0,h0),N*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0,A0,h0),N*>,and2)
((1GateCircuit (N,h,and2)) +* (1GateCircuit (h,(S0,A0,h0),and2))) +* (1GateCircuit ((S0,A0,h0),N,and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*N,h*>,and2)) +* (1GateCircStr (<*h,(S0,A0,h0)*>,and2))) +* (1GateCircStr (<*(S0,A0,h0),N*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*N,h*>,and2)) +* (1GateCircStr (<*h,(S0,A0,h0)*>,and2))) +* (1GateCircStr (<*(S0,A0,h0),N*>,and2))
1GateCircuit ([<*N,h*>,and2],[<*h,(S0,A0,h0)*>,and2],[<*(S0,A0,h0),N*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*N,h*>,and2],[<*h,(S0,A0,h0)*>,and2],[<*(S0,A0,h0),N*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*N,h*>,and2],[<*h,(S0,A0,h0)*>,and2],[<*(S0,A0,h0),N*>,and2]*>,or3)
1GateCircuit (<*[<*N,h*>,and2],[<*h,(S0,A0,h0)*>,and2],[<*(S0,A0,h0),N*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*N,h*>,and2],[<*h,(S0,A0,h0)*>,and2],[<*(S0,A0,h0),N*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*N,h*>,and2],[<*h,(S0,A0,h0)*>,and2],[<*(S0,A0,h0),N*>,and2]*>,or3)
(GFA0CarryICirc (N,h,(S0,A0,h0))) +* (1GateCircuit ([<*N,h*>,and2],[<*h,(S0,A0,h0)*>,and2],[<*(S0,A0,h0),N*>,and2],or3)) is strict non-empty finitely-generated V95((GFA0CarryIStr (N,h,(S0,A0,h0))) +* (1GateCircStr (<*[<*N,h*>,and2],[<*h,(S0,A0,h0)*>,and2],[<*(S0,A0,h0),N*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA0CarryIStr (N,h,(S0,A0,h0))) +* (1GateCircStr (<*[<*N,h*>,and2],[<*h,(S0,A0,h0)*>,and2],[<*(S0,A0,h0),N*>,and2]*>,or3))
(GFA0AdderCirc (N,h,(S0,A0,h0))) +* (GFA0CarryCirc (N,h,(S0,A0,h0))) is strict non-empty finitely-generated V95((GFA0AdderStr (N,h,(S0,A0,h0))) +* (GFA0CarryStr (N,h,(S0,A0,h0)))) gate`2=den Boolean MSAlgebra over (GFA0AdderStr (N,h,(S0,A0,h0))) +* (GFA0CarryStr (N,h,(S0,A0,h0)))
(S0,A0,h0) +* (BitGFA0Circ (N,h,(S0,A0,h0))) is strict non-empty finitely-generated V95((S0,A0,h0) +* (BitGFA0Str (N,h,(S0,A0,h0)))) gate`2=den Boolean MSAlgebra over (S0,A0,h0) +* (BitGFA0Str (N,h,(S0,A0,h0)))
((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>)) is Element of InnerVertices ((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>))
the carrier of ((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>)) is non empty set
InnerVertices ((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>)) is non empty Element of K27( the carrier of ((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>)))
K27( the carrier of ((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>))) is set
GFA0CarryOutput (N,h,(S0,A0,h0)) is Element of InnerVertices (GFA0CarryStr (N,h,(S0,A0,h0)))
the carrier of (GFA0CarryStr (N,h,(S0,A0,h0))) is non empty set
InnerVertices (GFA0CarryStr (N,h,(S0,A0,h0))) is non empty Element of K27( the carrier of (GFA0CarryStr (N,h,(S0,A0,h0))))
K27( the carrier of (GFA0CarryStr (N,h,(S0,A0,h0)))) is set
[<*[<*N,h*>,and2],[<*h,(S0,A0,h0)*>,and2],[<*(S0,A0,h0),N*>,and2]*>,or3] is non empty pair set
(S0,(A0 ^ <*N*>),(h0 ^ <*h*>)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(S0,(A0 ^ <*N*>),(h0 ^ <*h*>)) is strict non-empty finitely-generated V95((S0,(A0 ^ <*N*>),(h0 ^ <*h*>))) gate`2=den Boolean MSAlgebra over (S0,(A0 ^ <*N*>),(h0 ^ <*h*>))
o0 is Relation-like NAT -defined Function-like V14( NAT ) set
o0 . S0 is set
f1 is Relation-like NAT -defined Function-like V14( NAT ) set
f1 . S0 is set
o0 . 0 is set
f1 . 0 is set
g1 is Relation-like NAT -defined Function-like V14( NAT ) set
g1 . 0 is set
(S0,(A0 ^ <*N*>),(h0 ^ <*h*>)) is Element of InnerVertices (S0,(A0 ^ <*N*>),(h0 ^ <*h*>))
the carrier of (S0,(A0 ^ <*N*>),(h0 ^ <*h*>)) is non empty set
InnerVertices (S0,(A0 ^ <*N*>),(h0 ^ <*h*>)) is non empty Element of K27( the carrier of (S0,(A0 ^ <*N*>),(h0 ^ <*h*>)))
K27( the carrier of (S0,(A0 ^ <*N*>),(h0 ^ <*h*>))) is set
g1 . S0 is set
o0 . (S0 + 1) is set
f1 . (S0 + 1) is set
g1 . (S0 + 1) is set
len A0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
len h0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
(A0 ^ <*N*>) . (S0 + 1) is set
(h0 ^ <*h*>) . (S0 + 1) is set
A0 ^ {} is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
h0 ^ {} is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
S0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
S0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
A0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
h0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
((S0 + 1),A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(S0,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
A0 . (S0 + 1) is set
h0 . (S0 + 1) is set
(S0,A0,h0) is Element of InnerVertices (S0,A0,h0)
the carrier of (S0,A0,h0) is non empty set
InnerVertices (S0,A0,h0) is non empty Element of K27( the carrier of (S0,A0,h0))
K27( the carrier of (S0,A0,h0)) is set
BitGFA0Str ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0),xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2] is non empty pair set
<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2],(S0,A0,h0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2],(S0,A0,h0)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2],(S0,A0,h0)*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0 . (S0 + 1)),(S0,A0,h0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(S0,A0,h0),(A0 . (S0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2))) +* (1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2] is non empty pair set
[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2] is non empty pair set
[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2] is non empty pair set
<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (GFA0CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(S0,A0,h0) +* (BitGFA0Str ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((S0 + 1),A0,h0) is strict non-empty finitely-generated V95(((S0 + 1),A0,h0)) gate`2=den Boolean MSAlgebra over ((S0 + 1),A0,h0)
(S0,A0,h0) is strict non-empty finitely-generated V95((S0,A0,h0)) gate`2=den Boolean MSAlgebra over (S0,A0,h0)
BitGFA0Circ ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is strict non-empty finitely-generated V95( BitGFA0Str ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) gate`2=den Boolean MSAlgebra over BitGFA0Str ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))
GFA0AdderCirc ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is strict non-empty finitely-generated V95( GFA0AdderStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) gate`2=den Boolean MSAlgebra over GFA0AdderStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))
2GatesCircuit ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0),xor2) is strict non-empty finitely-generated V95( 2GatesCircStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0),xor2)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0),xor2)
1GateCircuit ((A0 . (S0 + 1)),(h0 . (S0 + 1)),xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2)
1GateCircuit (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2)
1GateCircuit ([<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2],(S0,A0,h0),xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2],(S0,A0,h0)*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2],(S0,A0,h0)*>,xor2)
1GateCircuit (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2],(S0,A0,h0)*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2],(S0,A0,h0)*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2],(S0,A0,h0)*>,xor2)
(1GateCircuit ((A0 . (S0 + 1)),(h0 . (S0 + 1)),xor2)) +* (1GateCircuit ([<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2],(S0,A0,h0),xor2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2],(S0,A0,h0)*>,xor2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2],(S0,A0,h0)*>,xor2))
GFA0CarryCirc ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is strict non-empty finitely-generated V95( GFA0CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) gate`2=den Boolean MSAlgebra over GFA0CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))
GFA0CarryICirc ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is strict non-empty finitely-generated V95( GFA0CarryIStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) gate`2=den Boolean MSAlgebra over GFA0CarryIStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))
1GateCircuit ((A0 . (S0 + 1)),(h0 . (S0 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2)
1GateCircuit (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2)
1GateCircuit ((h0 . (S0 + 1)),(S0,A0,h0),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2)
1GateCircuit (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2)
(1GateCircuit ((A0 . (S0 + 1)),(h0 . (S0 + 1)),and2)) +* (1GateCircuit ((h0 . (S0 + 1)),(S0,A0,h0),and2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2))
1GateCircuit ((S0,A0,h0),(A0 . (S0 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2)
1GateCircuit (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2)
((1GateCircuit ((A0 . (S0 + 1)),(h0 . (S0 + 1)),and2)) +* (1GateCircuit ((h0 . (S0 + 1)),(S0,A0,h0),and2))) +* (1GateCircuit ((S0,A0,h0),(A0 . (S0 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2))) +* (1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2))) +* (1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2))
1GateCircuit ([<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3)
(GFA0CarryICirc ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (1GateCircuit ([<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA0CarryIStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA0CarryIStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3))
(GFA0AdderCirc ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (GFA0CarryCirc ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) is strict non-empty finitely-generated V95((GFA0AdderStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (GFA0CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)))) gate`2=den Boolean MSAlgebra over (GFA0AdderStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (GFA0CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)))
(S0,A0,h0) +* (BitGFA0Circ ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) is strict non-empty finitely-generated V95((S0,A0,h0) +* (BitGFA0Str ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)))) gate`2=den Boolean MSAlgebra over (S0,A0,h0) +* (BitGFA0Str ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)))
((S0 + 1),A0,h0) is Element of InnerVertices ((S0 + 1),A0,h0)
the carrier of ((S0 + 1),A0,h0) is non empty set
InnerVertices ((S0 + 1),A0,h0) is non empty Element of K27( the carrier of ((S0 + 1),A0,h0))
K27( the carrier of ((S0 + 1),A0,h0)) is set
GFA0CarryOutput ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is Element of InnerVertices (GFA0CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)))
the carrier of (GFA0CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) is non empty set
InnerVertices (GFA0CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) is non empty Element of K27( the carrier of (GFA0CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))))
K27( the carrier of (GFA0CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)))) is set
[<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3] is non empty pair set
N is Relation-like NAT -defined Function-like V14( NAT ) set
N . S0 is set
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . S0 is set
N . 0 is set
h . 0 is set
Sn is Relation-like NAT -defined Function-like V14( NAT ) set
Sn . 0 is set
Sn . S0 is set
N . (S0 + 1) is set
h . (S0 + 1) is set
Sn . (S0 + 1) is set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
S0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (n,g,S0) is non empty Element of K27( the carrier of (n,g,S0))
the carrier of (n,g,S0) is non empty set
K27( the carrier of (n,g,S0)) is set
(f,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (f,g,S0) is non empty Element of K27( the carrier of (f,g,S0))
the carrier of (f,g,S0) is non empty set
K27( the carrier of (f,g,S0)) is set
A0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
n + A0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
n + 0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
((n + 0),g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + 0),g,S0) is non empty Element of K27( the carrier of ((n + 0),g,S0))
the carrier of ((n + 0),g,S0) is non empty set
K27( the carrier of ((n + 0),g,S0)) is set
h0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
n + h0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
((n + h0),g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + h0),g,S0) is non empty Element of K27( the carrier of ((n + h0),g,S0))
the carrier of ((n + h0),g,S0) is non empty set
K27( the carrier of ((n + h0),g,S0)) is set
h0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
n + (h0 + 1) is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() set
((n + (h0 + 1)),g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + (h0 + 1)),g,S0) is non empty Element of K27( the carrier of ((n + (h0 + 1)),g,S0))
the carrier of ((n + (h0 + 1)),g,S0) is non empty set
K27( the carrier of ((n + (h0 + 1)),g,S0)) is set
(n + h0) + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
g . ((n + h0) + 1) is set
S0 . ((n + h0) + 1) is set
((n + h0),g,S0) is Element of InnerVertices ((n + h0),g,S0)
BitGFA0Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0),xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,xor2] is non empty pair set
<*[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,xor2],((n + h0),g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,xor2],((n + h0),g,S0)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,xor2)) +* (1GateCircStr (<*[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,xor2],((n + h0),g,S0)*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,and2)) +* (1GateCircStr (<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((n + h0),g,S0),(g . ((n + h0) + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*((n + h0),g,S0),(g . ((n + h0) + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,and2)) +* (1GateCircStr (<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*>,and2))) +* (1GateCircStr (<*((n + h0),g,S0),(g . ((n + h0) + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,and2] is non empty pair set
[<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*>,and2] is non empty pair set
[<*((n + h0),g,S0),(g . ((n + h0) + 1))*>,and2] is non empty pair set
<*[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,and2],[<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*>,and2],[<*((n + h0),g,S0),(g . ((n + h0) + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,and2],[<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*>,and2],[<*((n + h0),g,S0),(g . ((n + h0) + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))) +* (1GateCircStr (<*[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,and2],[<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*>,and2],[<*((n + h0),g,S0),(g . ((n + h0) + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))) +* (GFA0CarryStr ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitGFA0Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))) is non empty Element of K27( the carrier of (BitGFA0Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))))
the carrier of (BitGFA0Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))) is non empty set
K27( the carrier of (BitGFA0Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)))) is set
(InnerVertices (n,g,S0)) \/ (InnerVertices (BitGFA0Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)))) is non empty set
(InnerVertices ((n + h0),g,S0)) \/ (InnerVertices (BitGFA0Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)))) is non empty set
((n + h0),g,S0) +* (BitGFA0Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (((n + h0),g,S0) +* (BitGFA0Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)))) is non empty Element of K27( the carrier of (((n + h0),g,S0) +* (BitGFA0Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)))))
the carrier of (((n + h0),g,S0) +* (BitGFA0Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)))) is non empty set
K27( the carrier of (((n + h0),g,S0) +* (BitGFA0Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))))) is set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
n + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
((n + 1),f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + 1),f,g) is non empty Element of K27( the carrier of ((n + 1),f,g))
the carrier of ((n + 1),f,g) is non empty set
K27( the carrier of ((n + 1),f,g)) is set
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (n,f,g) is non empty Element of K27( the carrier of (n,f,g))
the carrier of (n,f,g) is non empty set
K27( the carrier of (n,f,g)) is set
f . (n + 1) is set
g . (n + 1) is set
(n,f,g) is Element of InnerVertices (n,f,g)
BitGFA0Str ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (n + 1)),(g . (n + 1)),(n,f,g),xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),(g . (n + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,xor2] is non empty pair set
<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2],(n,f,g)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2],(n,f,g)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2],(n,f,g)*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (n + 1)),(n,f,g)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2)) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n,f,g),(f . (n + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(n,f,g),(f . (n + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2)) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2))) +* (1GateCircStr (<*(n,f,g),(f . (n + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*(f . (n + 1)),(g . (n + 1))*>,and2] is non empty pair set
[<*(g . (n + 1)),(n,f,g)*>,and2] is non empty pair set
[<*(n,f,g),(f . (n + 1))*>,and2] is non empty pair set
<*[<*(f . (n + 1)),(g . (n + 1))*>,and2],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(n,f,g),(f . (n + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(n,f,g),(f . (n + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(n,f,g),(f . (n + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (GFA0CarryStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitGFA0Str ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty Element of K27( the carrier of (BitGFA0Str ((f . (n + 1)),(g . (n + 1)),(n,f,g))))
the carrier of (BitGFA0Str ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty set
K27( the carrier of (BitGFA0Str ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is set
(InnerVertices (n,f,g)) \/ (InnerVertices (BitGFA0Str ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is non empty set
(n,f,g) +* (BitGFA0Str ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n,f,g) +* (BitGFA0Str ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is non empty Element of K27( the carrier of ((n,f,g) +* (BitGFA0Str ((f . (n + 1)),(g . (n + 1)),(n,f,g)))))
the carrier of ((n,f,g) +* (BitGFA0Str ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is non empty set
K27( the carrier of ((n,f,g) +* (BitGFA0Str ((f . (n + 1)),(g . (n + 1)),(n,f,g))))) is set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
S0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(f,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (f,g,S0) is non empty set
InnerVertices (f,g,S0) is non empty Element of K27( the carrier of (f,g,S0))
K27( the carrier of (f,g,S0)) is set
g . n is set
S0 . n is set
N is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
N + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
A0 is Element of InnerVertices (f,g,S0)
(N,g,S0) is Element of InnerVertices (N,g,S0)
(N,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (N,g,S0) is non empty set
InnerVertices (N,g,S0) is non empty Element of K27( the carrier of (N,g,S0))
K27( the carrier of (N,g,S0)) is set
GFA0AdderOutput ((g . n),(S0 . n),(N,g,S0)) is Element of InnerVertices (GFA0AdderStr ((g . n),(S0 . n),(N,g,S0)))
GFA0AdderStr ((g . n),(S0 . n),(N,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . n),(S0 . n),(N,g,S0),xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . n),(S0 . n)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . n),(S0 . n)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . n),(S0 . n)*>,xor2] is non empty pair set
<*[<*(g . n),(S0 . n)*>,xor2],(N,g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . n),(S0 . n)*>,xor2],(N,g,S0)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . n),(S0 . n)*>,xor2)) +* (1GateCircStr (<*[<*(g . n),(S0 . n)*>,xor2],(N,g,S0)*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA0AdderStr ((g . n),(S0 . n),(N,g,S0))) is non empty set
InnerVertices (GFA0AdderStr ((g . n),(S0 . n),(N,g,S0))) is non empty Element of K27( the carrier of (GFA0AdderStr ((g . n),(S0 . n),(N,g,S0))))
K27( the carrier of (GFA0AdderStr ((g . n),(S0 . n),(N,g,S0)))) is set
2GatesCircOutput ((g . n),(S0 . n),(N,g,S0),xor2) is non empty pair Element of InnerVertices (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),xor2))
the carrier of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),xor2)) is non empty set
InnerVertices (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),xor2)) is non empty Element of K27( the carrier of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),xor2)))
K27( the carrier of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),xor2))) is set
[<*[<*(g . n),(S0 . n)*>,xor2],(N,g,S0)*>,xor2] is non empty pair set
h is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
h + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
h0 is Element of InnerVertices (f,g,S0)
(h,g,S0) is Element of InnerVertices (h,g,S0)
(h,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (h,g,S0) is non empty set
InnerVertices (h,g,S0) is non empty Element of K27( the carrier of (h,g,S0))
K27( the carrier of (h,g,S0)) is set
GFA0AdderOutput ((g . n),(S0 . n),(h,g,S0)) is Element of InnerVertices (GFA0AdderStr ((g . n),(S0 . n),(h,g,S0)))
GFA0AdderStr ((g . n),(S0 . n),(h,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . n),(S0 . n),(h,g,S0),xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*(g . n),(S0 . n)*>,xor2],(h,g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . n),(S0 . n)*>,xor2],(h,g,S0)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . n),(S0 . n)*>,xor2)) +* (1GateCircStr (<*[<*(g . n),(S0 . n)*>,xor2],(h,g,S0)*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA0AdderStr ((g . n),(S0 . n),(h,g,S0))) is non empty set
InnerVertices (GFA0AdderStr ((g . n),(S0 . n),(h,g,S0))) is non empty Element of K27( the carrier of (GFA0AdderStr ((g . n),(S0 . n),(h,g,S0))))
K27( the carrier of (GFA0AdderStr ((g . n),(S0 . n),(h,g,S0)))) is set
2GatesCircOutput ((g . n),(S0 . n),(h,g,S0),xor2) is non empty pair Element of InnerVertices (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),xor2))
the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),xor2)) is non empty set
InnerVertices (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),xor2)) is non empty Element of K27( the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),xor2)))
K27( the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),xor2))) is set
[<*[<*(g . n),(S0 . n)*>,xor2],(h,g,S0)*>,xor2] is non empty pair set
A0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
1 + A0 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
h0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
(h0,g,S0) is Element of InnerVertices (h0,g,S0)
(h0,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (h0,g,S0) is non empty set
InnerVertices (h0,g,S0) is non empty Element of K27( the carrier of (h0,g,S0))
K27( the carrier of (h0,g,S0)) is set
GFA0AdderOutput ((g . n),(S0 . n),(h0,g,S0)) is Element of InnerVertices (GFA0AdderStr ((g . n),(S0 . n),(h0,g,S0)))
GFA0AdderStr ((g . n),(S0 . n),(h0,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . n),(S0 . n),(h0,g,S0),xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . n),(S0 . n)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . n),(S0 . n)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . n),(S0 . n)*>,xor2] is non empty pair set
<*[<*(g . n),(S0 . n)*>,xor2],(h0,g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . n),(S0 . n)*>,xor2],(h0,g,S0)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . n),(S0 . n)*>,xor2)) +* (1GateCircStr (<*[<*(g . n),(S0 . n)*>,xor2],(h0,g,S0)*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA0AdderStr ((g . n),(S0 . n),(h0,g,S0))) is non empty set
InnerVertices (GFA0AdderStr ((g . n),(S0 . n),(h0,g,S0))) is non empty Element of K27( the carrier of (GFA0AdderStr ((g . n),(S0 . n),(h0,g,S0))))
K27( the carrier of (GFA0AdderStr ((g . n),(S0 . n),(h0,g,S0)))) is set
2GatesCircOutput ((g . n),(S0 . n),(h0,g,S0),xor2) is non empty pair Element of InnerVertices (2GatesCircStr ((g . n),(S0 . n),(h0,g,S0),xor2))
the carrier of (2GatesCircStr ((g . n),(S0 . n),(h0,g,S0),xor2)) is non empty set
InnerVertices (2GatesCircStr ((g . n),(S0 . n),(h0,g,S0),xor2)) is non empty Element of K27( the carrier of (2GatesCircStr ((g . n),(S0 . n),(h0,g,S0),xor2)))
K27( the carrier of (2GatesCircStr ((g . n),(S0 . n),(h0,g,S0),xor2))) is set
[<*[<*(g . n),(S0 . n)*>,xor2],(h0,g,S0)*>,xor2] is non empty pair set
(n,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices H1(n) is non empty Element of K27( the carrier of H1(n))
the carrier of H1(n) is non empty set
K27( the carrier of H1(n)) is set
InnerVertices H1(f) is non empty Element of K27( the carrier of H1(f))
the carrier of H1(f) is non empty set
K27( the carrier of H1(f)) is set
h0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
g . (h0 + 1) is set
S0 . (h0 + 1) is set
BitGFA0Str ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0),xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (h0 + 1)),(S0 . (h0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,xor2] is non empty pair set
<*[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,xor2],(h0,g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,xor2],(h0,g,S0)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,xor2],(h0,g,S0)*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(S0 . (h0 + 1)),(h0,g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(S0 . (h0 + 1)),(h0,g,S0)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,and2)) +* (1GateCircStr (<*(S0 . (h0 + 1)),(h0,g,S0)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0,g,S0),(g . (h0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0,g,S0),(g . (h0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,and2)) +* (1GateCircStr (<*(S0 . (h0 + 1)),(h0,g,S0)*>,and2))) +* (1GateCircStr (<*(h0,g,S0),(g . (h0 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,and2] is non empty pair set
[<*(S0 . (h0 + 1)),(h0,g,S0)*>,and2] is non empty pair set
[<*(h0,g,S0),(g . (h0 + 1))*>,and2] is non empty pair set
<*[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,and2],[<*(S0 . (h0 + 1)),(h0,g,S0)*>,and2],[<*(h0,g,S0),(g . (h0 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,and2],[<*(S0 . (h0 + 1)),(h0,g,S0)*>,and2],[<*(h0,g,S0),(g . (h0 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0))) +* (1GateCircStr (<*[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,and2],[<*(S0 . (h0 + 1)),(h0,g,S0)*>,and2],[<*(h0,g,S0),(g . (h0 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0))) +* (GFA0CarryStr ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices H2(h0) is non empty Element of K27( the carrier of H2(h0))
the carrier of H2(h0) is non empty set
K27( the carrier of H2(h0)) is set
H1(h0) +* H2(h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of H1(h0) is non empty set
the carrier of H2(h0) \/ the carrier of H1(h0) is non empty set
h is Element of the carrier of H2(h0)
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
S0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
((f + 1),n,g,S0) is Element of InnerVertices (n,g,S0)
(n,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (n,g,S0) is non empty set
InnerVertices (n,g,S0) is non empty Element of K27( the carrier of (n,g,S0))
K27( the carrier of (n,g,S0)) is set
g . (f + 1) is set
S0 . (f + 1) is set
(f,g,S0) is Element of InnerVertices (f,g,S0)
(f,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (f,g,S0) is non empty set
InnerVertices (f,g,S0) is non empty Element of K27( the carrier of (f,g,S0))
K27( the carrier of (f,g,S0)) is set
GFA0AdderOutput ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0)) is Element of InnerVertices (GFA0AdderStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0)))
GFA0AdderStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (f + 1)),(S0 . (f + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (f + 1)),(S0 . (f + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2] is non empty pair set
<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2],(f,g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2],(f,g,S0)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . (f + 1)),(S0 . (f + 1))*>,xor2)) +* (1GateCircStr (<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2],(f,g,S0)*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA0AdderStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0))) is non empty set
InnerVertices (GFA0AdderStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0))) is non empty Element of K27( the carrier of (GFA0AdderStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0))))
K27( the carrier of (GFA0AdderStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0)))) is set
2GatesCircOutput ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),xor2) is non empty pair Element of InnerVertices (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),xor2))
the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),xor2)) is non empty set
InnerVertices (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),xor2)) is non empty Element of K27( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),xor2)))
K27( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),xor2))) is set
[<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2],(f,g,S0)*>,xor2] is non empty pair set
A0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
A0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
(A0,g,S0) is Element of InnerVertices (A0,g,S0)
(A0,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (A0,g,S0) is non empty set
InnerVertices (A0,g,S0) is non empty Element of K27( the carrier of (A0,g,S0))
K27( the carrier of (A0,g,S0)) is set
GFA0AdderOutput ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0)) is Element of InnerVertices (GFA0AdderStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0)))
GFA0AdderStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2],(A0,g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2],(A0,g,S0)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . (f + 1)),(S0 . (f + 1))*>,xor2)) +* (1GateCircStr (<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2],(A0,g,S0)*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA0AdderStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0))) is non empty set
InnerVertices (GFA0AdderStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0))) is non empty Element of K27( the carrier of (GFA0AdderStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0))))
K27( the carrier of (GFA0AdderStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0)))) is set
2GatesCircOutput ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),xor2) is non empty pair Element of InnerVertices (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),xor2))
the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),xor2)) is non empty set
InnerVertices (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),xor2)) is non empty Element of K27( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),xor2)))
K27( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),xor2))) is set
[<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2],(A0,g,S0)*>,xor2] is non empty pair set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (n,f,g) is non empty Element of K27( the carrier of (n,f,g))
the carrier of (n,f,g) is non empty set
K27( the carrier of (n,f,g)) is set
(0,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices H1( 0 ) is non empty Element of K27( the carrier of H1( 0 ))
the carrier of H1( 0 ) is non empty set
K27( the carrier of H1( 0 )) is set
A0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
(A0,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices H1(A0) is non empty Element of K27( the carrier of H1(A0))
the carrier of H1(A0) is non empty set
K27( the carrier of H1(A0)) is set
A0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
((A0 + 1),f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f . (A0 + 1) is set
g . (A0 + 1) is set
(A0,f,g) is Element of InnerVertices (A0,f,g)
the carrier of (A0,f,g) is non empty set
InnerVertices (A0,f,g) is non empty Element of K27( the carrier of (A0,f,g))
K27( the carrier of (A0,f,g)) is set
BitGFA0Str ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g),xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (A0 + 1)),(g . (A0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (A0 + 1)),(g . (A0 + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (A0 + 1)),(g . (A0 + 1))*>,xor2] is non empty pair set
<*[<*(f . (A0 + 1)),(g . (A0 + 1))*>,xor2],(A0,f,g)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (A0 + 1)),(g . (A0 + 1))*>,xor2],(A0,f,g)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (A0 + 1)),(g . (A0 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (A0 + 1)),(g . (A0 + 1))*>,xor2],(A0,f,g)*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (A0 + 1)),(g . (A0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (A0 + 1)),(A0,f,g)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (A0 + 1)),(A0,f,g)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (A0 + 1)),(g . (A0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (A0 + 1)),(A0,f,g)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0,f,g),(f . (A0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(A0,f,g),(f . (A0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (A0 + 1)),(g . (A0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (A0 + 1)),(A0,f,g)*>,and2))) +* (1GateCircStr (<*(A0,f,g),(f . (A0 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
[<*(f . (A0 + 1)),(g . (A0 + 1))*>,and2] is non empty pair set
[<*(g . (A0 + 1)),(A0,f,g)*>,and2] is non empty pair set
[<*(A0,f,g),(f . (A0 + 1))*>,and2] is non empty pair set
<*[<*(f . (A0 + 1)),(g . (A0 + 1))*>,and2],[<*(g . (A0 + 1)),(A0,f,g)*>,and2],[<*(A0,f,g),(f . (A0 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (A0 + 1)),(g . (A0 + 1))*>,and2],[<*(g . (A0 + 1)),(A0,f,g)*>,and2],[<*(A0,f,g),(f . (A0 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g))) +* (1GateCircStr (<*[<*(f . (A0 + 1)),(g . (A0 + 1))*>,and2],[<*(g . (A0 + 1)),(A0,f,g)*>,and2],[<*(A0,f,g),(f . (A0 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g))) +* (GFA0CarryStr ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
H1(A0) +* H2(A0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices H2(A0) is non empty Element of K27( the carrier of H2(A0))
the carrier of H2(A0) is non empty set
K27( the carrier of H2(A0)) is set
InnerVertices H1(A0 + 1) is non empty Element of K27( the carrier of H1(A0 + 1))
the carrier of H1(A0 + 1) is non empty set
K27( the carrier of H1(A0 + 1)) is set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,f,g) is Element of InnerVertices (n,f,g)
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (n,f,g) is non empty set
InnerVertices (n,f,g) is non empty Element of K27( the carrier of (n,f,g))
K27( the carrier of (n,f,g)) is set
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
(0,f,g) is Element of InnerVertices (0,f,g)
(0,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (0,f,g) is non empty set
InnerVertices (0,f,g) is non empty Element of K27( the carrier of (0,f,g))
K27( the carrier of (0,f,g)) is set
Sn is Relation-like NAT -defined Function-like V14( NAT ) set
Sn . 0 is set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
(Sn,f,g) is Element of InnerVertices (Sn,f,g)
(Sn,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (Sn,f,g) is non empty set
InnerVertices (Sn,f,g) is non empty Element of K27( the carrier of (Sn,f,g))
K27( the carrier of (Sn,f,g)) is set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
((Sn + 1),f,g) is Element of InnerVertices ((Sn + 1),f,g)
((Sn + 1),f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of ((Sn + 1),f,g) is non empty set
InnerVertices ((Sn + 1),f,g) is non empty Element of K27( the carrier of ((Sn + 1),f,g))
K27( the carrier of ((Sn + 1),f,g)) is set
f . (Sn + 1) is set
g . (Sn + 1) is set
GFA0CarryOutput ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g)) is Element of InnerVertices (GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g)))
GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (Sn + 1)),(g . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (Sn + 1)),(Sn,f,g)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (Sn + 1)),(Sn,f,g)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(g . (Sn + 1)),(Sn,f,g)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(Sn,f,g),(f . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(Sn,f,g),(f . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(g . (Sn + 1)),(Sn,f,g)*>,and2))) +* (1GateCircStr (<*(Sn,f,g),(f . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2] is non empty pair set
[<*(g . (Sn + 1)),(Sn,f,g)*>,and2] is non empty pair set
[<*(Sn,f,g),(f . (Sn + 1))*>,and2] is non empty pair set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),(Sn,f,g)*>,and2],[<*(Sn,f,g),(f . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),(Sn,f,g)*>,and2],[<*(Sn,f,g),(f . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g))) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),(Sn,f,g)*>,and2],[<*(Sn,f,g),(f . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g))) is non empty set
InnerVertices (GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g))) is non empty Element of K27( the carrier of (GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g))))
K27( the carrier of (GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g)))) is set
[<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),(Sn,f,g)*>,and2],[<*(Sn,f,g),(f . (Sn + 1))*>,and2]*>,or3] is non empty pair set
or3 is Relation-like Function-like V18(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((3 -tuples_on BOOLEAN),BOOLEAN))
A0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
h0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
proj1 ((0 -tuples_on BOOLEAN) --> FALSE) is set
(0,A0,h0) is non empty pair Element of InnerVertices (0,A0,h0)
(0,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (0,A0,h0) is non empty set
InnerVertices (0,A0,h0) is non empty Element of K27( the carrier of (0,A0,h0))
K27( the carrier of (0,A0,h0)) is set
(0,A0,h0) `1 is set
(0,A0,h0) `2 is set
proj1 ((0,A0,h0) `2) is set
card ((0,A0,h0) `1) is V21() V22() V23() cardinal set
N is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
(N,A0,h0) is non empty pair Element of InnerVertices (N,A0,h0)
(N,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (N,A0,h0) is non empty set
InnerVertices (N,A0,h0) is non empty Element of K27( the carrier of (N,A0,h0))
K27( the carrier of (N,A0,h0)) is set
(N,A0,h0) `1 is set
(N,A0,h0) `2 is set
proj1 ((N,A0,h0) `2) is set
card ((N,A0,h0) `1) is V21() V22() V23() cardinal set
N + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
((N + 1),A0,h0) is non empty pair Element of InnerVertices ((N + 1),A0,h0)
((N + 1),A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of ((N + 1),A0,h0) is non empty set
InnerVertices ((N + 1),A0,h0) is non empty Element of K27( the carrier of ((N + 1),A0,h0))
K27( the carrier of ((N + 1),A0,h0)) is set
A0 . (N + 1) is set
h0 . (N + 1) is set
GFA0CarryOutput ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0)) is Element of InnerVertices (GFA0CarryStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0)))
GFA0CarryStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . (N + 1)),(h0 . (N + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0 . (N + 1)),(N,A0,h0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0 . (N + 1)),(N,A0,h0)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (N + 1)),(N,A0,h0)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(N,A0,h0),(A0 . (N + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(N,A0,h0),(A0 . (N + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (N + 1)),(N,A0,h0)*>,and2))) +* (1GateCircStr (<*(N,A0,h0),(A0 . (N + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2] is non empty pair set
[<*(h0 . (N + 1)),(N,A0,h0)*>,and2] is non empty pair set
[<*(N,A0,h0),(A0 . (N + 1))*>,and2] is non empty pair set
<*[<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2],[<*(h0 . (N + 1)),(N,A0,h0)*>,and2],[<*(N,A0,h0),(A0 . (N + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2],[<*(h0 . (N + 1)),(N,A0,h0)*>,and2],[<*(N,A0,h0),(A0 . (N + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0))) +* (1GateCircStr (<*[<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2],[<*(h0 . (N + 1)),(N,A0,h0)*>,and2],[<*(N,A0,h0),(A0 . (N + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA0CarryStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0))) is non empty set
InnerVertices (GFA0CarryStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0))) is non empty Element of K27( the carrier of (GFA0CarryStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0))))
K27( the carrier of (GFA0CarryStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0)))) is set
[<*[<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2],[<*(h0 . (N + 1)),(N,A0,h0)*>,and2],[<*(N,A0,h0),(A0 . (N + 1))*>,and2]*>,or3] is non empty pair set
proj1 or3 is set
((N + 1),A0,h0) `1 is set
((N + 1),A0,h0) `2 is set
proj1 (((N + 1),A0,h0) `2) is set
card (((N + 1),A0,h0) `1) is V21() V22() V23() cardinal set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,f,g) is non empty pair Element of InnerVertices (n,f,g)
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (n,f,g) is non empty set
InnerVertices (n,f,g) is non empty Element of K27( the carrier of (n,f,g))
K27( the carrier of (n,f,g)) is set
S0 is set
A0 is Relation-like Function-like V18(2 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((2 -tuples_on BOOLEAN),BOOLEAN))
[S0,A0] is non empty pair set
proj1 A0 is set
[S0,A0] `2 is set
proj1 ([S0,A0] `2) is set
(n,f,g) `2 is set
proj1 ((n,f,g) `2) is set
A0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like nonpair-yielding set
h0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like nonpair-yielding set
N is Relation-like NAT -defined Function-like V14( NAT ) set
(0,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices H1( 0 ) is non empty Element of K27( the carrier of H1( 0 ))
the carrier of H1( 0 ) is non empty set
K27( the carrier of H1( 0 )) is set
InputVertices H1( 0 ) is Element of K27( the carrier of H1( 0 ))
N . 0 is set
(0,A0,h0) is non empty pair Element of InnerVertices (0,A0,h0)
the carrier of (0,A0,h0) is non empty set
InnerVertices (0,A0,h0) is non empty Element of K27( the carrier of (0,A0,h0))
K27( the carrier of (0,A0,h0)) is set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
A0 . (Sn + 1) is non pair set
h0 . (Sn + 1) is non pair set
An is set
BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],An*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],An*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0 . (Sn + 1)),An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*An,(A0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*An,(A0 . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2))) +* (1GateCircStr (<*An,(A0 . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2] is non empty pair set
[<*(h0 . (Sn + 1)),An*>,and2] is non empty pair set
[<*An,(A0 . (Sn + 1))*>,and2] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),An*>,and2],[<*An,(A0 . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),An*>,and2],[<*An,(A0 . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),An*>,and2],[<*An,(A0 . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) +* (GFA0CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) is non empty Element of K27( the carrier of (BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)))
the carrier of (BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) is non empty set
K27( the carrier of (BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An))) is set
An is set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
N . Sn is set
(Sn,A0,h0) is non empty pair Element of InnerVertices (Sn,A0,h0)
(Sn,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (Sn,A0,h0) is non empty set
InnerVertices (Sn,A0,h0) is non empty Element of K27( the carrier of (Sn,A0,h0))
K27( the carrier of (Sn,A0,h0)) is set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
A0 . (Sn + 1) is non pair set
h0 . (Sn + 1) is non pair set
<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2] is non empty pair set
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2] is non empty pair set
BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],An*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],An*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0 . (Sn + 1)),An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*An,(A0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*An,(A0 . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2))) +* (1GateCircStr (<*An,(A0 . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(h0 . (Sn + 1)),An*>,and2] is non empty pair set
[<*An,(A0 . (Sn + 1))*>,and2] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),An*>,and2],[<*An,(A0 . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),An*>,and2],[<*An,(A0 . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),An*>,and2],[<*An,(A0 . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) +* (GFA0CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices H2(An,Sn) is Element of K27( the carrier of H2(An,Sn))
the carrier of H2(An,Sn) is non empty set
K27( the carrier of H2(An,Sn)) is set
{(A0 . (Sn + 1)),(h0 . (Sn + 1)),An} is V28() set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
N . Sn is set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
A0 . (Sn + 1) is non pair set
h0 . (Sn + 1) is non pair set
An is set
BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],An*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],An*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0 . (Sn + 1)),An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*An,(A0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*An,(A0 . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2))) +* (1GateCircStr (<*An,(A0 . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2] is non empty pair set
[<*(h0 . (Sn + 1)),An*>,and2] is non empty pair set
[<*An,(A0 . (Sn + 1))*>,and2] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),An*>,and2],[<*An,(A0 . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),An*>,and2],[<*An,(A0 . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),An*>,and2],[<*An,(A0 . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) +* (GFA0CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of H2(An,Sn) is non empty set
InputVertices H2(An,Sn) is Element of K27( the carrier of H2(An,Sn))
K27( the carrier of H2(An,Sn)) is set
{An} is non empty V12() V28() 1 -element set
(InputVertices H2(An,Sn)) \ {An} is Element of K27( the carrier of H2(An,Sn))
{(A0 . (Sn + 1)),(h0 . (Sn + 1)),An} is V28() set
o0 is non empty pair set
An is non empty V56() ManySortedSign
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
(Sn,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
o0 is set
N . Sn is set
(Sn,A0,h0) is non empty pair Element of InnerVertices (Sn,A0,h0)
the carrier of (Sn,A0,h0) is non empty set
InnerVertices (Sn,A0,h0) is non empty Element of K27( the carrier of (Sn,A0,h0))
K27( the carrier of (Sn,A0,h0)) is set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
N . (Sn + 1) is set
((Sn + 1),A0,h0) is non empty pair Element of InnerVertices ((Sn + 1),A0,h0)
((Sn + 1),A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of ((Sn + 1),A0,h0) is non empty set
InnerVertices ((Sn + 1),A0,h0) is non empty Element of K27( the carrier of ((Sn + 1),A0,h0))
K27( the carrier of ((Sn + 1),A0,h0)) is set
A0 . (Sn + 1) is non pair set
h0 . (Sn + 1) is non pair set
BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],o0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],o0*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],o0*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0 . (Sn + 1)),o0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0 . (Sn + 1)),o0*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (Sn + 1)),o0*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*o0,(A0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*o0,(A0 . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (Sn + 1)),o0*>,and2))) +* (1GateCircStr (<*o0,(A0 . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2] is non empty pair set
[<*(h0 . (Sn + 1)),o0*>,and2] is non empty pair set
[<*o0,(A0 . (Sn + 1))*>,and2] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),o0*>,and2],[<*o0,(A0 . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),o0*>,and2],[<*o0,(A0 . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),o0*>,and2],[<*o0,(A0 . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)) +* (GFA0CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
An +* H2(o0,Sn) is non empty non void V56() strict ManySortedSign
GFA0CarryOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0) is Element of InnerVertices (GFA0CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))
the carrier of (GFA0CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)) is non empty set
InnerVertices (GFA0CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)) is non empty Element of K27( the carrier of (GFA0CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)))
K27( the carrier of (GFA0CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))) is set
[<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),o0*>,and2],[<*o0,(A0 . (Sn + 1))*>,and2]*>,or3] is non empty pair set
InputVertices H2(o0,Sn) is Element of K27( the carrier of H2(o0,Sn))
the carrier of H2(o0,Sn) is non empty set
K27( the carrier of H2(o0,Sn)) is set
{(A0 . (Sn + 1)),(h0 . (Sn + 1)),o0} is V28() set
InnerVertices H2(o0,Sn) is non empty Element of K27( the carrier of H2(o0,Sn))
{[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2]} is Relation-like Function-like constant non empty V12() V28() 1 -element set
GFA0AdderOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0) is Element of InnerVertices (GFA0AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))
the carrier of (GFA0AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)) is non empty set
InnerVertices (GFA0AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)) is non empty Element of K27( the carrier of (GFA0AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)))
K27( the carrier of (GFA0AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))) is set
2GatesCircOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0,xor2) is non empty pair Element of InnerVertices (2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0,xor2))
the carrier of (2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0,xor2)) is non empty set
InnerVertices (2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0,xor2)) is non empty Element of K27( the carrier of (2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0,xor2)))
K27( the carrier of (2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0,xor2))) is set
[<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],o0*>,xor2] is non empty pair set
{(GFA0AdderOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))} is non empty V12() V28() 1 -element set
{[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2]} \/ {(GFA0AdderOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))} is non empty V28() set
{[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),o0*>,and2],[<*o0,(A0 . (Sn + 1))*>,and2]} is Relation-like V28() set
({[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2]} \/ {(GFA0AdderOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))}) \/ {[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),o0*>,and2],[<*o0,(A0 . (Sn + 1))*>,and2]} is non empty V28() set
{(GFA0CarryOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))} is non empty V12() V28() 1 -element set
(({[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2]} \/ {(GFA0AdderOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))}) \/ {[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),o0*>,and2],[<*o0,(A0 . (Sn + 1))*>,and2]}) \/ {(GFA0CarryOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))} is non empty V28() set
{H5(o0,Sn)} is non empty V12() V28() 1 -element set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
((Sn + 1),A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices ((Sn + 1),A0,h0) is Element of K27( the carrier of ((Sn + 1),A0,h0))
the carrier of ((Sn + 1),A0,h0) is non empty set
K27( the carrier of ((Sn + 1),A0,h0)) is set
(Sn,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (Sn,A0,h0) is Element of K27( the carrier of (Sn,A0,h0))
the carrier of (Sn,A0,h0) is non empty set
K27( the carrier of (Sn,A0,h0)) is set
A0 . (Sn + 1) is non pair set
h0 . (Sn + 1) is non pair set
(Sn,A0,h0) is non empty pair Element of InnerVertices (Sn,A0,h0)
InnerVertices (Sn,A0,h0) is non empty Element of K27( the carrier of (Sn,A0,h0))
BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0),xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],(Sn,A0,h0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],(Sn,A0,h0)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2],(Sn,A0,h0)*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0 . (Sn + 1)),(Sn,A0,h0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0 . (Sn + 1)),(Sn,A0,h0)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (Sn + 1)),(Sn,A0,h0)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(Sn,A0,h0),(A0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(Sn,A0,h0),(A0 . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(h0 . (Sn + 1)),(Sn,A0,h0)*>,and2))) +* (1GateCircStr (<*(Sn,A0,h0),(A0 . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2] is non empty pair set
[<*(h0 . (Sn + 1)),(Sn,A0,h0)*>,and2] is non empty pair set
[<*(Sn,A0,h0),(A0 . (Sn + 1))*>,and2] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),(Sn,A0,h0)*>,and2],[<*(Sn,A0,h0),(A0 . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),(Sn,A0,h0)*>,and2],[<*(Sn,A0,h0),(A0 . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0))) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2],[<*(h0 . (Sn + 1)),(Sn,A0,h0)*>,and2],[<*(Sn,A0,h0),(A0 . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0))) +* (GFA0CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0))) is non empty set
InputVertices (BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0))) is Element of K27( the carrier of (BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0))))
K27( the carrier of (BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0)))) is set
{(Sn,A0,h0)} is Relation-like non empty V12() V28() 1 -element set
(InputVertices (BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0)))) \ {(Sn,A0,h0)} is Element of K27( the carrier of (BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0))))
(InputVertices (Sn,A0,h0)) \/ ((InputVertices (BitGFA0Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0)))) \ {(Sn,A0,h0)}) is set
N . Sn is set
g is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty non pair V21() V22() V23() V25() V26() V27() V28() V29() V32() cardinal 0 -element V37() FinSequence-like FinSubsequence-like FinSequence-membered non with_pair nonpair-yielding ext-real non positive non negative V115() V126() set
S0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty non pair V21() V22() V23() V25() V26() V27() V28() V29() V32() cardinal 0 -element V37() FinSequence-like FinSubsequence-like FinSequence-membered non with_pair nonpair-yielding ext-real non positive non negative V115() V126() set
(0,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (0,g,S0) is Element of K27( the carrier of (0,g,S0))
the carrier of (0,g,S0) is non empty set
K27( the carrier of (0,g,S0)) is set
proj2 g is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V12() non pair V21() V22() V23() V25() V26() V27() V28() V29() V32() cardinal {} -element V37() FinSequence-like FinSubsequence-like FinSequence-membered non with_pair nonpair-yielding ext-real non positive non negative V115() V126() set
proj2 S0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V12() non pair V21() V22() V23() V25() V26() V27() V28() V29() V32() cardinal {} -element V37() FinSequence-like FinSubsequence-like FinSequence-membered non with_pair nonpair-yielding ext-real non positive non negative V115() V126() set
(proj2 g) \/ (proj2 S0) is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty non pair V21() V22() V23() V25() V26() V27() V28() V29() V32() cardinal {} -element V37() FinSequence-like FinSubsequence-like FinSequence-membered non with_pair nonpair-yielding ext-real non positive non negative V115() V126() set
proj2 {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V12() non pair V21() V22() V23() V25() V26() V27() V28() V29() V32() cardinal {} -element V37() FinSequence-like FinSubsequence-like FinSequence-membered non with_pair nonpair-yielding ext-real non positive non negative V115() V126() set
g is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
g + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
S0 is Relation-like NAT -defined Function-like V28() g + 1 -element FinSequence-like FinSubsequence-like nonpair-yielding set
A0 is Relation-like NAT -defined Function-like V28() g + 1 -element FinSequence-like FinSubsequence-like nonpair-yielding set
((g + 1),S0,A0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices ((g + 1),S0,A0) is Element of K27( the carrier of ((g + 1),S0,A0))
the carrier of ((g + 1),S0,A0) is non empty set
K27( the carrier of ((g + 1),S0,A0)) is set
proj2 S0 is V28() non with_pair set
proj2 A0 is V28() non with_pair set
(proj2 S0) \/ (proj2 A0) is V28() non with_pair set
h0 is Relation-like NAT -defined Function-like V28() g -element FinSequence-like FinSubsequence-like nonpair-yielding set
N is non pair set
<*N*> is Relation-like NAT -defined Function-like constant non empty V12() V28() 1 -element FinSequence-like FinSubsequence-like nonpair-yielding set
h0 ^ <*N*> is Relation-like NAT -defined Function-like non empty V28() g + 1 -element FinSequence-like FinSubsequence-like set
h is Relation-like NAT -defined Function-like V28() g -element FinSequence-like FinSubsequence-like nonpair-yielding set
Sn is non pair set
<*Sn*> is Relation-like NAT -defined Function-like constant non empty V12() V28() 1 -element FinSequence-like FinSubsequence-like nonpair-yielding set
h ^ <*Sn*> is Relation-like NAT -defined Function-like non empty V28() g + 1 -element FinSequence-like FinSubsequence-like set
dom <*N*> is non empty V12() V28() 1 -element Element of K27(NAT)
len h0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
S0 . (g + 1) is non pair set
<*N*> . 1 is non pair set
dom <*Sn*> is non empty V12() V28() 1 -element Element of K27(NAT)
len h is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
A0 . (g + 1) is non pair set
<*Sn*> . 1 is non pair set
(g,S0,A0) is non empty pair Element of InnerVertices (g,S0,A0)
(g,S0,A0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (g,S0,A0) is non empty set
InnerVertices (g,S0,A0) is non empty Element of K27( the carrier of (g,S0,A0))
K27( the carrier of (g,S0,A0)) is set
{N,Sn,H1(g)} is V28() set
{H1(g),N,Sn} is V28() set
proj2 h0 is V28() non with_pair set
proj2 <*N*> is non empty V12() V28() 1 -element non with_pair set
(proj2 h0) \/ (proj2 <*N*>) is non empty V28() non with_pair set
{N} is non empty V12() V28() 1 -element non with_pair set
(proj2 h0) \/ {N} is non empty V28() non with_pair set
proj2 h is V28() non with_pair set
proj2 <*Sn*> is non empty V12() V28() 1 -element non with_pair set
(proj2 h) \/ (proj2 <*Sn*>) is non empty V28() non with_pair set
{Sn} is non empty V12() V28() 1 -element non with_pair set
(proj2 h) \/ {Sn} is non empty V28() non with_pair set
<*N,Sn*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
[<*N,Sn*>,and2] is non empty pair set
[<*N,Sn*>,xor2] is non empty pair set
h0 ^ {} is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
h ^ {} is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(g,h0,h) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (g,h0,h) is Element of K27( the carrier of (g,h0,h))
the carrier of (g,h0,h) is non empty set
K27( the carrier of (g,h0,h)) is set
BitGFA0Str (N,Sn,H1(g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr (N,Sn,(g,S0,A0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (N,Sn,(g,S0,A0),xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*N,Sn*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*N,Sn*>,xor2],(g,S0,A0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*N,Sn*>,xor2],(g,S0,A0)*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*N,Sn*>,xor2)) +* (1GateCircStr (<*[<*N,Sn*>,xor2],(g,S0,A0)*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr (N,Sn,(g,S0,A0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr (N,Sn,(g,S0,A0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*N,Sn*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*Sn,(g,S0,A0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*Sn,(g,S0,A0)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*N,Sn*>,and2)) +* (1GateCircStr (<*Sn,(g,S0,A0)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g,S0,A0),N*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g,S0,A0),N*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*N,Sn*>,and2)) +* (1GateCircStr (<*Sn,(g,S0,A0)*>,and2))) +* (1GateCircStr (<*(g,S0,A0),N*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*Sn,(g,S0,A0)*>,and2] is non empty pair set
[<*(g,S0,A0),N*>,and2] is non empty pair set
<*[<*N,Sn*>,and2],[<*Sn,(g,S0,A0)*>,and2],[<*(g,S0,A0),N*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*N,Sn*>,and2],[<*Sn,(g,S0,A0)*>,and2],[<*(g,S0,A0),N*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr (N,Sn,(g,S0,A0))) +* (1GateCircStr (<*[<*N,Sn*>,and2],[<*Sn,(g,S0,A0)*>,and2],[<*(g,S0,A0),N*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr (N,Sn,(g,S0,A0))) +* (GFA0CarryStr (N,Sn,(g,S0,A0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BitGFA0Str (N,Sn,H1(g))) is non empty set
InputVertices (BitGFA0Str (N,Sn,H1(g))) is Element of K27( the carrier of (BitGFA0Str (N,Sn,H1(g))))
K27( the carrier of (BitGFA0Str (N,Sn,H1(g)))) is set
{H1(g)} is Relation-like non empty V12() V28() 1 -element set
(InputVertices (BitGFA0Str (N,Sn,H1(g)))) \ {H1(g)} is Element of K27( the carrier of (BitGFA0Str (N,Sn,H1(g))))
(InputVertices (g,h0,h)) \/ ((InputVertices (BitGFA0Str (N,Sn,H1(g)))) \ {H1(g)}) is set
(proj2 h0) \/ (proj2 h) is V28() non with_pair set
((proj2 h0) \/ (proj2 h)) \/ ((InputVertices (BitGFA0Str (N,Sn,H1(g)))) \ {H1(g)}) is set
{N,Sn,H1(g)} \ {H1(g)} is V28() Element of K27({N,Sn,H1(g)})
K27({N,Sn,H1(g)}) is V28() V32() set
((proj2 h0) \/ (proj2 h)) \/ ({N,Sn,H1(g)} \ {H1(g)}) is V28() set
{N,Sn} is non empty V28() non with_pair set
((proj2 h0) \/ (proj2 h)) \/ {N,Sn} is non empty V28() non with_pair set
{N} \/ {Sn} is non empty V28() non with_pair set
((proj2 h0) \/ (proj2 h)) \/ ({N} \/ {Sn}) is non empty V28() non with_pair set
((proj2 h0) \/ (proj2 h)) \/ {N} is non empty V28() non with_pair set
(((proj2 h0) \/ (proj2 h)) \/ {N}) \/ {Sn} is non empty V28() non with_pair set
((proj2 h0) \/ {N}) \/ (proj2 h) is non empty V28() non with_pair set
(((proj2 h0) \/ {N}) \/ (proj2 h)) \/ {Sn} is non empty V28() non with_pair set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
2 * n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
1 + (2 * n) is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f is Relation-like NAT -defined Function-like V28() n -element FinSequence-like FinSubsequence-like nonpair-yielding set
g is Relation-like NAT -defined Function-like V28() n -element FinSequence-like FinSubsequence-like nonpair-yielding set
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,f,g) is strict non-empty finitely-generated V95((n,f,g)) gate`2=den Boolean MSAlgebra over (n,f,g)
the Sorts of (n,f,g) is Relation-like the carrier of (n,f,g) -defined Function-like V14( the carrier of (n,f,g)) set
the carrier of (n,f,g) is non empty set
K106( the Sorts of (n,f,g)) is set
N is Relation-like Function-like V18( NAT , NAT ) Element of K27(K28(NAT,NAT))
N . 0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
N . 1 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
N . 2 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (Sn + 1) is non pair set
g . (Sn + 1) is non pair set
h is set
BitGFA0Circ ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V95( BitGFA0Str ((f . (Sn + 1)),(g . (Sn + 1)),h)) gate`2=den Boolean MSAlgebra over BitGFA0Str ((f . (Sn + 1)),(g . (Sn + 1)),h)
BitGFA0Str ((f . (Sn + 1)),(g . (Sn + 1)),h) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),h) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (Sn + 1)),(g . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2] is non empty pair set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2],h*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2],h*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2],h*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),h) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),h) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (Sn + 1)),h*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (Sn + 1)),h*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*h,(f . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*h,(f . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2))) +* (1GateCircStr (<*h,(f . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2] is non empty pair set
[<*(g . (Sn + 1)),h*>,and2] is non empty pair set
[<*h,(f . (Sn + 1))*>,and2] is non empty pair set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),h*>,and2],[<*h,(f . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),h*>,and2],[<*h,(f . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),h*>,and2],[<*h,(f . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderCirc ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V95( GFA0AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) gate`2=den Boolean MSAlgebra over GFA0AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),h)
2GatesCircuit ((f . (Sn + 1)),(g . (Sn + 1)),h,xor2) is strict non-empty finitely-generated V95( 2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,xor2)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,xor2)
1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2)
1GateCircuit (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2)
1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2],h,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2],h*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2],h*>,xor2)
1GateCircuit (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2],h*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2],h*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2],h*>,xor2)
(1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),xor2)) +* (1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2],h,xor2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2],h*>,xor2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2],h*>,xor2))
GFA0CarryCirc ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V95( GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) gate`2=den Boolean MSAlgebra over GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),h)
GFA0CarryICirc ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V95( GFA0CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) gate`2=den Boolean MSAlgebra over GFA0CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)
1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2)
1GateCircuit (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2)
1GateCircuit ((g . (Sn + 1)),h,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (Sn + 1)),h*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (Sn + 1)),h*>,and2)
1GateCircuit (<*(g . (Sn + 1)),h*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (Sn + 1)),h*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (Sn + 1)),h*>,and2)
(1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),and2)) +* (1GateCircuit ((g . (Sn + 1)),h,and2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2))
1GateCircuit (h,(f . (Sn + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*h,(f . (Sn + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*h,(f . (Sn + 1))*>,and2)
1GateCircuit (<*h,(f . (Sn + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*h,(f . (Sn + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*h,(f . (Sn + 1))*>,and2)
((1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),and2)) +* (1GateCircuit ((g . (Sn + 1)),h,and2))) +* (1GateCircuit (h,(f . (Sn + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2))) +* (1GateCircStr (<*h,(f . (Sn + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2))) +* (1GateCircStr (<*h,(f . (Sn + 1))*>,and2))
1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),h*>,and2],[<*h,(f . (Sn + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),h*>,and2],[<*h,(f . (Sn + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),h*>,and2],[<*h,(f . (Sn + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),h*>,and2],[<*h,(f . (Sn + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),h*>,and2],[<*h,(f . (Sn + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),h*>,and2],[<*h,(f . (Sn + 1))*>,and2]*>,or3)
(GFA0CarryICirc ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),h*>,and2],[<*h,(f . (Sn + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA0CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),h*>,and2],[<*h,(f . (Sn + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA0CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2],[<*(g . (Sn + 1)),h*>,and2],[<*h,(f . (Sn + 1))*>,and2]*>,or3))
(GFA0AdderCirc ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (GFA0CarryCirc ((f . (Sn + 1)),(g . (Sn + 1)),h)) is strict non-empty finitely-generated V95((GFA0AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),h))) gate`2=den Boolean MSAlgebra over (GFA0AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (GFA0CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),h))
the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))) is Relation-like the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) -defined Function-like V14( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)))) set
the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) is non empty set
K106( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE)))) is set
h is Element of K106( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))))
Following (h,1) is Element of K106( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))))
Following h is Element of K106( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))))
Following (h,H4( 0 )) is Element of K106( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))))
h is Relation-like NAT -defined Function-like V14( NAT ) set
o0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
o0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (o0 + 1) is non pair set
g . (o0 + 1) is non pair set
h . o0 is set
f1 is set
BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),f1,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (o0 + 1)),(g . (o0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2] is non empty pair set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],f1*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],f1*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (o0 + 1)),f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (o0 + 1)),f1*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),f1*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f1,(f . (o0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f1,(f . (o0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),f1*>,and2))) +* (1GateCircStr (<*f1,(f . (o0 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2] is non empty pair set
[<*(g . (o0 + 1)),f1*>,and2] is non empty pair set
[<*f1,(f . (o0 + 1))*>,and2] is non empty pair set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),f1*>,and2],[<*f1,(f . (o0 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),f1*>,and2],[<*f1,(f . (o0 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),f1*>,and2],[<*f1,(f . (o0 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitGFA0Circ ((f . (o0 + 1)),(g . (o0 + 1)),f1) is strict non-empty finitely-generated V95( BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),f1)) gate`2=den Boolean MSAlgebra over BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),f1)
GFA0AdderCirc ((f . (o0 + 1)),(g . (o0 + 1)),f1) is strict non-empty finitely-generated V95( GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) gate`2=den Boolean MSAlgebra over GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)
2GatesCircuit ((f . (o0 + 1)),(g . (o0 + 1)),f1,xor2) is strict non-empty finitely-generated V95( 2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),f1,xor2)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),f1,xor2)
1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)
1GateCircuit (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)
1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],f1,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],f1*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],f1*>,xor2)
1GateCircuit (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],f1*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],f1*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],f1*>,xor2)
(1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),xor2)) +* (1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],f1,xor2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],f1*>,xor2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2],f1*>,xor2))
GFA0CarryCirc ((f . (o0 + 1)),(g . (o0 + 1)),f1) is strict non-empty finitely-generated V95( GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) gate`2=den Boolean MSAlgebra over GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)
GFA0CarryICirc ((f . (o0 + 1)),(g . (o0 + 1)),f1) is strict non-empty finitely-generated V95( GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) gate`2=den Boolean MSAlgebra over GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)
1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)
1GateCircuit (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)
1GateCircuit ((g . (o0 + 1)),f1,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (o0 + 1)),f1*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (o0 + 1)),f1*>,and2)
1GateCircuit (<*(g . (o0 + 1)),f1*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (o0 + 1)),f1*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (o0 + 1)),f1*>,and2)
(1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2)) +* (1GateCircuit ((g . (o0 + 1)),f1,and2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),f1*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),f1*>,and2))
1GateCircuit (f1,(f . (o0 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*f1,(f . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f1,(f . (o0 + 1))*>,and2)
1GateCircuit (<*f1,(f . (o0 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*f1,(f . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f1,(f . (o0 + 1))*>,and2)
((1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2)) +* (1GateCircuit ((g . (o0 + 1)),f1,and2))) +* (1GateCircuit (f1,(f . (o0 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),f1*>,and2))) +* (1GateCircStr (<*f1,(f . (o0 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2)) +* (1GateCircStr (<*(g . (o0 + 1)),f1*>,and2))) +* (1GateCircStr (<*f1,(f . (o0 + 1))*>,and2))
1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),f1*>,and2],[<*f1,(f . (o0 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),f1*>,and2],[<*f1,(f . (o0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),f1*>,and2],[<*f1,(f . (o0 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),f1*>,and2],[<*f1,(f . (o0 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),f1*>,and2],[<*f1,(f . (o0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),f1*>,and2],[<*f1,(f . (o0 + 1))*>,and2]*>,or3)
(GFA0CarryICirc ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),f1*>,and2],[<*f1,(f . (o0 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),f1*>,and2],[<*f1,(f . (o0 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA0CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2],[<*(g . (o0 + 1)),f1*>,and2],[<*f1,(f . (o0 + 1))*>,and2]*>,or3))
(GFA0AdderCirc ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (GFA0CarryCirc ((f . (o0 + 1)),(g . (o0 + 1)),f1)) is strict non-empty finitely-generated V95((GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),f1))) gate`2=den Boolean MSAlgebra over (GFA0AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (GFA0CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),f1))
g1 is non-empty finitely-generated V95(H1(f1,o0)) MSAlgebra over H1(f1,o0)
the Sorts of g1 is Relation-like the carrier of H1(f1,o0) -defined Function-like V14( the carrier of H1(f1,o0)) set
the carrier of H1(f1,o0) is non empty set
K106( the Sorts of g1) is set
(o0,f,g) is non empty pair Element of InnerVertices (o0,f,g)
(o0,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (o0,f,g) is non empty set
InnerVertices (o0,f,g) is non empty Element of K27( the carrier of (o0,f,g))
K27( the carrier of (o0,f,g)) is set
h1 is Element of K106( the Sorts of g1)
Following (h1,(N . 1)) is Element of K106( the Sorts of g1)
the Sorts of g1 is Relation-like the carrier of (BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),f1)) -defined Function-like V14( the carrier of (BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),f1))) set
the carrier of (BitGFA0Str ((f . (o0 + 1)),(g . (o0 + 1)),f1)) is non empty set
K106( the Sorts of g1) is set
(0,f,g) is non empty pair Element of InnerVertices (0,f,g)
(0,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (0,f,g) is non empty set
InnerVertices (0,f,g) is non empty Element of K27( the carrier of (0,f,g))
K27( the carrier of (0,f,g)) is set
f1 is Relation-like NAT -defined Function-like V14( NAT ) set
f1 . n is set
g1 is Relation-like NAT -defined Function-like V14( NAT ) set
g1 . n is set
f1 . 0 is set
g1 . 0 is set
h1 is Relation-like NAT -defined Function-like V14( NAT ) set
h1 . 0 is set
f1 is set
h1 . f1 is set
f2 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
(f2,f,g) is non empty pair Element of InnerVertices (f2,f,g)
(f2,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (f2,f,g) is non empty set
InnerVertices (f2,f,g) is non empty Element of K27( the carrier of (f2,f,g))
K27( the carrier of (f2,f,g)) is set
h . f1 is set
h . 0 is set
f1 . H4(2) is set
g1 . H4(2) is set
f2 is non empty V56() ManySortedSign
f1 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f1 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (f1 + 1) is non pair set
g . (f1 + 1) is non pair set
f0 is set
BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),f0,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f1 + 1)),(g . (f1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2] is non empty pair set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],f0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],f0*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],f0*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (f1 + 1)),f0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (f1 + 1)),f0*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f1 + 1)),f0*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f0,(f . (f1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f0,(f . (f1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f1 + 1)),f0*>,and2))) +* (1GateCircStr (<*f0,(f . (f1 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2] is non empty pair set
[<*(g . (f1 + 1)),f0*>,and2] is non empty pair set
[<*f0,(f . (f1 + 1))*>,and2] is non empty pair set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f0*>,and2],[<*f0,(f . (f1 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f0*>,and2],[<*f0,(f . (f1 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f0*>,and2],[<*f0,(f . (f1 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f1 . f1 is set
f3 is non-empty MSAlgebra over f2
g1 . f1 is set
h . f1 is set
n is non-empty MSAlgebra over BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),f0)
BitGFA0Circ ((f . (f1 + 1)),(g . (f1 + 1)),f0) is strict non-empty finitely-generated V95( BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),f0)) gate`2=den Boolean MSAlgebra over BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),f0)
GFA0AdderCirc ((f . (f1 + 1)),(g . (f1 + 1)),f0) is strict non-empty finitely-generated V95( GFA0AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) gate`2=den Boolean MSAlgebra over GFA0AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)
2GatesCircuit ((f . (f1 + 1)),(g . (f1 + 1)),f0,xor2) is strict non-empty finitely-generated V95( 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),f0,xor2)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),f0,xor2)
1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2)
1GateCircuit (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2)
1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],f0,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],f0*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],f0*>,xor2)
1GateCircuit (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],f0*>,xor2) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],f0*>,xor2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],f0*>,xor2)
(1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),xor2)) +* (1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],f0,xor2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],f0*>,xor2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],f0*>,xor2))
GFA0CarryCirc ((f . (f1 + 1)),(g . (f1 + 1)),f0) is strict non-empty finitely-generated V95( GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) gate`2=den Boolean MSAlgebra over GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)
GFA0CarryICirc ((f . (f1 + 1)),(g . (f1 + 1)),f0) is strict non-empty finitely-generated V95( GFA0CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) gate`2=den Boolean MSAlgebra over GFA0CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)
1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)
1GateCircuit (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)
1GateCircuit ((g . (f1 + 1)),f0,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (f1 + 1)),f0*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (f1 + 1)),f0*>,and2)
1GateCircuit (<*(g . (f1 + 1)),f0*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (f1 + 1)),f0*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (f1 + 1)),f0*>,and2)
(1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2)) +* (1GateCircuit ((g . (f1 + 1)),f0,and2)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f1 + 1)),f0*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f1 + 1)),f0*>,and2))
1GateCircuit (f0,(f . (f1 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*f0,(f . (f1 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f0,(f . (f1 + 1))*>,and2)
1GateCircuit (<*f0,(f . (f1 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*f0,(f . (f1 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f0,(f . (f1 + 1))*>,and2)
((1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2)) +* (1GateCircuit ((g . (f1 + 1)),f0,and2))) +* (1GateCircuit (f0,(f . (f1 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f1 + 1)),f0*>,and2))) +* (1GateCircStr (<*f0,(f . (f1 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f1 + 1)),f0*>,and2))) +* (1GateCircStr (<*f0,(f . (f1 + 1))*>,and2))
1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f0*>,and2],[<*f0,(f . (f1 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f0*>,and2],[<*f0,(f . (f1 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f0*>,and2],[<*f0,(f . (f1 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f0*>,and2],[<*f0,(f . (f1 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f0*>,and2],[<*f0,(f . (f1 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f0*>,and2],[<*f0,(f . (f1 + 1))*>,and2]*>,or3)
(GFA0CarryICirc ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f0*>,and2],[<*f0,(f . (f1 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA0CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f0*>,and2],[<*f0,(f . (f1 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA0CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f0*>,and2],[<*f0,(f . (f1 + 1))*>,and2]*>,or3))
(GFA0AdderCirc ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (GFA0CarryCirc ((f . (f1 + 1)),(g . (f1 + 1)),f0)) is strict non-empty finitely-generated V95((GFA0AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0))) gate`2=den Boolean MSAlgebra over (GFA0AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0))
f1 . (f1 + 1) is set
f2 +* (BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),f0)) is non empty non void V56() strict ManySortedSign
g1 . (f1 + 1) is set
f3 +* n is strict non-empty MSAlgebra over f2 +* (BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),f0))
h . (f1 + 1) is set
GFA0CarryOutput ((f . (f1 + 1)),(g . (f1 + 1)),f0) is Element of InnerVertices (GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0))
the carrier of (GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) is non empty set
InnerVertices (GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) is non empty Element of K27( the carrier of (GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)))
K27( the carrier of (GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0))) is set
[<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f0*>,and2],[<*f0,(f . (f1 + 1))*>,and2]*>,or3] is non empty pair set
InnerVertices (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) is non empty Element of K27( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))))
K27( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)))) is set
InputVertices (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) is Element of K27( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))))
{[{},((0 -tuples_on BOOLEAN) --> FALSE)]} is Relation-like Function-like constant non empty V12() V28() 1 -element set
f1 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f1 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (f1 + 1) is non pair set
g . (f1 + 1) is non pair set
f2 is set
BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),f2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),f2,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f1 + 1)),(g . (f1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2] is non empty pair set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],f2*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],f2*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2],f2*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (f1 + 1)),f2*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (f1 + 1)),f2*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f1 + 1)),f2*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f2,(f . (f1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f2,(f . (f1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f1 + 1)),f2*>,and2))) +* (1GateCircStr (<*f2,(f . (f1 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2] is non empty pair set
[<*(g . (f1 + 1)),f2*>,and2] is non empty pair set
[<*f2,(f . (f1 + 1))*>,and2] is non empty pair set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f2*>,and2],[<*f2,(f . (f1 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f2*>,and2],[<*f2,(f . (f1 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f2)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2],[<*(g . (f1 + 1)),f2*>,and2],[<*f2,(f . (f1 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f2)) +* (GFA0CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),f2)) is non empty Element of K27( the carrier of (BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),f2)))
the carrier of (BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),f2)) is non empty set
K27( the carrier of (BitGFA0Str ((f . (f1 + 1)),(g . (f1 + 1)),f2))) is set
f3 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
h . f3 is set
f3 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (f3 + 1) is non pair set
g . (f3 + 1) is non pair set
f0 is set
BitGFA0Str ((f . (f3 + 1)),(g . (f3 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (f3 + 1)),(g . (f3 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (f3 + 1)),(g . (f3 + 1)),f0,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f3 + 1)),(g . (f3 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(f . (f3 + 1)),(g . (f3 + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f3 + 1)),(g . (f3 + 1))*>,xor2] is non empty pair set
<*[<*(f . (f3 + 1)),(g . (f3 + 1))*>,xor2],f0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f3 + 1)),(g . (f3 + 1))*>,xor2],f0*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f3 + 1)),(g . (f3 + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (f3 + 1)),(g . (f3 + 1))*>,xor2],f0*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryStr ((f . (f3 + 1)),(g . (f3 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (f3 + 1)),(g . (f3 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (f3 + 1)),(g . (f3 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (f3 + 1)),f0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (f3 + 1)),f0*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f3 + 1)),(g . (f3 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f3 + 1)),f0*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f0,(f . (f3 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f0,(f . (f3 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (f3 + 1)),(g . (f3 + 1))*>,and2)) +* (1GateCircStr (<*(g . (f3 + 1)),f0*>,and2))) +* (1GateCircStr (<*f0,(f . (f3 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f3 + 1)),(g . (f3 + 1))*>,and2] is non empty pair set
[<*(g . (f3 + 1)),f0*>,and2] is non empty pair set
[<*f0,(f . (f3 + 1))*>,and2] is non empty pair set
<*[<*(f . (f3 + 1)),(g . (f3 + 1))*>,and2],[<*(g . (f3 + 1)),f0*>,and2],[<*f0,(f . (f3 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f3 + 1)),(g . (f3 + 1))*>,and2],[<*(g . (f3 + 1)),f0*>,and2],[<*f0,(f . (f3 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (f3 + 1)),(g . (f3 + 1)),f0)) +* (1GateCircStr (<*[<*(f . (f3 + 1)),(g . (f3 + 1))*>,and2],[<*(g . (f3 + 1)),f0*>,and2],[<*f0,(f . (f3 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (f3 + 1)),(g . (f3 + 1)),f0)) +* (GFA0CarryStr ((f . (f3 + 1)),(g . (f3 + 1)),f0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of H1(f0,f3) is non empty set
InputVertices H1(f0,f3) is Element of K27( the carrier of H1(f0,f3))
K27( the carrier of H1(f0,f3)) is set
{f0} is non empty V12() V28() 1 -element set
(InputVertices H1(f0,f3)) \ {f0} is Element of K27( the carrier of H1(f0,f3))
(f3,f,g) is non empty pair Element of InnerVertices (f3,f,g)
(f3,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (f3,f,g) is non empty set
InnerVertices (f3,f,g) is non empty Element of K27( the carrier of (f3,f,g))
K27( the carrier of (f3,f,g)) is set
{(f . (f3 + 1)),(g . (f3 + 1)),f0} is V28() set
n is non empty pair set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
h . n is set
n + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
h . (n + 1) is set
f . (n + 1) is non pair set
g . (n + 1) is non pair set
x is set
GFA0CarryOutput ((f . (n + 1)),(g . (n + 1)),x) is Element of InnerVertices (GFA0CarryStr ((f . (n + 1)),(g . (n + 1)),x))
GFA0CarryStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0CarryIStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),(g . (n + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (n + 1)),x*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (n + 1)),x*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2)) +* (1GateCircStr (<*(g . (n + 1)),x*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*x,(f . (n + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*x,(f . (n + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2)) +* (1GateCircStr (<*(g . (n + 1)),x*>,and2))) +* (1GateCircStr (<*x,(f . (n + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,and2] is non empty pair set
[<*(g . (n + 1)),x*>,and2] is non empty pair set
[<*x,(f . (n + 1))*>,and2] is non empty pair set
<*[<*(f . (n + 1)),(g . (n + 1))*>,and2],[<*(g . (n + 1)),x*>,and2],[<*x,(f . (n + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2],[<*(g . (n + 1)),x*>,and2],[<*x,(f . (n + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0CarryIStr ((f . (n + 1)),(g . (n + 1)),x)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2],[<*(g . (n + 1)),x*>,and2],[<*x,(f . (n + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA0CarryStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
InnerVertices (GFA0CarryStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty Element of K27( the carrier of (GFA0CarryStr ((f . (n + 1)),(g . (n + 1)),x)))
K27( the carrier of (GFA0CarryStr ((f . (n + 1)),(g . (n + 1)),x))) is set
[<*[<*(f . (n + 1)),(g . (n + 1))*>,and2],[<*(g . (n + 1)),x*>,and2],[<*x,(f . (n + 1))*>,and2]*>,or3] is non empty pair set
BitGFA0Str ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA0AdderStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,xor2] is non empty pair set
<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2],x*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2],x*>,xor2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,xor2)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2],x*>,xor2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA0AdderStr ((f . (n + 1)),(g . (n + 1)),x)) +* (GFA0CarryStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices H1(x,n) is Element of K27( the carrier of H1(x,n))
the carrier of H1(x,n) is non empty set
K27( the carrier of H1(x,n)) is set
InnerVertices H1(x,n) is non empty Element of K27( the carrier of H1(x,n))
(n,f,g) is non empty pair Element of InnerVertices (n,f,g)
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (n,f,g) is non empty set
InnerVertices (n,f,g) is non empty Element of K27( the carrier of (n,f,g))
K27( the carrier of (n,f,g)) is set
((n + 1),f,g) is non empty pair Element of InnerVertices ((n + 1),f,g)
((n + 1),f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of ((n + 1),f,g) is non empty set
InnerVertices ((n + 1),f,g) is non empty Element of K27( the carrier of ((n + 1),f,g))
K27( the carrier of ((n + 1),f,g)) is set
{(f . (n + 1)),(g . (n + 1)),x} is V28() set
{[<*(f . (n + 1)),(g . (n + 1))*>,xor2]} is Relation-like Function-like constant non empty V12() V28() 1 -element set
GFA0AdderOutput ((f . (n + 1)),(g . (n + 1)),x) is Element of InnerVertices (GFA0AdderStr ((f . (n + 1)),(g . (n + 1)),x))
the carrier of (GFA0AdderStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
InnerVertices (GFA0AdderStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty Element of K27( the carrier of (GFA0AdderStr ((f . (n + 1)),(g . (n + 1)),x)))
K27( the carrier of (GFA0AdderStr ((f . (n + 1)),(g . (n + 1)),x))) is set
2GatesCircOutput ((f . (n + 1)),(g . (n + 1)),x,xor2) is non empty pair Element of InnerVertices (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,xor2))
the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,xor2)) is non empty set
InnerVertices (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,xor2)) is non empty Element of K27( the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,xor2)))
K27( the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,xor2))) is set
[<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2],x*>,xor2] is non empty pair set
{(GFA0AdderOutput ((f . (n + 1)),(g . (n + 1)),x))} is non empty V12() V28() 1 -element set
{[<*(f . (n + 1)),(g . (n + 1))*>,xor2]} \/ {(GFA0AdderOutput ((f . (n + 1)),(g . (n + 1)),x))} is non empty V28() set
{[<*(f . (n + 1)),(g . (n + 1))*>,and2],[<*(g . (n + 1)),x*>,and2],[<*x,(f . (n + 1))*>,and2]} is Relation-like V28() set
({[<*(f . (n + 1)),(g . (n + 1))*>,xor2]} \/ {(GFA0AdderOutput ((f . (n + 1)),(g . (n + 1)),x))}) \/ {[<*(f . (n + 1)),(g . (n + 1))*>,and2],[<*(g . (n + 1)),x*>,and2],[<*x,(f . (n + 1))*>,and2]} is non empty V28() set
{(GFA0CarryOutput ((f . (n + 1)),(g . (n + 1)),x))} is non empty V12() V28() 1 -element set
(({[<*(f . (n + 1)),(g . (n + 1))*>,xor2]} \/ {(GFA0AdderOutput ((f . (n + 1)),(g . (n + 1)),x))}) \/ {[<*(f . (n + 1)),(g . (n + 1))*>,and2],[<*(g . (n + 1)),x*>,and2],[<*x,(f . (n + 1))*>,and2]}) \/ {(GFA0CarryOutput ((f . (n + 1)),(g . (n + 1)),x))} is non empty V28() set
{H3(x,n)} is non empty V12() V28() 1 -element set
H4(2) * H4(1) is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
H4( 0 ) + (H4(2) * H4(1)) is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
f1 is Element of K106( the Sorts of (n,f,g))
Following (f1,(1 + (2 * n))) is Element of K106( the Sorts of (n,f,g))
TRUE is boolean Element of BOOLEAN
(0 -tuples_on BOOLEAN) --> TRUE is Relation-like Function-like V18(0 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((0 -tuples_on BOOLEAN),BOOLEAN))
1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
[{},((0 -tuples_on BOOLEAN) --> TRUE)] is non empty pair set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
S0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
N is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
Sn is Relation-like NAT -defined Function-like V14( NAT ) set
Sn . n is set
Sn . 0 is set
An is Relation-like NAT -defined Function-like V14( NAT ) set
An . 0 is set
h is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
o0 is Relation-like NAT -defined Function-like V14( NAT ) set
o0 . n is set
o0 . 0 is set
f1 is Relation-like NAT -defined Function-like V14( NAT ) set
f1 . 0 is set
S0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
N is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . S0 is set
h . 0 is set
Sn is Relation-like NAT -defined Function-like V14( NAT ) set
Sn . 0 is set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE)) is strict non-empty finitely-generated V95( 1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) gate`2=den Boolean MSAlgebra over 1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))
h is non empty V56() ManySortedSign
o0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
o0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (o0 + 1) is set
g . (o0 + 1) is set
An is set
BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (o0 + 1)),(g . (o0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c] is non empty pair set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (o0 + 1)),An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (o0 + 1)),An*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*An,(f . (o0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*An,(f . (o0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2a))) +* (1GateCircStr (<*An,(f . (o0 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c] is non empty pair set
[<*(g . (o0 + 1)),An*>,and2a] is non empty pair set
[<*An,(f . (o0 + 1))*>,and2] is non empty pair set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
Sn is non-empty MSAlgebra over h
BitGFA1Circ ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),An)
GFA1AdderCirc ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)
2GatesCircuit ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2c) is strict non-empty finitely-generated V95( 2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2c)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2c)
1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)
1GateCircuit (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)
1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c)
1GateCircuit (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c)
(1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),xor2c)) +* (1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An,xor2c)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c))
GFA1CarryCirc ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An)
GFA1CarryICirc ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)
1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)
1GateCircuit (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)
1GateCircuit ((g . (o0 + 1)),An,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (o0 + 1)),An*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (o0 + 1)),An*>,and2a)
1GateCircuit (<*(g . (o0 + 1)),An*>,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (o0 + 1)),An*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (o0 + 1)),An*>,and2a)
(1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2c)) +* (1GateCircuit ((g . (o0 + 1)),An,and2a)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2a))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2a))
1GateCircuit (An,(f . (o0 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)
1GateCircuit (<*An,(f . (o0 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)
((1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2c)) +* (1GateCircuit ((g . (o0 + 1)),An,and2a))) +* (1GateCircuit (An,(f . (o0 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2a))) +* (1GateCircStr (<*An,(f . (o0 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2a))) +* (1GateCircStr (<*An,(f . (o0 + 1))*>,and2))
1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3)
(GFA1CarryICirc ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3))
(GFA1AdderCirc ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA1CarryCirc ((f . (o0 + 1)),(g . (o0 + 1)),An)) is strict non-empty finitely-generated V95((GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An))) gate`2=den Boolean MSAlgebra over (GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An))
Sn +* (BitGFA1Circ ((f . (o0 + 1)),(g . (o0 + 1)),An)) is strict non-empty MSAlgebra over h +* (BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),An))
h +* (BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),An)) is non empty non void V56() strict ManySortedSign
An is Relation-like NAT -defined Function-like V14( NAT ) set
An . n is set
h is strict non-empty finitely-generated V95((n,f,g)) gate`2=den Boolean MSAlgebra over (n,f,g)
o0 is Relation-like NAT -defined Function-like V14( NAT ) set
o0 . n is set
An . 0 is set
o0 . 0 is set
f1 is Relation-like NAT -defined Function-like V14( NAT ) set
f1 . 0 is set
g1 is Relation-like NAT -defined Function-like V14( NAT ) set
g1 . n is set
Sn is strict non-empty finitely-generated V95((n,f,g)) gate`2=den Boolean MSAlgebra over (n,f,g)
h1 is Relation-like NAT -defined Function-like V14( NAT ) set
h1 . n is set
g1 . 0 is set
h1 . 0 is set
f1 is Relation-like NAT -defined Function-like V14( NAT ) set
f1 . 0 is set
h is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
An is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
An + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (An + 1) is set
g . (An + 1) is set
Sn is set
BitGFA1Str ((f . (An + 1)),(g . (An + 1)),Sn) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (An + 1)),(g . (An + 1)),Sn) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (An + 1)),(g . (An + 1)),Sn,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (An + 1)),(g . (An + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (An + 1)),(g . (An + 1))*>,xor2c] is non empty pair set
<*[<*(f . (An + 1)),(g . (An + 1))*>,xor2c],Sn*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,xor2c],Sn*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,xor2c],Sn*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((f . (An + 1)),(g . (An + 1)),Sn) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (An + 1)),(g . (An + 1)),Sn) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (An + 1)),Sn*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (An + 1)),Sn*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2c)) +* (1GateCircStr (<*(g . (An + 1)),Sn*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*Sn,(f . (An + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*Sn,(f . (An + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2c)) +* (1GateCircStr (<*(g . (An + 1)),Sn*>,and2a))) +* (1GateCircStr (<*Sn,(f . (An + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (An + 1)),(g . (An + 1))*>,and2c] is non empty pair set
[<*(g . (An + 1)),Sn*>,and2a] is non empty pair set
[<*Sn,(f . (An + 1))*>,and2] is non empty pair set
<*[<*(f . (An + 1)),(g . (An + 1))*>,and2c],[<*(g . (An + 1)),Sn*>,and2a],[<*Sn,(f . (An + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,and2c],[<*(g . (An + 1)),Sn*>,and2a],[<*Sn,(f . (An + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (An + 1)),(g . (An + 1)),Sn)) +* (1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,and2c],[<*(g . (An + 1)),Sn*>,and2a],[<*Sn,(f . (An + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (An + 1)),(g . (An + 1)),Sn)) +* (GFA1CarryStr ((f . (An + 1)),(g . (An + 1)),Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h +* (BitGFA1Str ((f . (An + 1)),(g . (An + 1)),Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
o0 is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
g1 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
g1 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (g1 + 1) is set
g . (g1 + 1) is set
f1 is set
BitGFA1Str ((f . (g1 + 1)),(g . (g1 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (g1 + 1)),(g . (g1 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (g1 + 1)),(g . (g1 + 1)),f1,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (g1 + 1)),(g . (g1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (g1 + 1)),(g . (g1 + 1))*>,xor2c] is non empty pair set
<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,xor2c],f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,xor2c],f1*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,xor2c],f1*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((f . (g1 + 1)),(g . (g1 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (g1 + 1)),f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (g1 + 1)),f1*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f1,(f . (g1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f1,(f . (g1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,and2a))) +* (1GateCircStr (<*f1,(f . (g1 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2c] is non empty pair set
[<*(g . (g1 + 1)),f1*>,and2a] is non empty pair set
[<*f1,(f . (g1 + 1))*>,and2] is non empty pair set
<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2c],[<*(g . (g1 + 1)),f1*>,and2a],[<*f1,(f . (g1 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2c],[<*(g . (g1 + 1)),f1*>,and2a],[<*f1,(f . (g1 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2c],[<*(g . (g1 + 1)),f1*>,and2a],[<*f1,(f . (g1 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) +* (GFA1CarryStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
o0 +* (BitGFA1Str ((f . (g1 + 1)),(g . (g1 + 1)),f1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h1 is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f2 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f2 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (f2 + 1) is set
g . (f2 + 1) is set
f1 is set
BitGFA1Str ((f . (f2 + 1)),(g . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (f2 + 1)),(g . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (f2 + 1)),(g . (f2 + 1)),f1,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f2 + 1)),(g . (f2 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (f2 + 1)),(g . (f2 + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f2 + 1)),(g . (f2 + 1))*>,xor2c] is non empty pair set
<*[<*(f . (f2 + 1)),(g . (f2 + 1))*>,xor2c],f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f2 + 1)),(g . (f2 + 1))*>,xor2c],f1*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f2 + 1)),(g . (f2 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (f2 + 1)),(g . (f2 + 1))*>,xor2c],f1*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((f . (f2 + 1)),(g . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (f2 + 1)),(g . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (f2 + 1)),(g . (f2 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (f2 + 1)),f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (f2 + 1)),f1*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f2 + 1)),(g . (f2 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f2 + 1)),f1*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f1,(f . (f2 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f1,(f . (f2 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (f2 + 1)),(g . (f2 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f2 + 1)),f1*>,and2a))) +* (1GateCircStr (<*f1,(f . (f2 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f2 + 1)),(g . (f2 + 1))*>,and2c] is non empty pair set
[<*(g . (f2 + 1)),f1*>,and2a] is non empty pair set
[<*f1,(f . (f2 + 1))*>,and2] is non empty pair set
<*[<*(f . (f2 + 1)),(g . (f2 + 1))*>,and2c],[<*(g . (f2 + 1)),f1*>,and2a],[<*f1,(f . (f2 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f2 + 1)),(g . (f2 + 1))*>,and2c],[<*(g . (f2 + 1)),f1*>,and2a],[<*f1,(f . (f2 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (f2 + 1)),(g . (f2 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (f2 + 1)),(g . (f2 + 1))*>,and2c],[<*(g . (f2 + 1)),f1*>,and2a],[<*f1,(f . (f2 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (f2 + 1)),(g . (f2 + 1)),f1)) +* (GFA1CarryStr ((f . (f2 + 1)),(g . (f2 + 1)),f1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h1 +* (BitGFA1Str ((f . (f2 + 1)),(g . (f2 + 1)),f1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f3 is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
n + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (n + 1) is set
g . (n + 1) is set
f0 is set
BitGFA1Str ((f . (n + 1)),(g . (n + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (n + 1)),(g . (n + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (n + 1)),(g . (n + 1)),f0,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),(g . (n + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,xor2c] is non empty pair set
<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2c],f0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2c],f0*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2c],f0*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((f . (n + 1)),(g . (n + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (n + 1)),(g . (n + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (n + 1)),f0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (n + 1)),f0*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2c)) +* (1GateCircStr (<*(g . (n + 1)),f0*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f0,(f . (n + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f0,(f . (n + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2c)) +* (1GateCircStr (<*(g . (n + 1)),f0*>,and2a))) +* (1GateCircStr (<*f0,(f . (n + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,and2c] is non empty pair set
[<*(g . (n + 1)),f0*>,and2a] is non empty pair set
[<*f0,(f . (n + 1))*>,and2] is non empty pair set
<*[<*(f . (n + 1)),(g . (n + 1))*>,and2c],[<*(g . (n + 1)),f0*>,and2a],[<*f0,(f . (n + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2c],[<*(g . (n + 1)),f0*>,and2a],[<*f0,(f . (n + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (n + 1)),(g . (n + 1)),f0)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2c],[<*(g . (n + 1)),f0*>,and2a],[<*f0,(f . (n + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (n + 1)),(g . (n + 1)),f0)) +* (GFA1CarryStr ((f . (n + 1)),(g . (n + 1)),f0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f3 +* (BitGFA1Str ((f . (n + 1)),(g . (n + 1)),f0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
x is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h2 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
h2 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (h2 + 1) is set
g . (h2 + 1) is set
g2 is set
BitGFA1Str ((f . (h2 + 1)),(g . (h2 + 1)),g2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (h2 + 1)),(g . (h2 + 1)),g2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (h2 + 1)),(g . (h2 + 1)),g2,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (h2 + 1)),(g . (h2 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (h2 + 1)),(g . (h2 + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (h2 + 1)),(g . (h2 + 1))*>,xor2c] is non empty pair set
<*[<*(f . (h2 + 1)),(g . (h2 + 1))*>,xor2c],g2*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (h2 + 1)),(g . (h2 + 1))*>,xor2c],g2*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (h2 + 1)),(g . (h2 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (h2 + 1)),(g . (h2 + 1))*>,xor2c],g2*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((f . (h2 + 1)),(g . (h2 + 1)),g2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (h2 + 1)),(g . (h2 + 1)),g2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (h2 + 1)),(g . (h2 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (h2 + 1)),g2*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (h2 + 1)),g2*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (h2 + 1)),(g . (h2 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (h2 + 1)),g2*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*g2,(f . (h2 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*g2,(f . (h2 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (h2 + 1)),(g . (h2 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (h2 + 1)),g2*>,and2a))) +* (1GateCircStr (<*g2,(f . (h2 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (h2 + 1)),(g . (h2 + 1))*>,and2c] is non empty pair set
[<*(g . (h2 + 1)),g2*>,and2a] is non empty pair set
[<*g2,(f . (h2 + 1))*>,and2] is non empty pair set
<*[<*(f . (h2 + 1)),(g . (h2 + 1))*>,and2c],[<*(g . (h2 + 1)),g2*>,and2a],[<*g2,(f . (h2 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (h2 + 1)),(g . (h2 + 1))*>,and2c],[<*(g . (h2 + 1)),g2*>,and2a],[<*g2,(f . (h2 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (h2 + 1)),(g . (h2 + 1)),g2)) +* (1GateCircStr (<*[<*(f . (h2 + 1)),(g . (h2 + 1))*>,and2c],[<*(g . (h2 + 1)),g2*>,and2a],[<*g2,(f . (h2 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (h2 + 1)),(g . (h2 + 1)),g2)) +* (GFA1CarryStr ((f . (h2 + 1)),(g . (h2 + 1)),g2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
x +* (BitGFA1Str ((f . (h2 + 1)),(g . (h2 + 1)),g2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h is non empty V56() ManySortedSign
o0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
o0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (o0 + 1) is set
g . (o0 + 1) is set
An is set
BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (o0 + 1)),(g . (o0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c] is non empty pair set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (o0 + 1)),An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (o0 + 1)),An*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*An,(f . (o0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*An,(f . (o0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2a))) +* (1GateCircStr (<*An,(f . (o0 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c] is non empty pair set
[<*(g . (o0 + 1)),An*>,and2a] is non empty pair set
[<*An,(f . (o0 + 1))*>,and2] is non empty pair set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
Sn is non-empty MSAlgebra over h
BitGFA1Circ ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),An)
GFA1AdderCirc ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)
2GatesCircuit ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2c) is strict non-empty finitely-generated V95( 2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2c)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),An,xor2c)
1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)
1GateCircuit (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)
1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c)
1GateCircuit (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c)
(1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),xor2c)) +* (1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An,xor2c)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],An*>,xor2c))
GFA1CarryCirc ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An)
GFA1CarryICirc ((f . (o0 + 1)),(g . (o0 + 1)),An) is strict non-empty finitely-generated V95( GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) gate`2=den Boolean MSAlgebra over GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)
1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)
1GateCircuit (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)
1GateCircuit ((g . (o0 + 1)),An,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (o0 + 1)),An*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (o0 + 1)),An*>,and2a)
1GateCircuit (<*(g . (o0 + 1)),An*>,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (o0 + 1)),An*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (o0 + 1)),An*>,and2a)
(1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2c)) +* (1GateCircuit ((g . (o0 + 1)),An,and2a)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2a))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2a))
1GateCircuit (An,(f . (o0 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)
1GateCircuit (<*An,(f . (o0 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*An,(f . (o0 + 1))*>,and2)
((1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2c)) +* (1GateCircuit ((g . (o0 + 1)),An,and2a))) +* (1GateCircuit (An,(f . (o0 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2a))) +* (1GateCircStr (<*An,(f . (o0 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2a))) +* (1GateCircStr (<*An,(f . (o0 + 1))*>,and2))
1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3)
(GFA1CarryICirc ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),An*>,and2a],[<*An,(f . (o0 + 1))*>,and2]*>,or3))
(GFA1AdderCirc ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA1CarryCirc ((f . (o0 + 1)),(g . (o0 + 1)),An)) is strict non-empty finitely-generated V95((GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An))) gate`2=den Boolean MSAlgebra over (GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),An))
Sn +* (BitGFA1Circ ((f . (o0 + 1)),(g . (o0 + 1)),An)) is strict non-empty MSAlgebra over h +* (BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),An))
h +* (BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),An)) is non empty non void V56() strict ManySortedSign
h is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
Sn is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f1 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f1 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (f1 + 1) is set
g . (f1 + 1) is set
o0 is set
BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f1 + 1)),(g . (f1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c] is non empty pair set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],o0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],o0*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],o0*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (f1 + 1)),o0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (f1 + 1)),o0*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*o0,(f . (f1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*o0,(f . (f1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2a))) +* (1GateCircStr (<*o0,(f . (f1 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c] is non empty pair set
[<*(g . (f1 + 1)),o0*>,and2a] is non empty pair set
[<*o0,(f . (f1 + 1))*>,and2] is non empty pair set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),o0*>,and2a],[<*o0,(f . (f1 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),o0*>,and2a],[<*o0,(f . (f1 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),o0*>,and2a],[<*o0,(f . (f1 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h +* (BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
An is strict non-empty finitely-generated V95(h) gate`2=den Boolean MSAlgebra over h
BitGFA1Circ ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V95( BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),o0)
GFA1AdderCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V95( GFA1AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over GFA1AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
2GatesCircuit ((f . (f1 + 1)),(g . (f1 + 1)),o0,xor2c) is strict non-empty finitely-generated V95( 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,xor2c)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,xor2c)
1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c)
1GateCircuit (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c)
1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],o0,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],o0*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],o0*>,xor2c)
1GateCircuit (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],o0*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],o0*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],o0*>,xor2c)
(1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),xor2c)) +* (1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],o0,xor2c)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],o0*>,xor2c))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],o0*>,xor2c))
GFA1CarryCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V95( GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
GFA1CarryICirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V95( GFA1CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over GFA1CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)
1GateCircuit (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)
1GateCircuit ((g . (f1 + 1)),o0,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (f1 + 1)),o0*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (f1 + 1)),o0*>,and2a)
1GateCircuit (<*(g . (f1 + 1)),o0*>,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (f1 + 1)),o0*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (f1 + 1)),o0*>,and2a)
(1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2c)) +* (1GateCircuit ((g . (f1 + 1)),o0,and2a)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2a))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2a))
1GateCircuit (o0,(f . (f1 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*o0,(f . (f1 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*o0,(f . (f1 + 1))*>,and2)
1GateCircuit (<*o0,(f . (f1 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*o0,(f . (f1 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*o0,(f . (f1 + 1))*>,and2)
((1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2c)) +* (1GateCircuit ((g . (f1 + 1)),o0,and2a))) +* (1GateCircuit (o0,(f . (f1 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2a))) +* (1GateCircStr (<*o0,(f . (f1 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2a))) +* (1GateCircStr (<*o0,(f . (f1 + 1))*>,and2))
1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),o0*>,and2a],[<*o0,(f . (f1 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),o0*>,and2a],[<*o0,(f . (f1 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),o0*>,and2a],[<*o0,(f . (f1 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),o0*>,and2a],[<*o0,(f . (f1 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),o0*>,and2a],[<*o0,(f . (f1 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),o0*>,and2a],[<*o0,(f . (f1 + 1))*>,and2]*>,or3)
(GFA1CarryICirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),o0*>,and2a],[<*o0,(f . (f1 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA1CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),o0*>,and2a],[<*o0,(f . (f1 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA1CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),o0*>,and2a],[<*o0,(f . (f1 + 1))*>,and2]*>,or3))
(GFA1AdderCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (GFA1CarryCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is strict non-empty finitely-generated V95((GFA1AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))) gate`2=den Boolean MSAlgebra over (GFA1AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))
An +* (BitGFA1Circ ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is strict non-empty finitely-generated V95(h +* (BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),o0))) gate`2=den Boolean MSAlgebra over h +* (BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),o0))
Sn is Relation-like NAT -defined Function-like V14( NAT ) set
Sn . n is set
h is strict non-empty finitely-generated V95((n,f,g)) gate`2=den Boolean MSAlgebra over (n,f,g)
An is Relation-like NAT -defined Function-like V14( NAT ) set
An . n is set
Sn . 0 is set
An . 0 is set
o0 is Relation-like NAT -defined Function-like V14( NAT ) set
o0 . 0 is set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (n,f,g) is non empty set
InnerVertices (n,f,g) is non empty Element of K27( the carrier of (n,f,g))
K27( the carrier of (n,f,g)) is set
A0 is Element of InnerVertices (n,f,g)
h0 is Element of InnerVertices (n,f,g)
N is Relation-like NAT -defined Function-like V14( NAT ) set
N . n is set
N . 0 is set
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . n is set
h . 0 is set
proj1 N is set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
N . (Sn + 1) is set
f . (Sn + 1) is set
g . (Sn + 1) is set
N . Sn is set
GFA1CarryOutput ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn)) is Element of InnerVertices (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn)))
GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (Sn + 1)),(g . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (Sn + 1)),(N . Sn)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (Sn + 1)),(N . Sn)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(g . (Sn + 1)),(N . Sn)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(N . Sn),(f . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(N . Sn),(f . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(g . (Sn + 1)),(N . Sn)*>,and2a))) +* (1GateCircStr (<*(N . Sn),(f . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c] is non empty pair set
[<*(g . (Sn + 1)),(N . Sn)*>,and2a] is non empty pair set
[<*(N . Sn),(f . (Sn + 1))*>,and2] is non empty pair set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(N . Sn)*>,and2a],[<*(N . Sn),(f . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(N . Sn)*>,and2a],[<*(N . Sn),(f . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(N . Sn)*>,and2a],[<*(N . Sn),(f . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))) is non empty set
InnerVertices (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))) is non empty Element of K27( the carrier of (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))))
K27( the carrier of (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn)))) is set
[<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(N . Sn)*>,and2a],[<*(N . Sn),(f . (Sn + 1))*>,and2]*>,or3] is non empty pair set
proj1 h is set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
h . (Sn + 1) is set
f . (Sn + 1) is set
g . (Sn + 1) is set
h . Sn is set
GFA1CarryOutput ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)) is Element of InnerVertices (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)))
GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (Sn + 1)),(g . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (Sn + 1)),(h . Sn)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (Sn + 1)),(h . Sn)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(g . (Sn + 1)),(h . Sn)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h . Sn),(f . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h . Sn),(f . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(g . (Sn + 1)),(h . Sn)*>,and2a))) +* (1GateCircStr (<*(h . Sn),(f . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c] is non empty pair set
[<*(g . (Sn + 1)),(h . Sn)*>,and2a] is non empty pair set
[<*(h . Sn),(f . (Sn + 1))*>,and2] is non empty pair set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(h . Sn)*>,and2a],[<*(h . Sn),(f . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(h . Sn)*>,and2a],[<*(h . Sn),(f . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(h . Sn)*>,and2a],[<*(h . Sn),(f . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) is non empty set
InnerVertices (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) is non empty Element of K27( the carrier of (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))))
K27( the carrier of (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)))) is set
[<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(h . Sn)*>,and2a],[<*(h . Sn),(f . (Sn + 1))*>,and2]*>,or3] is non empty pair set
N is Relation-like NAT -defined Function-like V14( NAT ) set
N . n is set
N . 0 is set
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . 0 is set
InnerVertices (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) is non empty Element of K27( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))))
the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) is non empty set
K27( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)))) is set
{[{},((0 -tuples_on BOOLEAN) --> TRUE)]} is Relation-like Function-like constant non empty V12() V28() 1 -element set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
N . Sn is set
h . Sn is set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
N . (Sn + 1) is set
h . (Sn + 1) is set
An is non empty V56() ManySortedSign
InnerVertices An is Element of K27( the carrier of An)
the carrier of An is non empty set
K27( the carrier of An) is set
An is non empty V56() ManySortedSign
InnerVertices An is Element of K27( the carrier of An)
the carrier of An is non empty set
K27( the carrier of An) is set
f . (Sn + 1) is set
g . (Sn + 1) is set
GFA1CarryOutput ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)) is Element of InnerVertices (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)))
GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (Sn + 1)),(g . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (Sn + 1)),(h . Sn)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (Sn + 1)),(h . Sn)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(g . (Sn + 1)),(h . Sn)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h . Sn),(f . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h . Sn),(f . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(g . (Sn + 1)),(h . Sn)*>,and2a))) +* (1GateCircStr (<*(h . Sn),(f . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c] is non empty pair set
[<*(g . (Sn + 1)),(h . Sn)*>,and2a] is non empty pair set
[<*(h . Sn),(f . (Sn + 1))*>,and2] is non empty pair set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(h . Sn)*>,and2a],[<*(h . Sn),(f . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(h . Sn)*>,and2a],[<*(h . Sn),(f . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(h . Sn)*>,and2a],[<*(h . Sn),(f . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) is non empty set
InnerVertices (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) is non empty Element of K27( the carrier of (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))))
K27( the carrier of (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)))) is set
[<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(h . Sn)*>,and2a],[<*(h . Sn),(f . (Sn + 1))*>,and2]*>,or3] is non empty pair set
BitGFA1Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn),xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c] is non empty pair set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c],(h . Sn)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c],(h . Sn)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c],(h . Sn)*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) +* (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitGFA1Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) is non empty Element of K27( the carrier of (BitGFA1Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))))
the carrier of (BitGFA1Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) is non empty set
K27( the carrier of (BitGFA1Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)))) is set
An +* (BitGFA1Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))) is non empty non void V56() strict ManySortedSign
InnerVertices (An +* (BitGFA1Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)))) is non empty Element of K27( the carrier of (An +* (BitGFA1Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)))))
the carrier of (An +* (BitGFA1Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn)))) is non empty set
K27( the carrier of (An +* (BitGFA1Str ((f . (Sn + 1)),(g . (Sn + 1)),(h . Sn))))) is set
h . n is set
An is non empty V56() ManySortedSign
InnerVertices An is Element of K27( the carrier of An)
the carrier of An is non empty set
K27( the carrier of An) is set
Sn is Element of InnerVertices (n,f,g)
An is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
An + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
h . (An + 1) is set
f . (An + 1) is set
g . (An + 1) is set
h . An is set
GFA1CarryOutput ((f . (An + 1)),(g . (An + 1)),(h . An)) is Element of InnerVertices (GFA1CarryStr ((f . (An + 1)),(g . (An + 1)),(h . An)))
GFA1CarryStr ((f . (An + 1)),(g . (An + 1)),(h . An)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (An + 1)),(g . (An + 1)),(h . An)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (An + 1)),(g . (An + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (An + 1)),(h . An)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (An + 1)),(h . An)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2c)) +* (1GateCircStr (<*(g . (An + 1)),(h . An)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h . An),(f . (An + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h . An),(f . (An + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2c)) +* (1GateCircStr (<*(g . (An + 1)),(h . An)*>,and2a))) +* (1GateCircStr (<*(h . An),(f . (An + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (An + 1)),(g . (An + 1))*>,and2c] is non empty pair set
[<*(g . (An + 1)),(h . An)*>,and2a] is non empty pair set
[<*(h . An),(f . (An + 1))*>,and2] is non empty pair set
<*[<*(f . (An + 1)),(g . (An + 1))*>,and2c],[<*(g . (An + 1)),(h . An)*>,and2a],[<*(h . An),(f . (An + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,and2c],[<*(g . (An + 1)),(h . An)*>,and2a],[<*(h . An),(f . (An + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (An + 1)),(g . (An + 1)),(h . An))) +* (1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,and2c],[<*(g . (An + 1)),(h . An)*>,and2a],[<*(h . An),(f . (An + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA1CarryStr ((f . (An + 1)),(g . (An + 1)),(h . An))) is non empty set
InnerVertices (GFA1CarryStr ((f . (An + 1)),(g . (An + 1)),(h . An))) is non empty Element of K27( the carrier of (GFA1CarryStr ((f . (An + 1)),(g . (An + 1)),(h . An))))
K27( the carrier of (GFA1CarryStr ((f . (An + 1)),(g . (An + 1)),(h . An)))) is set
[<*[<*(f . (An + 1)),(g . (An + 1))*>,and2c],[<*(g . (An + 1)),(h . An)*>,and2a],[<*(h . An),(f . (An + 1))*>,and2]*>,or3] is non empty pair set
f1 is non empty V56() ManySortedSign
o0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
N . o0 is set
g1 is set
h . o0 is set
N . An is set
o0 is non empty V56() ManySortedSign
n is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V14( NAT ) set
g . 0 is set
S0 is Relation-like NAT -defined Function-like V14( NAT ) set
S0 . 0 is set
A0 is Relation-like NAT -defined Function-like V14( NAT ) set
A0 . 0 is set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
(Sn,n,f) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
g . Sn is set
(Sn,n,f) is strict non-empty finitely-generated V95((Sn,n,f)) gate`2=den Boolean MSAlgebra over (Sn,n,f)
S0 . Sn is set
(Sn,n,f) is Element of InnerVertices (Sn,n,f)
the carrier of (Sn,n,f) is non empty set
InnerVertices (Sn,n,f) is non empty Element of K27( the carrier of (Sn,n,f))
K27( the carrier of (Sn,n,f)) is set
A0 . Sn is set
An is Relation-like NAT -defined Function-like V14( NAT ) set
An . Sn is set
o0 is Relation-like NAT -defined Function-like V14( NAT ) set
o0 . Sn is set
An . 0 is set
o0 . 0 is set
f1 is Relation-like NAT -defined Function-like V14( NAT ) set
f1 . 0 is set
g1 is non empty V56() ManySortedSign
f2 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f2 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
n . (f2 + 1) is set
f . (f2 + 1) is set
f1 is set
BitGFA1Str ((n . (f2 + 1)),(f . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((n . (f2 + 1)),(f . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((n . (f2 + 1)),(f . (f2 + 1)),f1,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (f2 + 1)),(f . (f2 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c] is non empty pair set
<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c],f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c],f1*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c],f1*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((n . (f2 + 1)),(f . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((n . (f2 + 1)),(f . (f2 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f2 + 1)),f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (f2 + 1)),f1*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c)) +* (1GateCircStr (<*(f . (f2 + 1)),f1*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f1,(n . (f2 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f1,(n . (f2 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c)) +* (1GateCircStr (<*(f . (f2 + 1)),f1*>,and2a))) +* (1GateCircStr (<*f1,(n . (f2 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c] is non empty pair set
[<*(f . (f2 + 1)),f1*>,and2a] is non empty pair set
[<*f1,(n . (f2 + 1))*>,and2] is non empty pair set
<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c],[<*(f . (f2 + 1)),f1*>,and2a],[<*f1,(n . (f2 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c],[<*(f . (f2 + 1)),f1*>,and2a],[<*f1,(n . (f2 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c],[<*(f . (f2 + 1)),f1*>,and2a],[<*f1,(n . (f2 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (GFA1CarryStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h1 is non-empty MSAlgebra over g1
BitGFA1Circ ((n . (f2 + 1)),(f . (f2 + 1)),f1) is strict non-empty finitely-generated V95( BitGFA1Str ((n . (f2 + 1)),(f . (f2 + 1)),f1)) gate`2=den Boolean MSAlgebra over BitGFA1Str ((n . (f2 + 1)),(f . (f2 + 1)),f1)
GFA1AdderCirc ((n . (f2 + 1)),(f . (f2 + 1)),f1) is strict non-empty finitely-generated V95( GFA1AdderStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) gate`2=den Boolean MSAlgebra over GFA1AdderStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)
2GatesCircuit ((n . (f2 + 1)),(f . (f2 + 1)),f1,xor2c) is strict non-empty finitely-generated V95( 2GatesCircStr ((n . (f2 + 1)),(f . (f2 + 1)),f1,xor2c)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((n . (f2 + 1)),(f . (f2 + 1)),f1,xor2c)
1GateCircuit ((n . (f2 + 1)),(f . (f2 + 1)),xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c)
1GateCircuit (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c)
1GateCircuit ([<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c],f1,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c],f1*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c],f1*>,xor2c)
1GateCircuit (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c],f1*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c],f1*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c],f1*>,xor2c)
(1GateCircuit ((n . (f2 + 1)),(f . (f2 + 1)),xor2c)) +* (1GateCircuit ([<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c],f1,xor2c)) is strict non-empty finitely-generated V95((1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c],f1*>,xor2c))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,xor2c],f1*>,xor2c))
GFA1CarryCirc ((n . (f2 + 1)),(f . (f2 + 1)),f1) is strict non-empty finitely-generated V95( GFA1CarryStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) gate`2=den Boolean MSAlgebra over GFA1CarryStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)
GFA1CarryICirc ((n . (f2 + 1)),(f . (f2 + 1)),f1) is strict non-empty finitely-generated V95( GFA1CarryIStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) gate`2=den Boolean MSAlgebra over GFA1CarryIStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)
1GateCircuit ((n . (f2 + 1)),(f . (f2 + 1)),and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c)
1GateCircuit (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c)
1GateCircuit ((f . (f2 + 1)),f1,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f2 + 1)),f1*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f2 + 1)),f1*>,and2a)
1GateCircuit (<*(f . (f2 + 1)),f1*>,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f2 + 1)),f1*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f2 + 1)),f1*>,and2a)
(1GateCircuit ((n . (f2 + 1)),(f . (f2 + 1)),and2c)) +* (1GateCircuit ((f . (f2 + 1)),f1,and2a)) is strict non-empty finitely-generated V95((1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c)) +* (1GateCircStr (<*(f . (f2 + 1)),f1*>,and2a))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c)) +* (1GateCircStr (<*(f . (f2 + 1)),f1*>,and2a))
1GateCircuit (f1,(n . (f2 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*f1,(n . (f2 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f1,(n . (f2 + 1))*>,and2)
1GateCircuit (<*f1,(n . (f2 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*f1,(n . (f2 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f1,(n . (f2 + 1))*>,and2)
((1GateCircuit ((n . (f2 + 1)),(f . (f2 + 1)),and2c)) +* (1GateCircuit ((f . (f2 + 1)),f1,and2a))) +* (1GateCircuit (f1,(n . (f2 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c)) +* (1GateCircStr (<*(f . (f2 + 1)),f1*>,and2a))) +* (1GateCircStr (<*f1,(n . (f2 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c)) +* (1GateCircStr (<*(f . (f2 + 1)),f1*>,and2a))) +* (1GateCircStr (<*f1,(n . (f2 + 1))*>,and2))
1GateCircuit ([<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c],[<*(f . (f2 + 1)),f1*>,and2a],[<*f1,(n . (f2 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c],[<*(f . (f2 + 1)),f1*>,and2a],[<*f1,(n . (f2 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c],[<*(f . (f2 + 1)),f1*>,and2a],[<*f1,(n . (f2 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c],[<*(f . (f2 + 1)),f1*>,and2a],[<*f1,(n . (f2 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c],[<*(f . (f2 + 1)),f1*>,and2a],[<*f1,(n . (f2 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c],[<*(f . (f2 + 1)),f1*>,and2a],[<*f1,(n . (f2 + 1))*>,and2]*>,or3)
(GFA1CarryICirc ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (1GateCircuit ([<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c],[<*(f . (f2 + 1)),f1*>,and2a],[<*f1,(n . (f2 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA1CarryIStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c],[<*(f . (f2 + 1)),f1*>,and2a],[<*f1,(n . (f2 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA1CarryIStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (1GateCircStr (<*[<*(n . (f2 + 1)),(f . (f2 + 1))*>,and2c],[<*(f . (f2 + 1)),f1*>,and2a],[<*f1,(n . (f2 + 1))*>,and2]*>,or3))
(GFA1AdderCirc ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (GFA1CarryCirc ((n . (f2 + 1)),(f . (f2 + 1)),f1)) is strict non-empty finitely-generated V95((GFA1AdderStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (GFA1CarryStr ((n . (f2 + 1)),(f . (f2 + 1)),f1))) gate`2=den Boolean MSAlgebra over (GFA1AdderStr ((n . (f2 + 1)),(f . (f2 + 1)),f1)) +* (GFA1CarryStr ((n . (f2 + 1)),(f . (f2 + 1)),f1))
h1 +* (BitGFA1Circ ((n . (f2 + 1)),(f . (f2 + 1)),f1)) is strict non-empty MSAlgebra over g1 +* (BitGFA1Str ((n . (f2 + 1)),(f . (f2 + 1)),f1))
g1 +* (BitGFA1Str ((n . (f2 + 1)),(f . (f2 + 1)),f1)) is non empty non void V56() strict ManySortedSign
proj1 A0 is set
g1 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
g1 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
A0 . (g1 + 1) is set
n . (g1 + 1) is set
f . (g1 + 1) is set
A0 . g1 is set
GFA1CarryOutput ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1)) is Element of InnerVertices (GFA1CarryStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1)))
GFA1CarryStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (g1 + 1)),(f . (g1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (g1 + 1)),(A0 . g1)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (g1 + 1)),(A0 . g1)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2c)) +* (1GateCircStr (<*(f . (g1 + 1)),(A0 . g1)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . g1),(n . (g1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(A0 . g1),(n . (g1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2c)) +* (1GateCircStr (<*(f . (g1 + 1)),(A0 . g1)*>,and2a))) +* (1GateCircStr (<*(A0 . g1),(n . (g1 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2c] is non empty pair set
[<*(f . (g1 + 1)),(A0 . g1)*>,and2a] is non empty pair set
[<*(A0 . g1),(n . (g1 + 1))*>,and2] is non empty pair set
<*[<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2c],[<*(f . (g1 + 1)),(A0 . g1)*>,and2a],[<*(A0 . g1),(n . (g1 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2c],[<*(f . (g1 + 1)),(A0 . g1)*>,and2a],[<*(A0 . g1),(n . (g1 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1))) +* (1GateCircStr (<*[<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2c],[<*(f . (g1 + 1)),(A0 . g1)*>,and2a],[<*(A0 . g1),(n . (g1 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA1CarryStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1))) is non empty set
InnerVertices (GFA1CarryStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1))) is non empty Element of K27( the carrier of (GFA1CarryStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1))))
K27( the carrier of (GFA1CarryStr ((n . (g1 + 1)),(f . (g1 + 1)),(A0 . g1)))) is set
[<*[<*(n . (g1 + 1)),(f . (g1 + 1))*>,and2c],[<*(f . (g1 + 1)),(A0 . g1)*>,and2a],[<*(A0 . g1),(n . (g1 + 1))*>,and2]*>,or3] is non empty pair set
g1 is Relation-like NAT -defined Function-like V14( NAT ) set
g1 . Sn is set
g1 . 0 is set
proj1 g1 is set
h1 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
h1 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
g1 . (h1 + 1) is set
n . (h1 + 1) is set
f . (h1 + 1) is set
g1 . h1 is set
GFA1CarryOutput ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1)) is Element of InnerVertices (GFA1CarryStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1)))
GFA1CarryStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (h1 + 1)),(f . (h1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (h1 + 1)),(g1 . h1)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (h1 + 1)),(g1 . h1)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2c)) +* (1GateCircStr (<*(f . (h1 + 1)),(g1 . h1)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g1 . h1),(n . (h1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g1 . h1),(n . (h1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2c)) +* (1GateCircStr (<*(f . (h1 + 1)),(g1 . h1)*>,and2a))) +* (1GateCircStr (<*(g1 . h1),(n . (h1 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2c] is non empty pair set
[<*(f . (h1 + 1)),(g1 . h1)*>,and2a] is non empty pair set
[<*(g1 . h1),(n . (h1 + 1))*>,and2] is non empty pair set
<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2c],[<*(f . (h1 + 1)),(g1 . h1)*>,and2a],[<*(g1 . h1),(n . (h1 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2c],[<*(f . (h1 + 1)),(g1 . h1)*>,and2a],[<*(g1 . h1),(n . (h1 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1))) +* (1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2c],[<*(f . (h1 + 1)),(g1 . h1)*>,and2a],[<*(g1 . h1),(n . (h1 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA1CarryStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1))) is non empty set
InnerVertices (GFA1CarryStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1))) is non empty Element of K27( the carrier of (GFA1CarryStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1))))
K27( the carrier of (GFA1CarryStr ((n . (h1 + 1)),(f . (h1 + 1)),(g1 . h1)))) is set
[<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2c],[<*(f . (h1 + 1)),(g1 . h1)*>,and2a],[<*(g1 . h1),(n . (h1 + 1))*>,and2]*>,or3] is non empty pair set
n is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(0,n,f) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(0,n,f) is strict non-empty finitely-generated V95((0,n,f)) gate`2=den Boolean MSAlgebra over (0,n,f)
(0,n,f) is Element of InnerVertices (0,n,f)
the carrier of (0,n,f) is non empty set
InnerVertices (0,n,f) is non empty Element of K27( the carrier of (0,n,f))
K27( the carrier of (0,n,f)) is set
h0 is Relation-like NAT -defined Function-like V14( NAT ) set
h0 . 0 is set
N is Relation-like NAT -defined Function-like V14( NAT ) set
N . 0 is set
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . 0 is set
h0 is Relation-like NAT -defined Function-like V14( NAT ) set
h0 . 0 is set
N is Relation-like NAT -defined Function-like V14( NAT ) set
N . 0 is set
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . 0 is set
{[{},((0 -tuples_on BOOLEAN) --> TRUE)]} is Relation-like Function-like constant non empty V12() V28() 1 -element set
h0 is Relation-like NAT -defined Function-like V14( NAT ) set
h0 . 0 is set
N is Relation-like NAT -defined Function-like V14( NAT ) set
N . 0 is set
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . 0 is set
S0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
A0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(1,S0,A0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
S0 . 1 is set
A0 . 1 is set
(1,S0,A0) is strict non-empty finitely-generated V95((1,S0,A0)) gate`2=den Boolean MSAlgebra over (1,S0,A0)
(1,S0,A0) is Element of InnerVertices (1,S0,A0)
the carrier of (1,S0,A0) is non empty set
InnerVertices (1,S0,A0) is non empty Element of K27( the carrier of (1,S0,A0))
K27( the carrier of (1,S0,A0)) is set
h0 is set
BitGFA1Str ((S0 . 1),(A0 . 1),h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((S0 . 1),(A0 . 1),h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((S0 . 1),(A0 . 1),h0,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(S0 . 1),(A0 . 1)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(S0 . 1),(A0 . 1)*>,xor2c] is non empty pair set
<*[<*(S0 . 1),(A0 . 1)*>,xor2c],h0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2c],h0*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2c)) +* (1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2c],h0*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((S0 . 1),(A0 . 1),h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((S0 . 1),(A0 . 1),h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . 1),h0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(A0 . 1),h0*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2c)) +* (1GateCircStr (<*(A0 . 1),h0*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*h0,(S0 . 1)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*h0,(S0 . 1)*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2c)) +* (1GateCircStr (<*(A0 . 1),h0*>,and2a))) +* (1GateCircStr (<*h0,(S0 . 1)*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(S0 . 1),(A0 . 1)*>,and2c] is non empty pair set
[<*(A0 . 1),h0*>,and2a] is non empty pair set
[<*h0,(S0 . 1)*>,and2] is non empty pair set
<*[<*(S0 . 1),(A0 . 1)*>,and2c],[<*(A0 . 1),h0*>,and2a],[<*h0,(S0 . 1)*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2c],[<*(A0 . 1),h0*>,and2a],[<*h0,(S0 . 1)*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((S0 . 1),(A0 . 1),h0)) +* (1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2c],[<*(A0 . 1),h0*>,and2a],[<*h0,(S0 . 1)*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((S0 . 1),(A0 . 1),h0)) +* (GFA1CarryStr ((S0 . 1),(A0 . 1),h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitGFA1Str ((S0 . 1),(A0 . 1),h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitGFA1Circ ((S0 . 1),(A0 . 1),h0) is strict non-empty finitely-generated V95( BitGFA1Str ((S0 . 1),(A0 . 1),h0)) gate`2=den Boolean MSAlgebra over BitGFA1Str ((S0 . 1),(A0 . 1),h0)
GFA1AdderCirc ((S0 . 1),(A0 . 1),h0) is strict non-empty finitely-generated V95( GFA1AdderStr ((S0 . 1),(A0 . 1),h0)) gate`2=den Boolean MSAlgebra over GFA1AdderStr ((S0 . 1),(A0 . 1),h0)
2GatesCircuit ((S0 . 1),(A0 . 1),h0,xor2c) is strict non-empty finitely-generated V95( 2GatesCircStr ((S0 . 1),(A0 . 1),h0,xor2c)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((S0 . 1),(A0 . 1),h0,xor2c)
1GateCircuit ((S0 . 1),(A0 . 1),xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2c)
1GateCircuit (<*(S0 . 1),(A0 . 1)*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2c)
1GateCircuit ([<*(S0 . 1),(A0 . 1)*>,xor2c],h0,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2c],h0*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2c],h0*>,xor2c)
1GateCircuit (<*[<*(S0 . 1),(A0 . 1)*>,xor2c],h0*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2c],h0*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2c],h0*>,xor2c)
(1GateCircuit ((S0 . 1),(A0 . 1),xor2c)) +* (1GateCircuit ([<*(S0 . 1),(A0 . 1)*>,xor2c],h0,xor2c)) is strict non-empty finitely-generated V95((1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2c)) +* (1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2c],h0*>,xor2c))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(S0 . 1),(A0 . 1)*>,xor2c)) +* (1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,xor2c],h0*>,xor2c))
GFA1CarryCirc ((S0 . 1),(A0 . 1),h0) is strict non-empty finitely-generated V95( GFA1CarryStr ((S0 . 1),(A0 . 1),h0)) gate`2=den Boolean MSAlgebra over GFA1CarryStr ((S0 . 1),(A0 . 1),h0)
GFA1CarryICirc ((S0 . 1),(A0 . 1),h0) is strict non-empty finitely-generated V95( GFA1CarryIStr ((S0 . 1),(A0 . 1),h0)) gate`2=den Boolean MSAlgebra over GFA1CarryIStr ((S0 . 1),(A0 . 1),h0)
1GateCircuit ((S0 . 1),(A0 . 1),and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2c)
1GateCircuit (<*(S0 . 1),(A0 . 1)*>,and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2c)
1GateCircuit ((A0 . 1),h0,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(A0 . 1),h0*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(A0 . 1),h0*>,and2a)
1GateCircuit (<*(A0 . 1),h0*>,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(A0 . 1),h0*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(A0 . 1),h0*>,and2a)
(1GateCircuit ((S0 . 1),(A0 . 1),and2c)) +* (1GateCircuit ((A0 . 1),h0,and2a)) is strict non-empty finitely-generated V95((1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2c)) +* (1GateCircStr (<*(A0 . 1),h0*>,and2a))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2c)) +* (1GateCircStr (<*(A0 . 1),h0*>,and2a))
1GateCircuit (h0,(S0 . 1),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*h0,(S0 . 1)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*h0,(S0 . 1)*>,and2)
1GateCircuit (<*h0,(S0 . 1)*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*h0,(S0 . 1)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*h0,(S0 . 1)*>,and2)
((1GateCircuit ((S0 . 1),(A0 . 1),and2c)) +* (1GateCircuit ((A0 . 1),h0,and2a))) +* (1GateCircuit (h0,(S0 . 1),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2c)) +* (1GateCircStr (<*(A0 . 1),h0*>,and2a))) +* (1GateCircStr (<*h0,(S0 . 1)*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(S0 . 1),(A0 . 1)*>,and2c)) +* (1GateCircStr (<*(A0 . 1),h0*>,and2a))) +* (1GateCircStr (<*h0,(S0 . 1)*>,and2))
1GateCircuit ([<*(S0 . 1),(A0 . 1)*>,and2c],[<*(A0 . 1),h0*>,and2a],[<*h0,(S0 . 1)*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2c],[<*(A0 . 1),h0*>,and2a],[<*h0,(S0 . 1)*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2c],[<*(A0 . 1),h0*>,and2a],[<*h0,(S0 . 1)*>,and2]*>,or3)
1GateCircuit (<*[<*(S0 . 1),(A0 . 1)*>,and2c],[<*(A0 . 1),h0*>,and2a],[<*h0,(S0 . 1)*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2c],[<*(A0 . 1),h0*>,and2a],[<*h0,(S0 . 1)*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2c],[<*(A0 . 1),h0*>,and2a],[<*h0,(S0 . 1)*>,and2]*>,or3)
(GFA1CarryICirc ((S0 . 1),(A0 . 1),h0)) +* (1GateCircuit ([<*(S0 . 1),(A0 . 1)*>,and2c],[<*(A0 . 1),h0*>,and2a],[<*h0,(S0 . 1)*>,and2],or3)) is strict non-empty finitely-generated V95((GFA1CarryIStr ((S0 . 1),(A0 . 1),h0)) +* (1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2c],[<*(A0 . 1),h0*>,and2a],[<*h0,(S0 . 1)*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA1CarryIStr ((S0 . 1),(A0 . 1),h0)) +* (1GateCircStr (<*[<*(S0 . 1),(A0 . 1)*>,and2c],[<*(A0 . 1),h0*>,and2a],[<*h0,(S0 . 1)*>,and2]*>,or3))
(GFA1AdderCirc ((S0 . 1),(A0 . 1),h0)) +* (GFA1CarryCirc ((S0 . 1),(A0 . 1),h0)) is strict non-empty finitely-generated V95((GFA1AdderStr ((S0 . 1),(A0 . 1),h0)) +* (GFA1CarryStr ((S0 . 1),(A0 . 1),h0))) gate`2=den Boolean MSAlgebra over (GFA1AdderStr ((S0 . 1),(A0 . 1),h0)) +* (GFA1CarryStr ((S0 . 1),(A0 . 1),h0))
(1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitGFA1Circ ((S0 . 1),(A0 . 1),h0)) is strict non-empty finitely-generated V95((1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitGFA1Str ((S0 . 1),(A0 . 1),h0))) gate`2=den Boolean MSAlgebra over (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitGFA1Str ((S0 . 1),(A0 . 1),h0))
GFA1CarryOutput ((S0 . 1),(A0 . 1),h0) is Element of InnerVertices (GFA1CarryStr ((S0 . 1),(A0 . 1),h0))
the carrier of (GFA1CarryStr ((S0 . 1),(A0 . 1),h0)) is non empty set
InnerVertices (GFA1CarryStr ((S0 . 1),(A0 . 1),h0)) is non empty Element of K27( the carrier of (GFA1CarryStr ((S0 . 1),(A0 . 1),h0)))
K27( the carrier of (GFA1CarryStr ((S0 . 1),(A0 . 1),h0))) is set
[<*[<*(S0 . 1),(A0 . 1)*>,and2c],[<*(A0 . 1),h0*>,and2a],[<*h0,(S0 . 1)*>,and2]*>,or3] is non empty pair set
N is Relation-like NAT -defined Function-like V14( NAT ) set
N . 1 is set
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . 1 is set
N . 0 is set
h . 0 is set
Sn is Relation-like NAT -defined Function-like V14( NAT ) set
Sn . 0 is set
0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
Sn . (0 + 1) is set
n is set
<*n*> is Relation-like NAT -defined Function-like constant non empty V12() V28() 1 -element FinSequence-like FinSubsequence-like set
f is set
<*f*> is Relation-like NAT -defined Function-like constant non empty V12() V28() 1 -element FinSequence-like FinSubsequence-like set
(1,<*n*>,<*f*>) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1,<*n*>,<*f*>) is strict non-empty finitely-generated V95((1,<*n*>,<*f*>)) gate`2=den Boolean MSAlgebra over (1,<*n*>,<*f*>)
(1,<*n*>,<*f*>) is Element of InnerVertices (1,<*n*>,<*f*>)
the carrier of (1,<*n*>,<*f*>) is non empty set
InnerVertices (1,<*n*>,<*f*>) is non empty Element of K27( the carrier of (1,<*n*>,<*f*>))
K27( the carrier of (1,<*n*>,<*f*>)) is set
<*n*> . 1 is set
<*f*> . 1 is set
g is set
BitGFA1Str (n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr (n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (n,f,g,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,f*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*n,f*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*n,f*>,xor2c] is non empty pair set
<*[<*n,f*>,xor2c],g*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*n,f*>,xor2c],g*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,xor2c)) +* (1GateCircStr (<*[<*n,f*>,xor2c],g*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr (n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr (n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f,g*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f,g*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,and2c)) +* (1GateCircStr (<*f,g*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*g,n*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*g,n*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2c)) +* (1GateCircStr (<*f,g*>,and2a))) +* (1GateCircStr (<*g,n*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*n,f*>,and2c] is non empty pair set
[<*f,g*>,and2a] is non empty pair set
[<*g,n*>,and2] is non empty pair set
<*[<*n,f*>,and2c],[<*f,g*>,and2a],[<*g,n*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*n,f*>,and2c],[<*f,g*>,and2a],[<*g,n*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2c],[<*f,g*>,and2a],[<*g,n*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr (n,f,g)) +* (GFA1CarryStr (n,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitGFA1Str (n,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitGFA1Circ (n,f,g) is strict non-empty finitely-generated V95( BitGFA1Str (n,f,g)) gate`2=den Boolean MSAlgebra over BitGFA1Str (n,f,g)
GFA1AdderCirc (n,f,g) is strict non-empty finitely-generated V95( GFA1AdderStr (n,f,g)) gate`2=den Boolean MSAlgebra over GFA1AdderStr (n,f,g)
2GatesCircuit (n,f,g,xor2c) is strict non-empty finitely-generated V95( 2GatesCircStr (n,f,g,xor2c)) gate`2=den Boolean MSAlgebra over 2GatesCircStr (n,f,g,xor2c)
1GateCircuit (n,f,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*n,f*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,xor2c)
1GateCircuit (<*n,f*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*n,f*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,xor2c)
1GateCircuit ([<*n,f*>,xor2c],g,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*n,f*>,xor2c],g*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,xor2c],g*>,xor2c)
1GateCircuit (<*[<*n,f*>,xor2c],g*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*n,f*>,xor2c],g*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,xor2c],g*>,xor2c)
(1GateCircuit (n,f,xor2c)) +* (1GateCircuit ([<*n,f*>,xor2c],g,xor2c)) is strict non-empty finitely-generated V95((1GateCircStr (<*n,f*>,xor2c)) +* (1GateCircStr (<*[<*n,f*>,xor2c],g*>,xor2c))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,xor2c)) +* (1GateCircStr (<*[<*n,f*>,xor2c],g*>,xor2c))
GFA1CarryCirc (n,f,g) is strict non-empty finitely-generated V95( GFA1CarryStr (n,f,g)) gate`2=den Boolean MSAlgebra over GFA1CarryStr (n,f,g)
GFA1CarryICirc (n,f,g) is strict non-empty finitely-generated V95( GFA1CarryIStr (n,f,g)) gate`2=den Boolean MSAlgebra over GFA1CarryIStr (n,f,g)
1GateCircuit (n,f,and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*n,f*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2c)
1GateCircuit (<*n,f*>,and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*n,f*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2c)
1GateCircuit (f,g,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*f,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2a)
1GateCircuit (<*f,g*>,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*f,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2a)
(1GateCircuit (n,f,and2c)) +* (1GateCircuit (f,g,and2a)) is strict non-empty finitely-generated V95((1GateCircStr (<*n,f*>,and2c)) +* (1GateCircStr (<*f,g*>,and2a))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,and2c)) +* (1GateCircStr (<*f,g*>,and2a))
1GateCircuit (g,n,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*g,n*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,and2)
1GateCircuit (<*g,n*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*g,n*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,and2)
((1GateCircuit (n,f,and2c)) +* (1GateCircuit (f,g,and2a))) +* (1GateCircuit (g,n,and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*n,f*>,and2c)) +* (1GateCircStr (<*f,g*>,and2a))) +* (1GateCircStr (<*g,n*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,and2c)) +* (1GateCircStr (<*f,g*>,and2a))) +* (1GateCircStr (<*g,n*>,and2))
1GateCircuit ([<*n,f*>,and2c],[<*f,g*>,and2a],[<*g,n*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*n,f*>,and2c],[<*f,g*>,and2a],[<*g,n*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2c],[<*f,g*>,and2a],[<*g,n*>,and2]*>,or3)
1GateCircuit (<*[<*n,f*>,and2c],[<*f,g*>,and2a],[<*g,n*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*n,f*>,and2c],[<*f,g*>,and2a],[<*g,n*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2c],[<*f,g*>,and2a],[<*g,n*>,and2]*>,or3)
(GFA1CarryICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,and2c],[<*f,g*>,and2a],[<*g,n*>,and2],or3)) is strict non-empty finitely-generated V95((GFA1CarryIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2c],[<*f,g*>,and2a],[<*g,n*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA1CarryIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2c],[<*f,g*>,and2a],[<*g,n*>,and2]*>,or3))
(GFA1AdderCirc (n,f,g)) +* (GFA1CarryCirc (n,f,g)) is strict non-empty finitely-generated V95((GFA1AdderStr (n,f,g)) +* (GFA1CarryStr (n,f,g))) gate`2=den Boolean MSAlgebra over (GFA1AdderStr (n,f,g)) +* (GFA1CarryStr (n,f,g))
(1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitGFA1Circ (n,f,g)) is strict non-empty finitely-generated V95((1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitGFA1Str (n,f,g))) gate`2=den Boolean MSAlgebra over (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitGFA1Str (n,f,g))
GFA1CarryOutput (n,f,g) is Element of InnerVertices (GFA1CarryStr (n,f,g))
the carrier of (GFA1CarryStr (n,f,g)) is non empty set
InnerVertices (GFA1CarryStr (n,f,g)) is non empty Element of K27( the carrier of (GFA1CarryStr (n,f,g)))
K27( the carrier of (GFA1CarryStr (n,f,g))) is set
[<*[<*n,f*>,and2c],[<*f,g*>,and2a],[<*g,n*>,and2]*>,or3] is non empty pair set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is Relation-like NAT -defined Function-like V28() n -element FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() n -element FinSequence-like FinSubsequence-like set
S0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
f ^ S0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
h0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g ^ h0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,(f ^ S0),(g ^ h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
A0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
f ^ A0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
N is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g ^ N is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,(f ^ A0),(g ^ N)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,(f ^ S0),(g ^ h0)) is strict non-empty finitely-generated V95((n,(f ^ S0),(g ^ h0))) gate`2=den Boolean MSAlgebra over (n,(f ^ S0),(g ^ h0))
(n,(f ^ A0),(g ^ N)) is strict non-empty finitely-generated V95((n,(f ^ A0),(g ^ N))) gate`2=den Boolean MSAlgebra over (n,(f ^ A0),(g ^ N))
(n,(f ^ S0),(g ^ h0)) is Element of InnerVertices (n,(f ^ S0),(g ^ h0))
the carrier of (n,(f ^ S0),(g ^ h0)) is non empty set
InnerVertices (n,(f ^ S0),(g ^ h0)) is non empty Element of K27( the carrier of (n,(f ^ S0),(g ^ h0)))
K27( the carrier of (n,(f ^ S0),(g ^ h0))) is set
(n,(f ^ A0),(g ^ N)) is Element of InnerVertices (n,(f ^ A0),(g ^ N))
the carrier of (n,(f ^ A0),(g ^ N)) is non empty set
InnerVertices (n,(f ^ A0),(g ^ N)) is non empty Element of K27( the carrier of (n,(f ^ A0),(g ^ N)))
K27( the carrier of (n,(f ^ A0),(g ^ N))) is set
h1 is Relation-like NAT -defined Function-like V14( NAT ) set
h1 . n is set
f1 is Relation-like NAT -defined Function-like V14( NAT ) set
f1 . n is set
h1 . 0 is set
f1 . 0 is set
f2 is Relation-like NAT -defined Function-like V14( NAT ) set
f2 . 0 is set
x is Relation-like NAT -defined Function-like V14( NAT ) set
x . n is set
g2 is Relation-like NAT -defined Function-like V14( NAT ) set
g2 . n is set
x . 0 is set
g2 . 0 is set
h2 is Relation-like NAT -defined Function-like V14( NAT ) set
h2 . 0 is set
i is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f2 . i is set
h2 . i is set
h1 . i is set
x . i is set
f1 . i is set
g2 . i is set
i + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f2 . (i + 1) is set
h2 . (i + 1) is set
h1 . (i + 1) is set
x . (i + 1) is set
f1 . (i + 1) is set
g2 . (i + 1) is set
len f is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
len g is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
dom f is V28() n -element Element of K27(NAT)
Seg n is V28() n -element Element of K27(NAT)
dom g is V28() n -element Element of K27(NAT)
0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
(f ^ S0) . (i + 1) is set
f . (i + 1) is set
(f ^ A0) . (i + 1) is set
(g ^ h0) . (i + 1) is set
g . (i + 1) is set
(g ^ N) . (i + 1) is set
A is non empty V56() ManySortedSign
S is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
h1 . S is set
c26 is non-empty MSAlgebra over A
f1 . S is set
c27 is set
f2 . S is set
S is non empty V56() ManySortedSign
c27 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
c27 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
(f ^ S0) . (c27 + 1) is set
(g ^ h0) . (c27 + 1) is set
c26 is set
BitGFA1Str (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c] is non empty pair set
<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c],c26*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c],c26*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c],c26*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((g ^ h0) . (c27 + 1)),c26*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c)) +* (1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*c26,((f ^ S0) . (c27 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c)) +* (1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2a))) +* (1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c] is non empty pair set
[<*((g ^ h0) . (c27 + 1)),c26*>,and2a] is non empty pair set
[<*c26,((f ^ S0) . (c27 + 1))*>,and2] is non empty pair set
<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c],[<*((g ^ h0) . (c27 + 1)),c26*>,and2a],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c],[<*((g ^ h0) . (c27 + 1)),c26*>,and2a],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c],[<*((g ^ h0) . (c27 + 1)),c26*>,and2a],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (GFA1CarryStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
A is non-empty MSAlgebra over S
BitGFA1Circ (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is strict non-empty finitely-generated V95( BitGFA1Str (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) gate`2=den Boolean MSAlgebra over BitGFA1Str (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)
GFA1AdderCirc (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is strict non-empty finitely-generated V95( GFA1AdderStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) gate`2=den Boolean MSAlgebra over GFA1AdderStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)
2GatesCircuit (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26,xor2c) is strict non-empty finitely-generated V95( 2GatesCircStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26,xor2c)) gate`2=den Boolean MSAlgebra over 2GatesCircStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26,xor2c)
1GateCircuit (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c)
1GateCircuit (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c)
1GateCircuit ([<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c],c26,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c],c26*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c],c26*>,xor2c)
1GateCircuit (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c],c26*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c],c26*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c],c26*>,xor2c)
(1GateCircuit (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),xor2c)) +* (1GateCircuit ([<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c],c26,xor2c)) is strict non-empty finitely-generated V95((1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c],c26*>,xor2c))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,xor2c],c26*>,xor2c))
GFA1CarryCirc (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is strict non-empty finitely-generated V95( GFA1CarryStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) gate`2=den Boolean MSAlgebra over GFA1CarryStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)
GFA1CarryICirc (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26) is strict non-empty finitely-generated V95( GFA1CarryIStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) gate`2=den Boolean MSAlgebra over GFA1CarryIStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)
1GateCircuit (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c)
1GateCircuit (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c)
1GateCircuit (((g ^ h0) . (c27 + 1)),c26,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2a)
1GateCircuit (<*((g ^ h0) . (c27 + 1)),c26*>,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2a)
(1GateCircuit (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),and2c)) +* (1GateCircuit (((g ^ h0) . (c27 + 1)),c26,and2a)) is strict non-empty finitely-generated V95((1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c)) +* (1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2a))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c)) +* (1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2a))
1GateCircuit (c26,((f ^ S0) . (c27 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2)
1GateCircuit (<*c26,((f ^ S0) . (c27 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2)
((1GateCircuit (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),and2c)) +* (1GateCircuit (((g ^ h0) . (c27 + 1)),c26,and2a))) +* (1GateCircuit (c26,((f ^ S0) . (c27 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c)) +* (1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2a))) +* (1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c)) +* (1GateCircStr (<*((g ^ h0) . (c27 + 1)),c26*>,and2a))) +* (1GateCircStr (<*c26,((f ^ S0) . (c27 + 1))*>,and2))
1GateCircuit ([<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c],[<*((g ^ h0) . (c27 + 1)),c26*>,and2a],[<*c26,((f ^ S0) . (c27 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c],[<*((g ^ h0) . (c27 + 1)),c26*>,and2a],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c],[<*((g ^ h0) . (c27 + 1)),c26*>,and2a],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c],[<*((g ^ h0) . (c27 + 1)),c26*>,and2a],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c],[<*((g ^ h0) . (c27 + 1)),c26*>,and2a],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c],[<*((g ^ h0) . (c27 + 1)),c26*>,and2a],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3)
(GFA1CarryICirc (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (1GateCircuit ([<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c],[<*((g ^ h0) . (c27 + 1)),c26*>,and2a],[<*c26,((f ^ S0) . (c27 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA1CarryIStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c],[<*((g ^ h0) . (c27 + 1)),c26*>,and2a],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA1CarryIStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (1GateCircStr (<*[<*((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1))*>,and2c],[<*((g ^ h0) . (c27 + 1)),c26*>,and2a],[<*c26,((f ^ S0) . (c27 + 1))*>,and2]*>,or3))
(GFA1AdderCirc (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (GFA1CarryCirc (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) is strict non-empty finitely-generated V95((GFA1AdderStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (GFA1CarryStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26))) gate`2=den Boolean MSAlgebra over (GFA1AdderStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) +* (GFA1CarryStr (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26))
A +* (BitGFA1Circ (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) is strict non-empty MSAlgebra over S +* (BitGFA1Str (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26))
S +* (BitGFA1Str (((f ^ S0) . (c27 + 1)),((g ^ h0) . (c27 + 1)),c26)) is non empty non void V56() strict ManySortedSign
S is non empty V56() ManySortedSign
A is non-empty MSAlgebra over S
GFA1CarryOutput (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is Element of InnerVertices (GFA1CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)))
GFA1CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((g ^ N) . (i + 1)),(h2 . i)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c)) +* (1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h2 . i),((f ^ A0) . (i + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c)) +* (1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a))) +* (1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c] is non empty pair set
[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a] is non empty pair set
[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2] is non empty pair set
<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA1CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) is non empty set
InnerVertices (GFA1CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) is non empty Element of K27( the carrier of (GFA1CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))))
K27( the carrier of (GFA1CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)))) is set
[<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3] is non empty pair set
BitGFA1Str (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i),xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c] is non empty pair set
<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c],(h2 . i)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c],(h2 . i)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c)) +* (1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c],(h2 . i)*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (GFA1CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
S +* (BitGFA1Str (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) is non empty non void V56() strict ManySortedSign
BitGFA1Circ (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is strict non-empty finitely-generated V95( BitGFA1Str (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) gate`2=den Boolean MSAlgebra over BitGFA1Str (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))
GFA1AdderCirc (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is strict non-empty finitely-generated V95( GFA1AdderStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) gate`2=den Boolean MSAlgebra over GFA1AdderStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))
2GatesCircuit (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i),xor2c) is strict non-empty finitely-generated V95( 2GatesCircStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i),xor2c)) gate`2=den Boolean MSAlgebra over 2GatesCircStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i),xor2c)
1GateCircuit (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c)
1GateCircuit (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c)
1GateCircuit ([<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c],(h2 . i),xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c],(h2 . i)*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c],(h2 . i)*>,xor2c)
1GateCircuit (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c],(h2 . i)*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c],(h2 . i)*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c],(h2 . i)*>,xor2c)
(1GateCircuit (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),xor2c)) +* (1GateCircuit ([<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c],(h2 . i),xor2c)) is strict non-empty finitely-generated V95((1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c)) +* (1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c],(h2 . i)*>,xor2c))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c)) +* (1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,xor2c],(h2 . i)*>,xor2c))
GFA1CarryCirc (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is strict non-empty finitely-generated V95( GFA1CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) gate`2=den Boolean MSAlgebra over GFA1CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))
GFA1CarryICirc (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)) is strict non-empty finitely-generated V95( GFA1CarryIStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) gate`2=den Boolean MSAlgebra over GFA1CarryIStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))
1GateCircuit (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c)
1GateCircuit (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c)
1GateCircuit (((g ^ N) . (i + 1)),(h2 . i),and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a)
1GateCircuit (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a)
(1GateCircuit (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),and2c)) +* (1GateCircuit (((g ^ N) . (i + 1)),(h2 . i),and2a)) is strict non-empty finitely-generated V95((1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c)) +* (1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c)) +* (1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a))
1GateCircuit ((h2 . i),((f ^ A0) . (i + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2)
1GateCircuit (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2)
((1GateCircuit (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),and2c)) +* (1GateCircuit (((g ^ N) . (i + 1)),(h2 . i),and2a))) +* (1GateCircuit ((h2 . i),((f ^ A0) . (i + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c)) +* (1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a))) +* (1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c)) +* (1GateCircStr (<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a))) +* (1GateCircStr (<*(h2 . i),((f ^ A0) . (i + 1))*>,and2))
1GateCircuit ([<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3)
(GFA1CarryICirc (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (1GateCircuit ([<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA1CarryIStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA1CarryIStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (1GateCircStr (<*[<*((f ^ A0) . (i + 1)),((g ^ N) . (i + 1))*>,and2c],[<*((g ^ N) . (i + 1)),(h2 . i)*>,and2a],[<*(h2 . i),((f ^ A0) . (i + 1))*>,and2]*>,or3))
(GFA1AdderCirc (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (GFA1CarryCirc (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) is strict non-empty finitely-generated V95((GFA1AdderStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (GFA1CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)))) gate`2=den Boolean MSAlgebra over (GFA1AdderStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) +* (GFA1CarryStr (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)))
A +* (BitGFA1Circ (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i))) is strict non-empty MSAlgebra over S +* (BitGFA1Str (((f ^ A0) . (i + 1)),((g ^ N) . (i + 1)),(h2 . i)))
f2 . n is set
h2 . n is set
S0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
S0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
A0 is Relation-like NAT -defined Function-like V28() S0 -element FinSequence-like FinSubsequence-like set
h0 is Relation-like NAT -defined Function-like V28() S0 -element FinSequence-like FinSubsequence-like set
(S0,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(S0,A0,h0) is Element of InnerVertices (S0,A0,h0)
the carrier of (S0,A0,h0) is non empty set
InnerVertices (S0,A0,h0) is non empty Element of K27( the carrier of (S0,A0,h0))
K27( the carrier of (S0,A0,h0)) is set
(S0,A0,h0) is strict non-empty finitely-generated V95((S0,A0,h0)) gate`2=den Boolean MSAlgebra over (S0,A0,h0)
N is set
<*N*> is Relation-like NAT -defined Function-like constant non empty V12() V28() 1 -element FinSequence-like FinSubsequence-like set
A0 ^ <*N*> is Relation-like NAT -defined Function-like non empty V28() S0 + 1 -element FinSequence-like FinSubsequence-like set
h is set
<*h*> is Relation-like NAT -defined Function-like constant non empty V12() V28() 1 -element FinSequence-like FinSubsequence-like set
h0 ^ <*h*> is Relation-like NAT -defined Function-like non empty V28() S0 + 1 -element FinSequence-like FinSubsequence-like set
((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitGFA1Str (N,h,(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr (N,h,(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (N,h,(S0,A0,h0),xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*N,h*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*N,h*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*N,h*>,xor2c] is non empty pair set
<*[<*N,h*>,xor2c],(S0,A0,h0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*N,h*>,xor2c],(S0,A0,h0)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*N,h*>,xor2c)) +* (1GateCircStr (<*[<*N,h*>,xor2c],(S0,A0,h0)*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr (N,h,(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr (N,h,(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*N,h*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*h,(S0,A0,h0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*h,(S0,A0,h0)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*N,h*>,and2c)) +* (1GateCircStr (<*h,(S0,A0,h0)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(S0,A0,h0),N*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(S0,A0,h0),N*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*N,h*>,and2c)) +* (1GateCircStr (<*h,(S0,A0,h0)*>,and2a))) +* (1GateCircStr (<*(S0,A0,h0),N*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*N,h*>,and2c] is non empty pair set
[<*h,(S0,A0,h0)*>,and2a] is non empty pair set
[<*(S0,A0,h0),N*>,and2] is non empty pair set
<*[<*N,h*>,and2c],[<*h,(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),N*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*N,h*>,and2c],[<*h,(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),N*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr (N,h,(S0,A0,h0))) +* (1GateCircStr (<*[<*N,h*>,and2c],[<*h,(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),N*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr (N,h,(S0,A0,h0))) +* (GFA1CarryStr (N,h,(S0,A0,h0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(S0,A0,h0) +* (BitGFA1Str (N,h,(S0,A0,h0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>)) is strict non-empty finitely-generated V95(((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>))) gate`2=den Boolean MSAlgebra over ((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>))
BitGFA1Circ (N,h,(S0,A0,h0)) is strict non-empty finitely-generated V95( BitGFA1Str (N,h,(S0,A0,h0))) gate`2=den Boolean MSAlgebra over BitGFA1Str (N,h,(S0,A0,h0))
GFA1AdderCirc (N,h,(S0,A0,h0)) is strict non-empty finitely-generated V95( GFA1AdderStr (N,h,(S0,A0,h0))) gate`2=den Boolean MSAlgebra over GFA1AdderStr (N,h,(S0,A0,h0))
2GatesCircuit (N,h,(S0,A0,h0),xor2c) is strict non-empty finitely-generated V95( 2GatesCircStr (N,h,(S0,A0,h0),xor2c)) gate`2=den Boolean MSAlgebra over 2GatesCircStr (N,h,(S0,A0,h0),xor2c)
1GateCircuit (N,h,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*N,h*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*N,h*>,xor2c)
1GateCircuit (<*N,h*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*N,h*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*N,h*>,xor2c)
1GateCircuit ([<*N,h*>,xor2c],(S0,A0,h0),xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*N,h*>,xor2c],(S0,A0,h0)*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*N,h*>,xor2c],(S0,A0,h0)*>,xor2c)
1GateCircuit (<*[<*N,h*>,xor2c],(S0,A0,h0)*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*N,h*>,xor2c],(S0,A0,h0)*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*N,h*>,xor2c],(S0,A0,h0)*>,xor2c)
(1GateCircuit (N,h,xor2c)) +* (1GateCircuit ([<*N,h*>,xor2c],(S0,A0,h0),xor2c)) is strict non-empty finitely-generated V95((1GateCircStr (<*N,h*>,xor2c)) +* (1GateCircStr (<*[<*N,h*>,xor2c],(S0,A0,h0)*>,xor2c))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*N,h*>,xor2c)) +* (1GateCircStr (<*[<*N,h*>,xor2c],(S0,A0,h0)*>,xor2c))
GFA1CarryCirc (N,h,(S0,A0,h0)) is strict non-empty finitely-generated V95( GFA1CarryStr (N,h,(S0,A0,h0))) gate`2=den Boolean MSAlgebra over GFA1CarryStr (N,h,(S0,A0,h0))
GFA1CarryICirc (N,h,(S0,A0,h0)) is strict non-empty finitely-generated V95( GFA1CarryIStr (N,h,(S0,A0,h0))) gate`2=den Boolean MSAlgebra over GFA1CarryIStr (N,h,(S0,A0,h0))
1GateCircuit (N,h,and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*N,h*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*N,h*>,and2c)
1GateCircuit (<*N,h*>,and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*N,h*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*N,h*>,and2c)
1GateCircuit (h,(S0,A0,h0),and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*h,(S0,A0,h0)*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*h,(S0,A0,h0)*>,and2a)
1GateCircuit (<*h,(S0,A0,h0)*>,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*h,(S0,A0,h0)*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*h,(S0,A0,h0)*>,and2a)
(1GateCircuit (N,h,and2c)) +* (1GateCircuit (h,(S0,A0,h0),and2a)) is strict non-empty finitely-generated V95((1GateCircStr (<*N,h*>,and2c)) +* (1GateCircStr (<*h,(S0,A0,h0)*>,and2a))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*N,h*>,and2c)) +* (1GateCircStr (<*h,(S0,A0,h0)*>,and2a))
1GateCircuit ((S0,A0,h0),N,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0,A0,h0),N*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0,A0,h0),N*>,and2)
1GateCircuit (<*(S0,A0,h0),N*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0,A0,h0),N*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0,A0,h0),N*>,and2)
((1GateCircuit (N,h,and2c)) +* (1GateCircuit (h,(S0,A0,h0),and2a))) +* (1GateCircuit ((S0,A0,h0),N,and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*N,h*>,and2c)) +* (1GateCircStr (<*h,(S0,A0,h0)*>,and2a))) +* (1GateCircStr (<*(S0,A0,h0),N*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*N,h*>,and2c)) +* (1GateCircStr (<*h,(S0,A0,h0)*>,and2a))) +* (1GateCircStr (<*(S0,A0,h0),N*>,and2))
1GateCircuit ([<*N,h*>,and2c],[<*h,(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),N*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*N,h*>,and2c],[<*h,(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),N*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*N,h*>,and2c],[<*h,(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),N*>,and2]*>,or3)
1GateCircuit (<*[<*N,h*>,and2c],[<*h,(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),N*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*N,h*>,and2c],[<*h,(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),N*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*N,h*>,and2c],[<*h,(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),N*>,and2]*>,or3)
(GFA1CarryICirc (N,h,(S0,A0,h0))) +* (1GateCircuit ([<*N,h*>,and2c],[<*h,(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),N*>,and2],or3)) is strict non-empty finitely-generated V95((GFA1CarryIStr (N,h,(S0,A0,h0))) +* (1GateCircStr (<*[<*N,h*>,and2c],[<*h,(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),N*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA1CarryIStr (N,h,(S0,A0,h0))) +* (1GateCircStr (<*[<*N,h*>,and2c],[<*h,(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),N*>,and2]*>,or3))
(GFA1AdderCirc (N,h,(S0,A0,h0))) +* (GFA1CarryCirc (N,h,(S0,A0,h0))) is strict non-empty finitely-generated V95((GFA1AdderStr (N,h,(S0,A0,h0))) +* (GFA1CarryStr (N,h,(S0,A0,h0)))) gate`2=den Boolean MSAlgebra over (GFA1AdderStr (N,h,(S0,A0,h0))) +* (GFA1CarryStr (N,h,(S0,A0,h0)))
(S0,A0,h0) +* (BitGFA1Circ (N,h,(S0,A0,h0))) is strict non-empty finitely-generated V95((S0,A0,h0) +* (BitGFA1Str (N,h,(S0,A0,h0)))) gate`2=den Boolean MSAlgebra over (S0,A0,h0) +* (BitGFA1Str (N,h,(S0,A0,h0)))
((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>)) is Element of InnerVertices ((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>))
the carrier of ((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>)) is non empty set
InnerVertices ((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>)) is non empty Element of K27( the carrier of ((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>)))
K27( the carrier of ((S0 + 1),(A0 ^ <*N*>),(h0 ^ <*h*>))) is set
GFA1CarryOutput (N,h,(S0,A0,h0)) is Element of InnerVertices (GFA1CarryStr (N,h,(S0,A0,h0)))
the carrier of (GFA1CarryStr (N,h,(S0,A0,h0))) is non empty set
InnerVertices (GFA1CarryStr (N,h,(S0,A0,h0))) is non empty Element of K27( the carrier of (GFA1CarryStr (N,h,(S0,A0,h0))))
K27( the carrier of (GFA1CarryStr (N,h,(S0,A0,h0)))) is set
[<*[<*N,h*>,and2c],[<*h,(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),N*>,and2]*>,or3] is non empty pair set
(S0,(A0 ^ <*N*>),(h0 ^ <*h*>)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(S0,(A0 ^ <*N*>),(h0 ^ <*h*>)) is strict non-empty finitely-generated V95((S0,(A0 ^ <*N*>),(h0 ^ <*h*>))) gate`2=den Boolean MSAlgebra over (S0,(A0 ^ <*N*>),(h0 ^ <*h*>))
o0 is Relation-like NAT -defined Function-like V14( NAT ) set
o0 . S0 is set
f1 is Relation-like NAT -defined Function-like V14( NAT ) set
f1 . S0 is set
o0 . 0 is set
f1 . 0 is set
g1 is Relation-like NAT -defined Function-like V14( NAT ) set
g1 . 0 is set
(S0,(A0 ^ <*N*>),(h0 ^ <*h*>)) is Element of InnerVertices (S0,(A0 ^ <*N*>),(h0 ^ <*h*>))
the carrier of (S0,(A0 ^ <*N*>),(h0 ^ <*h*>)) is non empty set
InnerVertices (S0,(A0 ^ <*N*>),(h0 ^ <*h*>)) is non empty Element of K27( the carrier of (S0,(A0 ^ <*N*>),(h0 ^ <*h*>)))
K27( the carrier of (S0,(A0 ^ <*N*>),(h0 ^ <*h*>))) is set
g1 . S0 is set
o0 . (S0 + 1) is set
f1 . (S0 + 1) is set
g1 . (S0 + 1) is set
len A0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
len h0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
(A0 ^ <*N*>) . (S0 + 1) is set
(h0 ^ <*h*>) . (S0 + 1) is set
A0 ^ {} is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
h0 ^ {} is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
S0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
S0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
A0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
h0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
((S0 + 1),A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(S0,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
A0 . (S0 + 1) is set
h0 . (S0 + 1) is set
(S0,A0,h0) is Element of InnerVertices (S0,A0,h0)
the carrier of (S0,A0,h0) is non empty set
InnerVertices (S0,A0,h0) is non empty Element of K27( the carrier of (S0,A0,h0))
K27( the carrier of (S0,A0,h0)) is set
BitGFA1Str ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0),xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c] is non empty pair set
<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c],(S0,A0,h0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c],(S0,A0,h0)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c],(S0,A0,h0)*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0 . (S0 + 1)),(S0,A0,h0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(S0,A0,h0),(A0 . (S0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a))) +* (1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c] is non empty pair set
[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a] is non empty pair set
[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2] is non empty pair set
<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (GFA1CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(S0,A0,h0) +* (BitGFA1Str ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((S0 + 1),A0,h0) is strict non-empty finitely-generated V95(((S0 + 1),A0,h0)) gate`2=den Boolean MSAlgebra over ((S0 + 1),A0,h0)
(S0,A0,h0) is strict non-empty finitely-generated V95((S0,A0,h0)) gate`2=den Boolean MSAlgebra over (S0,A0,h0)
BitGFA1Circ ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is strict non-empty finitely-generated V95( BitGFA1Str ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) gate`2=den Boolean MSAlgebra over BitGFA1Str ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))
GFA1AdderCirc ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is strict non-empty finitely-generated V95( GFA1AdderStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) gate`2=den Boolean MSAlgebra over GFA1AdderStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))
2GatesCircuit ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0),xor2c) is strict non-empty finitely-generated V95( 2GatesCircStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0),xor2c)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0),xor2c)
1GateCircuit ((A0 . (S0 + 1)),(h0 . (S0 + 1)),xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c)
1GateCircuit (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c)
1GateCircuit ([<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c],(S0,A0,h0),xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c],(S0,A0,h0)*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c],(S0,A0,h0)*>,xor2c)
1GateCircuit (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c],(S0,A0,h0)*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c],(S0,A0,h0)*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c],(S0,A0,h0)*>,xor2c)
(1GateCircuit ((A0 . (S0 + 1)),(h0 . (S0 + 1)),xor2c)) +* (1GateCircuit ([<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c],(S0,A0,h0),xor2c)) is strict non-empty finitely-generated V95((1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c],(S0,A0,h0)*>,xor2c))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,xor2c],(S0,A0,h0)*>,xor2c))
GFA1CarryCirc ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is strict non-empty finitely-generated V95( GFA1CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) gate`2=den Boolean MSAlgebra over GFA1CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))
GFA1CarryICirc ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is strict non-empty finitely-generated V95( GFA1CarryIStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) gate`2=den Boolean MSAlgebra over GFA1CarryIStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))
1GateCircuit ((A0 . (S0 + 1)),(h0 . (S0 + 1)),and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c)
1GateCircuit (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c)
1GateCircuit ((h0 . (S0 + 1)),(S0,A0,h0),and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a)
1GateCircuit (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a)
(1GateCircuit ((A0 . (S0 + 1)),(h0 . (S0 + 1)),and2c)) +* (1GateCircuit ((h0 . (S0 + 1)),(S0,A0,h0),and2a)) is strict non-empty finitely-generated V95((1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a))
1GateCircuit ((S0,A0,h0),(A0 . (S0 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2)
1GateCircuit (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2)
((1GateCircuit ((A0 . (S0 + 1)),(h0 . (S0 + 1)),and2c)) +* (1GateCircuit ((h0 . (S0 + 1)),(S0,A0,h0),and2a))) +* (1GateCircuit ((S0,A0,h0),(A0 . (S0 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a))) +* (1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a))) +* (1GateCircStr (<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2))
1GateCircuit ([<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3)
(GFA1CarryICirc ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (1GateCircuit ([<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA1CarryIStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA1CarryIStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (1GateCircStr (<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3))
(GFA1AdderCirc ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (GFA1CarryCirc ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) is strict non-empty finitely-generated V95((GFA1AdderStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (GFA1CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)))) gate`2=den Boolean MSAlgebra over (GFA1AdderStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) +* (GFA1CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)))
(S0,A0,h0) +* (BitGFA1Circ ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) is strict non-empty finitely-generated V95((S0,A0,h0) +* (BitGFA1Str ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)))) gate`2=den Boolean MSAlgebra over (S0,A0,h0) +* (BitGFA1Str ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)))
((S0 + 1),A0,h0) is Element of InnerVertices ((S0 + 1),A0,h0)
the carrier of ((S0 + 1),A0,h0) is non empty set
InnerVertices ((S0 + 1),A0,h0) is non empty Element of K27( the carrier of ((S0 + 1),A0,h0))
K27( the carrier of ((S0 + 1),A0,h0)) is set
GFA1CarryOutput ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)) is Element of InnerVertices (GFA1CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)))
the carrier of (GFA1CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) is non empty set
InnerVertices (GFA1CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))) is non empty Element of K27( the carrier of (GFA1CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0))))
K27( the carrier of (GFA1CarryStr ((A0 . (S0 + 1)),(h0 . (S0 + 1)),(S0,A0,h0)))) is set
[<*[<*(A0 . (S0 + 1)),(h0 . (S0 + 1))*>,and2c],[<*(h0 . (S0 + 1)),(S0,A0,h0)*>,and2a],[<*(S0,A0,h0),(A0 . (S0 + 1))*>,and2]*>,or3] is non empty pair set
N is Relation-like NAT -defined Function-like V14( NAT ) set
N . S0 is set
h is Relation-like NAT -defined Function-like V14( NAT ) set
h . S0 is set
N . 0 is set
h . 0 is set
Sn is Relation-like NAT -defined Function-like V14( NAT ) set
Sn . 0 is set
Sn . S0 is set
N . (S0 + 1) is set
h . (S0 + 1) is set
Sn . (S0 + 1) is set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
S0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (n,g,S0) is non empty Element of K27( the carrier of (n,g,S0))
the carrier of (n,g,S0) is non empty set
K27( the carrier of (n,g,S0)) is set
(f,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (f,g,S0) is non empty Element of K27( the carrier of (f,g,S0))
the carrier of (f,g,S0) is non empty set
K27( the carrier of (f,g,S0)) is set
A0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
n + A0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
n + 0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
((n + 0),g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + 0),g,S0) is non empty Element of K27( the carrier of ((n + 0),g,S0))
the carrier of ((n + 0),g,S0) is non empty set
K27( the carrier of ((n + 0),g,S0)) is set
h0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
n + h0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
((n + h0),g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + h0),g,S0) is non empty Element of K27( the carrier of ((n + h0),g,S0))
the carrier of ((n + h0),g,S0) is non empty set
K27( the carrier of ((n + h0),g,S0)) is set
h0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
n + (h0 + 1) is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() set
((n + (h0 + 1)),g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + (h0 + 1)),g,S0) is non empty Element of K27( the carrier of ((n + (h0 + 1)),g,S0))
the carrier of ((n + (h0 + 1)),g,S0) is non empty set
K27( the carrier of ((n + (h0 + 1)),g,S0)) is set
(n + h0) + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
g . ((n + h0) + 1) is set
S0 . ((n + h0) + 1) is set
((n + h0),g,S0) is Element of InnerVertices ((n + h0),g,S0)
BitGFA1Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0),xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,xor2c] is non empty pair set
<*[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,xor2c],((n + h0),g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,xor2c],((n + h0),g,S0)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,xor2c],((n + h0),g,S0)*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,and2c)) +* (1GateCircStr (<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((n + h0),g,S0),(g . ((n + h0) + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*((n + h0),g,S0),(g . ((n + h0) + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,and2c)) +* (1GateCircStr (<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*>,and2a))) +* (1GateCircStr (<*((n + h0),g,S0),(g . ((n + h0) + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,and2c] is non empty pair set
[<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*>,and2a] is non empty pair set
[<*((n + h0),g,S0),(g . ((n + h0) + 1))*>,and2] is non empty pair set
<*[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,and2c],[<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*>,and2a],[<*((n + h0),g,S0),(g . ((n + h0) + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,and2c],[<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*>,and2a],[<*((n + h0),g,S0),(g . ((n + h0) + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))) +* (1GateCircStr (<*[<*(g . ((n + h0) + 1)),(S0 . ((n + h0) + 1))*>,and2c],[<*(S0 . ((n + h0) + 1)),((n + h0),g,S0)*>,and2a],[<*((n + h0),g,S0),(g . ((n + h0) + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))) +* (GFA1CarryStr ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitGFA1Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))) is non empty Element of K27( the carrier of (BitGFA1Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))))
the carrier of (BitGFA1Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))) is non empty set
K27( the carrier of (BitGFA1Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)))) is set
(InnerVertices (n,g,S0)) \/ (InnerVertices (BitGFA1Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)))) is non empty set
(InnerVertices ((n + h0),g,S0)) \/ (InnerVertices (BitGFA1Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)))) is non empty set
((n + h0),g,S0) +* (BitGFA1Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (((n + h0),g,S0) +* (BitGFA1Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)))) is non empty Element of K27( the carrier of (((n + h0),g,S0) +* (BitGFA1Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)))))
the carrier of (((n + h0),g,S0) +* (BitGFA1Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0)))) is non empty set
K27( the carrier of (((n + h0),g,S0) +* (BitGFA1Str ((g . ((n + h0) + 1)),(S0 . ((n + h0) + 1)),((n + h0),g,S0))))) is set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
n + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
((n + 1),f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + 1),f,g) is non empty Element of K27( the carrier of ((n + 1),f,g))
the carrier of ((n + 1),f,g) is non empty set
K27( the carrier of ((n + 1),f,g)) is set
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (n,f,g) is non empty Element of K27( the carrier of (n,f,g))
the carrier of (n,f,g) is non empty set
K27( the carrier of (n,f,g)) is set
f . (n + 1) is set
g . (n + 1) is set
(n,f,g) is Element of InnerVertices (n,f,g)
BitGFA1Str ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (n + 1)),(g . (n + 1)),(n,f,g),xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),(g . (n + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,xor2c] is non empty pair set
<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2c],(n,f,g)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2c],(n,f,g)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2c],(n,f,g)*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (n + 1)),(n,f,g)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2c)) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n,f,g),(f . (n + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(n,f,g),(f . (n + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2c)) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2a))) +* (1GateCircStr (<*(n,f,g),(f . (n + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,and2c] is non empty pair set
[<*(g . (n + 1)),(n,f,g)*>,and2a] is non empty pair set
[<*(n,f,g),(f . (n + 1))*>,and2] is non empty pair set
<*[<*(f . (n + 1)),(g . (n + 1))*>,and2c],[<*(g . (n + 1)),(n,f,g)*>,and2a],[<*(n,f,g),(f . (n + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2c],[<*(g . (n + 1)),(n,f,g)*>,and2a],[<*(n,f,g),(f . (n + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2c],[<*(g . (n + 1)),(n,f,g)*>,and2a],[<*(n,f,g),(f . (n + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (GFA1CarryStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitGFA1Str ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty Element of K27( the carrier of (BitGFA1Str ((f . (n + 1)),(g . (n + 1)),(n,f,g))))
the carrier of (BitGFA1Str ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty set
K27( the carrier of (BitGFA1Str ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is set
(InnerVertices (n,f,g)) \/ (InnerVertices (BitGFA1Str ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is non empty set
(n,f,g) +* (BitGFA1Str ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n,f,g) +* (BitGFA1Str ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is non empty Element of K27( the carrier of ((n,f,g) +* (BitGFA1Str ((f . (n + 1)),(g . (n + 1)),(n,f,g)))))
the carrier of ((n,f,g) +* (BitGFA1Str ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is non empty set
K27( the carrier of ((n,f,g) +* (BitGFA1Str ((f . (n + 1)),(g . (n + 1)),(n,f,g))))) is set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
S0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(f,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (f,g,S0) is non empty set
InnerVertices (f,g,S0) is non empty Element of K27( the carrier of (f,g,S0))
K27( the carrier of (f,g,S0)) is set
g . n is set
S0 . n is set
N is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
N + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
A0 is Element of InnerVertices (f,g,S0)
(N,g,S0) is Element of InnerVertices (N,g,S0)
(N,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (N,g,S0) is non empty set
InnerVertices (N,g,S0) is non empty Element of K27( the carrier of (N,g,S0))
K27( the carrier of (N,g,S0)) is set
GFA1AdderOutput ((g . n),(S0 . n),(N,g,S0)) is Element of InnerVertices (GFA1AdderStr ((g . n),(S0 . n),(N,g,S0)))
GFA1AdderStr ((g . n),(S0 . n),(N,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . n),(S0 . n),(N,g,S0),xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . n),(S0 . n)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . n),(S0 . n)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . n),(S0 . n)*>,xor2c] is non empty pair set
<*[<*(g . n),(S0 . n)*>,xor2c],(N,g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . n),(S0 . n)*>,xor2c],(N,g,S0)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . n),(S0 . n)*>,xor2c)) +* (1GateCircStr (<*[<*(g . n),(S0 . n)*>,xor2c],(N,g,S0)*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA1AdderStr ((g . n),(S0 . n),(N,g,S0))) is non empty set
InnerVertices (GFA1AdderStr ((g . n),(S0 . n),(N,g,S0))) is non empty Element of K27( the carrier of (GFA1AdderStr ((g . n),(S0 . n),(N,g,S0))))
K27( the carrier of (GFA1AdderStr ((g . n),(S0 . n),(N,g,S0)))) is set
2GatesCircOutput ((g . n),(S0 . n),(N,g,S0),xor2c) is non empty pair Element of InnerVertices (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),xor2c))
the carrier of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),xor2c)) is non empty set
InnerVertices (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),xor2c)) is non empty Element of K27( the carrier of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),xor2c)))
K27( the carrier of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),xor2c))) is set
[<*[<*(g . n),(S0 . n)*>,xor2c],(N,g,S0)*>,xor2c] is non empty pair set
h is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
h + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
h0 is Element of InnerVertices (f,g,S0)
(h,g,S0) is Element of InnerVertices (h,g,S0)
(h,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (h,g,S0) is non empty set
InnerVertices (h,g,S0) is non empty Element of K27( the carrier of (h,g,S0))
K27( the carrier of (h,g,S0)) is set
GFA1AdderOutput ((g . n),(S0 . n),(h,g,S0)) is Element of InnerVertices (GFA1AdderStr ((g . n),(S0 . n),(h,g,S0)))
GFA1AdderStr ((g . n),(S0 . n),(h,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . n),(S0 . n),(h,g,S0),xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*(g . n),(S0 . n)*>,xor2c],(h,g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . n),(S0 . n)*>,xor2c],(h,g,S0)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . n),(S0 . n)*>,xor2c)) +* (1GateCircStr (<*[<*(g . n),(S0 . n)*>,xor2c],(h,g,S0)*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA1AdderStr ((g . n),(S0 . n),(h,g,S0))) is non empty set
InnerVertices (GFA1AdderStr ((g . n),(S0 . n),(h,g,S0))) is non empty Element of K27( the carrier of (GFA1AdderStr ((g . n),(S0 . n),(h,g,S0))))
K27( the carrier of (GFA1AdderStr ((g . n),(S0 . n),(h,g,S0)))) is set
2GatesCircOutput ((g . n),(S0 . n),(h,g,S0),xor2c) is non empty pair Element of InnerVertices (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),xor2c))
the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),xor2c)) is non empty set
InnerVertices (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),xor2c)) is non empty Element of K27( the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),xor2c)))
K27( the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),xor2c))) is set
[<*[<*(g . n),(S0 . n)*>,xor2c],(h,g,S0)*>,xor2c] is non empty pair set
A0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
1 + A0 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
h0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
(h0,g,S0) is Element of InnerVertices (h0,g,S0)
(h0,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (h0,g,S0) is non empty set
InnerVertices (h0,g,S0) is non empty Element of K27( the carrier of (h0,g,S0))
K27( the carrier of (h0,g,S0)) is set
GFA1AdderOutput ((g . n),(S0 . n),(h0,g,S0)) is Element of InnerVertices (GFA1AdderStr ((g . n),(S0 . n),(h0,g,S0)))
GFA1AdderStr ((g . n),(S0 . n),(h0,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . n),(S0 . n),(h0,g,S0),xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . n),(S0 . n)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . n),(S0 . n)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . n),(S0 . n)*>,xor2c] is non empty pair set
<*[<*(g . n),(S0 . n)*>,xor2c],(h0,g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . n),(S0 . n)*>,xor2c],(h0,g,S0)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . n),(S0 . n)*>,xor2c)) +* (1GateCircStr (<*[<*(g . n),(S0 . n)*>,xor2c],(h0,g,S0)*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA1AdderStr ((g . n),(S0 . n),(h0,g,S0))) is non empty set
InnerVertices (GFA1AdderStr ((g . n),(S0 . n),(h0,g,S0))) is non empty Element of K27( the carrier of (GFA1AdderStr ((g . n),(S0 . n),(h0,g,S0))))
K27( the carrier of (GFA1AdderStr ((g . n),(S0 . n),(h0,g,S0)))) is set
2GatesCircOutput ((g . n),(S0 . n),(h0,g,S0),xor2c) is non empty pair Element of InnerVertices (2GatesCircStr ((g . n),(S0 . n),(h0,g,S0),xor2c))
the carrier of (2GatesCircStr ((g . n),(S0 . n),(h0,g,S0),xor2c)) is non empty set
InnerVertices (2GatesCircStr ((g . n),(S0 . n),(h0,g,S0),xor2c)) is non empty Element of K27( the carrier of (2GatesCircStr ((g . n),(S0 . n),(h0,g,S0),xor2c)))
K27( the carrier of (2GatesCircStr ((g . n),(S0 . n),(h0,g,S0),xor2c))) is set
[<*[<*(g . n),(S0 . n)*>,xor2c],(h0,g,S0)*>,xor2c] is non empty pair set
(n,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices H1(n) is non empty Element of K27( the carrier of H1(n))
the carrier of H1(n) is non empty set
K27( the carrier of H1(n)) is set
InnerVertices H1(f) is non empty Element of K27( the carrier of H1(f))
the carrier of H1(f) is non empty set
K27( the carrier of H1(f)) is set
h0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
g . (h0 + 1) is set
S0 . (h0 + 1) is set
BitGFA1Str ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0),xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (h0 + 1)),(S0 . (h0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,xor2c] is non empty pair set
<*[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,xor2c],(h0,g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,xor2c],(h0,g,S0)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,xor2c],(h0,g,S0)*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(S0 . (h0 + 1)),(h0,g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(S0 . (h0 + 1)),(h0,g,S0)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,and2c)) +* (1GateCircStr (<*(S0 . (h0 + 1)),(h0,g,S0)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0,g,S0),(g . (h0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0,g,S0),(g . (h0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,and2c)) +* (1GateCircStr (<*(S0 . (h0 + 1)),(h0,g,S0)*>,and2a))) +* (1GateCircStr (<*(h0,g,S0),(g . (h0 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,and2c] is non empty pair set
[<*(S0 . (h0 + 1)),(h0,g,S0)*>,and2a] is non empty pair set
[<*(h0,g,S0),(g . (h0 + 1))*>,and2] is non empty pair set
<*[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,and2c],[<*(S0 . (h0 + 1)),(h0,g,S0)*>,and2a],[<*(h0,g,S0),(g . (h0 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,and2c],[<*(S0 . (h0 + 1)),(h0,g,S0)*>,and2a],[<*(h0,g,S0),(g . (h0 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0))) +* (1GateCircStr (<*[<*(g . (h0 + 1)),(S0 . (h0 + 1))*>,and2c],[<*(S0 . (h0 + 1)),(h0,g,S0)*>,and2a],[<*(h0,g,S0),(g . (h0 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0))) +* (GFA1CarryStr ((g . (h0 + 1)),(S0 . (h0 + 1)),(h0,g,S0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices H2(h0) is non empty Element of K27( the carrier of H2(h0))
the carrier of H2(h0) is non empty set
K27( the carrier of H2(h0)) is set
H1(h0) +* H2(h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of H1(h0) is non empty set
the carrier of H2(h0) \/ the carrier of H1(h0) is non empty set
h is Element of the carrier of H2(h0)
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
S0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
((f + 1),n,g,S0) is Element of InnerVertices (n,g,S0)
(n,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (n,g,S0) is non empty set
InnerVertices (n,g,S0) is non empty Element of K27( the carrier of (n,g,S0))
K27( the carrier of (n,g,S0)) is set
g . (f + 1) is set
S0 . (f + 1) is set
(f,g,S0) is Element of InnerVertices (f,g,S0)
(f,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (f,g,S0) is non empty set
InnerVertices (f,g,S0) is non empty Element of K27( the carrier of (f,g,S0))
K27( the carrier of (f,g,S0)) is set
GFA1AdderOutput ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0)) is Element of InnerVertices (GFA1AdderStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0)))
GFA1AdderStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (f + 1)),(S0 . (f + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (f + 1)),(S0 . (f + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2c] is non empty pair set
<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2c],(f,g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2c],(f,g,S0)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . (f + 1)),(S0 . (f + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2c],(f,g,S0)*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA1AdderStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0))) is non empty set
InnerVertices (GFA1AdderStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0))) is non empty Element of K27( the carrier of (GFA1AdderStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0))))
K27( the carrier of (GFA1AdderStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0)))) is set
2GatesCircOutput ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),xor2c) is non empty pair Element of InnerVertices (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),xor2c))
the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),xor2c)) is non empty set
InnerVertices (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),xor2c)) is non empty Element of K27( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),xor2c)))
K27( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),xor2c))) is set
[<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2c],(f,g,S0)*>,xor2c] is non empty pair set
A0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
A0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
(A0,g,S0) is Element of InnerVertices (A0,g,S0)
(A0,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (A0,g,S0) is non empty set
InnerVertices (A0,g,S0) is non empty Element of K27( the carrier of (A0,g,S0))
K27( the carrier of (A0,g,S0)) is set
GFA1AdderOutput ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0)) is Element of InnerVertices (GFA1AdderStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0)))
GFA1AdderStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2c],(A0,g,S0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2c],(A0,g,S0)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . (f + 1)),(S0 . (f + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2c],(A0,g,S0)*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA1AdderStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0))) is non empty set
InnerVertices (GFA1AdderStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0))) is non empty Element of K27( the carrier of (GFA1AdderStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0))))
K27( the carrier of (GFA1AdderStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0)))) is set
2GatesCircOutput ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),xor2c) is non empty pair Element of InnerVertices (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),xor2c))
the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),xor2c)) is non empty set
InnerVertices (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),xor2c)) is non empty Element of K27( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),xor2c)))
K27( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),xor2c))) is set
[<*[<*(g . (f + 1)),(S0 . (f + 1))*>,xor2c],(A0,g,S0)*>,xor2c] is non empty pair set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (n,f,g) is non empty Element of K27( the carrier of (n,f,g))
the carrier of (n,f,g) is non empty set
K27( the carrier of (n,f,g)) is set
(0,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices H1( 0 ) is non empty Element of K27( the carrier of H1( 0 ))
the carrier of H1( 0 ) is non empty set
K27( the carrier of H1( 0 )) is set
A0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
(A0,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices H1(A0) is non empty Element of K27( the carrier of H1(A0))
the carrier of H1(A0) is non empty set
K27( the carrier of H1(A0)) is set
A0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
((A0 + 1),f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f . (A0 + 1) is set
g . (A0 + 1) is set
(A0,f,g) is Element of InnerVertices (A0,f,g)
the carrier of (A0,f,g) is non empty set
InnerVertices (A0,f,g) is non empty Element of K27( the carrier of (A0,f,g))
K27( the carrier of (A0,f,g)) is set
BitGFA1Str ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g),xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (A0 + 1)),(g . (A0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (A0 + 1)),(g . (A0 + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (A0 + 1)),(g . (A0 + 1))*>,xor2c] is non empty pair set
<*[<*(f . (A0 + 1)),(g . (A0 + 1))*>,xor2c],(A0,f,g)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (A0 + 1)),(g . (A0 + 1))*>,xor2c],(A0,f,g)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (A0 + 1)),(g . (A0 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (A0 + 1)),(g . (A0 + 1))*>,xor2c],(A0,f,g)*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (A0 + 1)),(g . (A0 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (A0 + 1)),(A0,f,g)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (A0 + 1)),(A0,f,g)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (A0 + 1)),(g . (A0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (A0 + 1)),(A0,f,g)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0,f,g),(f . (A0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(A0,f,g),(f . (A0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (A0 + 1)),(g . (A0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (A0 + 1)),(A0,f,g)*>,and2a))) +* (1GateCircStr (<*(A0,f,g),(f . (A0 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (A0 + 1)),(g . (A0 + 1))*>,and2c] is non empty pair set
[<*(g . (A0 + 1)),(A0,f,g)*>,and2a] is non empty pair set
[<*(A0,f,g),(f . (A0 + 1))*>,and2] is non empty pair set
<*[<*(f . (A0 + 1)),(g . (A0 + 1))*>,and2c],[<*(g . (A0 + 1)),(A0,f,g)*>,and2a],[<*(A0,f,g),(f . (A0 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (A0 + 1)),(g . (A0 + 1))*>,and2c],[<*(g . (A0 + 1)),(A0,f,g)*>,and2a],[<*(A0,f,g),(f . (A0 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g))) +* (1GateCircStr (<*[<*(f . (A0 + 1)),(g . (A0 + 1))*>,and2c],[<*(g . (A0 + 1)),(A0,f,g)*>,and2a],[<*(A0,f,g),(f . (A0 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g))) +* (GFA1CarryStr ((f . (A0 + 1)),(g . (A0 + 1)),(A0,f,g))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
H1(A0) +* H2(A0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices H2(A0) is non empty Element of K27( the carrier of H2(A0))
the carrier of H2(A0) is non empty set
K27( the carrier of H2(A0)) is set
InnerVertices H1(A0 + 1) is non empty Element of K27( the carrier of H1(A0 + 1))
the carrier of H1(A0 + 1) is non empty set
K27( the carrier of H1(A0 + 1)) is set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,f,g) is Element of InnerVertices (n,f,g)
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (n,f,g) is non empty set
InnerVertices (n,f,g) is non empty Element of K27( the carrier of (n,f,g))
K27( the carrier of (n,f,g)) is set
(0,f,g) is Element of InnerVertices (0,f,g)
(0,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (0,f,g) is non empty set
InnerVertices (0,f,g) is non empty Element of K27( the carrier of (0,f,g))
K27( the carrier of (0,f,g)) is set
Sn is Relation-like NAT -defined Function-like V14( NAT ) set
Sn . 0 is set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
(Sn,f,g) is Element of InnerVertices (Sn,f,g)
(Sn,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (Sn,f,g) is non empty set
InnerVertices (Sn,f,g) is non empty Element of K27( the carrier of (Sn,f,g))
K27( the carrier of (Sn,f,g)) is set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
((Sn + 1),f,g) is Element of InnerVertices ((Sn + 1),f,g)
((Sn + 1),f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of ((Sn + 1),f,g) is non empty set
InnerVertices ((Sn + 1),f,g) is non empty Element of K27( the carrier of ((Sn + 1),f,g))
K27( the carrier of ((Sn + 1),f,g)) is set
f . (Sn + 1) is set
g . (Sn + 1) is set
GFA1CarryOutput ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g)) is Element of InnerVertices (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g)))
GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (Sn + 1)),(g . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (Sn + 1)),(Sn,f,g)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (Sn + 1)),(Sn,f,g)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(g . (Sn + 1)),(Sn,f,g)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(Sn,f,g),(f . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(Sn,f,g),(f . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(g . (Sn + 1)),(Sn,f,g)*>,and2a))) +* (1GateCircStr (<*(Sn,f,g),(f . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c] is non empty pair set
[<*(g . (Sn + 1)),(Sn,f,g)*>,and2a] is non empty pair set
[<*(Sn,f,g),(f . (Sn + 1))*>,and2] is non empty pair set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(Sn,f,g)*>,and2a],[<*(Sn,f,g),(f . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(Sn,f,g)*>,and2a],[<*(Sn,f,g),(f . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g))) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(Sn,f,g)*>,and2a],[<*(Sn,f,g),(f . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g))) is non empty set
InnerVertices (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g))) is non empty Element of K27( the carrier of (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g))))
K27( the carrier of (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),(Sn,f,g)))) is set
[<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),(Sn,f,g)*>,and2a],[<*(Sn,f,g),(f . (Sn + 1))*>,and2]*>,or3] is non empty pair set
A0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
h0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
proj1 ((0 -tuples_on BOOLEAN) --> TRUE) is set
(0,A0,h0) is non empty pair Element of InnerVertices (0,A0,h0)
(0,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (0,A0,h0) is non empty set
InnerVertices (0,A0,h0) is non empty Element of K27( the carrier of (0,A0,h0))
K27( the carrier of (0,A0,h0)) is set
(0,A0,h0) `1 is set
(0,A0,h0) `2 is set
proj1 ((0,A0,h0) `2) is set
card ((0,A0,h0) `1) is V21() V22() V23() cardinal set
N is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
(N,A0,h0) is non empty pair Element of InnerVertices (N,A0,h0)
(N,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (N,A0,h0) is non empty set
InnerVertices (N,A0,h0) is non empty Element of K27( the carrier of (N,A0,h0))
K27( the carrier of (N,A0,h0)) is set
(N,A0,h0) `1 is set
(N,A0,h0) `2 is set
proj1 ((N,A0,h0) `2) is set
card ((N,A0,h0) `1) is V21() V22() V23() cardinal set
N + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
((N + 1),A0,h0) is non empty pair Element of InnerVertices ((N + 1),A0,h0)
((N + 1),A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of ((N + 1),A0,h0) is non empty set
InnerVertices ((N + 1),A0,h0) is non empty Element of K27( the carrier of ((N + 1),A0,h0))
K27( the carrier of ((N + 1),A0,h0)) is set
A0 . (N + 1) is set
h0 . (N + 1) is set
GFA1CarryOutput ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0)) is Element of InnerVertices (GFA1CarryStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0)))
GFA1CarryStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . (N + 1)),(h0 . (N + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0 . (N + 1)),(N,A0,h0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0 . (N + 1)),(N,A0,h0)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (N + 1)),(N,A0,h0)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(N,A0,h0),(A0 . (N + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(N,A0,h0),(A0 . (N + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (N + 1)),(N,A0,h0)*>,and2a))) +* (1GateCircStr (<*(N,A0,h0),(A0 . (N + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2c] is non empty pair set
[<*(h0 . (N + 1)),(N,A0,h0)*>,and2a] is non empty pair set
[<*(N,A0,h0),(A0 . (N + 1))*>,and2] is non empty pair set
<*[<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2c],[<*(h0 . (N + 1)),(N,A0,h0)*>,and2a],[<*(N,A0,h0),(A0 . (N + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2c],[<*(h0 . (N + 1)),(N,A0,h0)*>,and2a],[<*(N,A0,h0),(A0 . (N + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0))) +* (1GateCircStr (<*[<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2c],[<*(h0 . (N + 1)),(N,A0,h0)*>,and2a],[<*(N,A0,h0),(A0 . (N + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA1CarryStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0))) is non empty set
InnerVertices (GFA1CarryStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0))) is non empty Element of K27( the carrier of (GFA1CarryStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0))))
K27( the carrier of (GFA1CarryStr ((A0 . (N + 1)),(h0 . (N + 1)),(N,A0,h0)))) is set
[<*[<*(A0 . (N + 1)),(h0 . (N + 1))*>,and2c],[<*(h0 . (N + 1)),(N,A0,h0)*>,and2a],[<*(N,A0,h0),(A0 . (N + 1))*>,and2]*>,or3] is non empty pair set
proj1 or3 is set
((N + 1),A0,h0) `1 is set
((N + 1),A0,h0) `2 is set
proj1 (((N + 1),A0,h0) `2) is set
card (((N + 1),A0,h0) `1) is V21() V22() V23() cardinal set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,f,g) is non empty pair Element of InnerVertices (n,f,g)
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (n,f,g) is non empty set
InnerVertices (n,f,g) is non empty Element of K27( the carrier of (n,f,g))
K27( the carrier of (n,f,g)) is set
S0 is set
A0 is Relation-like Function-like V18(2 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K27(K28((2 -tuples_on BOOLEAN),BOOLEAN))
[S0,A0] is non empty pair set
proj1 A0 is set
[S0,A0] `2 is set
proj1 ([S0,A0] `2) is set
(n,f,g) `2 is set
proj1 ((n,f,g) `2) is set
A0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like nonpair-yielding set
h0 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like nonpair-yielding set
N is Relation-like NAT -defined Function-like V14( NAT ) set
(0,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices H1( 0 ) is non empty Element of K27( the carrier of H1( 0 ))
the carrier of H1( 0 ) is non empty set
K27( the carrier of H1( 0 )) is set
InputVertices H1( 0 ) is Element of K27( the carrier of H1( 0 ))
N . 0 is set
(0,A0,h0) is non empty pair Element of InnerVertices (0,A0,h0)
the carrier of (0,A0,h0) is non empty set
InnerVertices (0,A0,h0) is non empty Element of K27( the carrier of (0,A0,h0))
K27( the carrier of (0,A0,h0)) is set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
A0 . (Sn + 1) is non pair set
h0 . (Sn + 1) is non pair set
An is set
BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],An*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],An*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0 . (Sn + 1)),An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*An,(A0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*An,(A0 . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2a))) +* (1GateCircStr (<*An,(A0 . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c] is non empty pair set
[<*(h0 . (Sn + 1)),An*>,and2a] is non empty pair set
[<*An,(A0 . (Sn + 1))*>,and2] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),An*>,and2a],[<*An,(A0 . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),An*>,and2a],[<*An,(A0 . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),An*>,and2a],[<*An,(A0 . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) +* (GFA1CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) is non empty Element of K27( the carrier of (BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)))
the carrier of (BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) is non empty set
K27( the carrier of (BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An))) is set
An is set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
N . Sn is set
(Sn,A0,h0) is non empty pair Element of InnerVertices (Sn,A0,h0)
(Sn,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (Sn,A0,h0) is non empty set
InnerVertices (Sn,A0,h0) is non empty Element of K27( the carrier of (Sn,A0,h0))
K27( the carrier of (Sn,A0,h0)) is set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
A0 . (Sn + 1) is non pair set
h0 . (Sn + 1) is non pair set
<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c] is non empty pair set
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c] is non empty pair set
BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],An*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],An*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0 . (Sn + 1)),An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*An,(A0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*An,(A0 . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2a))) +* (1GateCircStr (<*An,(A0 . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(h0 . (Sn + 1)),An*>,and2a] is non empty pair set
[<*An,(A0 . (Sn + 1))*>,and2] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),An*>,and2a],[<*An,(A0 . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),An*>,and2a],[<*An,(A0 . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),An*>,and2a],[<*An,(A0 . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) +* (GFA1CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices H2(An,Sn) is Element of K27( the carrier of H2(An,Sn))
the carrier of H2(An,Sn) is non empty set
K27( the carrier of H2(An,Sn)) is set
{(A0 . (Sn + 1)),(h0 . (Sn + 1)),An} is V28() set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
N . Sn is set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
A0 . (Sn + 1) is non pair set
h0 . (Sn + 1) is non pair set
An is set
BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],An*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],An*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0 . (Sn + 1)),An*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*An,(A0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*An,(A0 . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (Sn + 1)),An*>,and2a))) +* (1GateCircStr (<*An,(A0 . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c] is non empty pair set
[<*(h0 . (Sn + 1)),An*>,and2a] is non empty pair set
[<*An,(A0 . (Sn + 1))*>,and2] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),An*>,and2a],[<*An,(A0 . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),An*>,and2a],[<*An,(A0 . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),An*>,and2a],[<*An,(A0 . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) +* (GFA1CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),An)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of H2(An,Sn) is non empty set
InputVertices H2(An,Sn) is Element of K27( the carrier of H2(An,Sn))
K27( the carrier of H2(An,Sn)) is set
{An} is non empty V12() V28() 1 -element set
(InputVertices H2(An,Sn)) \ {An} is Element of K27( the carrier of H2(An,Sn))
{(A0 . (Sn + 1)),(h0 . (Sn + 1)),An} is V28() set
o0 is non empty pair set
An is non empty V56() ManySortedSign
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
(Sn,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
o0 is set
N . Sn is set
(Sn,A0,h0) is non empty pair Element of InnerVertices (Sn,A0,h0)
the carrier of (Sn,A0,h0) is non empty set
InnerVertices (Sn,A0,h0) is non empty Element of K27( the carrier of (Sn,A0,h0))
K27( the carrier of (Sn,A0,h0)) is set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
N . (Sn + 1) is set
((Sn + 1),A0,h0) is non empty pair Element of InnerVertices ((Sn + 1),A0,h0)
((Sn + 1),A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of ((Sn + 1),A0,h0) is non empty set
InnerVertices ((Sn + 1),A0,h0) is non empty Element of K27( the carrier of ((Sn + 1),A0,h0))
K27( the carrier of ((Sn + 1),A0,h0)) is set
A0 . (Sn + 1) is non pair set
h0 . (Sn + 1) is non pair set
BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],o0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],o0*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],o0*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0 . (Sn + 1)),o0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0 . (Sn + 1)),o0*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (Sn + 1)),o0*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*o0,(A0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*o0,(A0 . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (Sn + 1)),o0*>,and2a))) +* (1GateCircStr (<*o0,(A0 . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c] is non empty pair set
[<*(h0 . (Sn + 1)),o0*>,and2a] is non empty pair set
[<*o0,(A0 . (Sn + 1))*>,and2] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),o0*>,and2a],[<*o0,(A0 . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),o0*>,and2a],[<*o0,(A0 . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),o0*>,and2a],[<*o0,(A0 . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)) +* (GFA1CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
An +* H2(o0,Sn) is non empty non void V56() strict ManySortedSign
GFA1CarryOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0) is Element of InnerVertices (GFA1CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))
the carrier of (GFA1CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)) is non empty set
InnerVertices (GFA1CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)) is non empty Element of K27( the carrier of (GFA1CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)))
K27( the carrier of (GFA1CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))) is set
[<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),o0*>,and2a],[<*o0,(A0 . (Sn + 1))*>,and2]*>,or3] is non empty pair set
InputVertices H2(o0,Sn) is Element of K27( the carrier of H2(o0,Sn))
the carrier of H2(o0,Sn) is non empty set
K27( the carrier of H2(o0,Sn)) is set
{(A0 . (Sn + 1)),(h0 . (Sn + 1)),o0} is V28() set
InnerVertices H2(o0,Sn) is non empty Element of K27( the carrier of H2(o0,Sn))
{[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c]} is Relation-like Function-like constant non empty V12() V28() 1 -element set
GFA1AdderOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0) is Element of InnerVertices (GFA1AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))
the carrier of (GFA1AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)) is non empty set
InnerVertices (GFA1AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)) is non empty Element of K27( the carrier of (GFA1AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0)))
K27( the carrier of (GFA1AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))) is set
2GatesCircOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0,xor2c) is non empty pair Element of InnerVertices (2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0,xor2c))
the carrier of (2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0,xor2c)) is non empty set
InnerVertices (2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0,xor2c)) is non empty Element of K27( the carrier of (2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0,xor2c)))
K27( the carrier of (2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0,xor2c))) is set
[<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],o0*>,xor2c] is non empty pair set
{(GFA1AdderOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))} is non empty V12() V28() 1 -element set
{[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c]} \/ {(GFA1AdderOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))} is non empty V28() set
{[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),o0*>,and2a],[<*o0,(A0 . (Sn + 1))*>,and2]} is Relation-like V28() set
({[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c]} \/ {(GFA1AdderOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))}) \/ {[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),o0*>,and2a],[<*o0,(A0 . (Sn + 1))*>,and2]} is non empty V28() set
{(GFA1CarryOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))} is non empty V12() V28() 1 -element set
(({[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c]} \/ {(GFA1AdderOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))}) \/ {[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),o0*>,and2a],[<*o0,(A0 . (Sn + 1))*>,and2]}) \/ {(GFA1CarryOutput ((A0 . (Sn + 1)),(h0 . (Sn + 1)),o0))} is non empty V28() set
{H5(o0,Sn)} is non empty V12() V28() 1 -element set
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
((Sn + 1),A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices ((Sn + 1),A0,h0) is Element of K27( the carrier of ((Sn + 1),A0,h0))
the carrier of ((Sn + 1),A0,h0) is non empty set
K27( the carrier of ((Sn + 1),A0,h0)) is set
(Sn,A0,h0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (Sn,A0,h0) is Element of K27( the carrier of (Sn,A0,h0))
the carrier of (Sn,A0,h0) is non empty set
K27( the carrier of (Sn,A0,h0)) is set
A0 . (Sn + 1) is non pair set
h0 . (Sn + 1) is non pair set
(Sn,A0,h0) is non empty pair Element of InnerVertices (Sn,A0,h0)
InnerVertices (Sn,A0,h0) is non empty Element of K27( the carrier of (Sn,A0,h0))
BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0),xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],(Sn,A0,h0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],(Sn,A0,h0)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,xor2c],(Sn,A0,h0)*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h0 . (Sn + 1)),(Sn,A0,h0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(h0 . (Sn + 1)),(Sn,A0,h0)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (Sn + 1)),(Sn,A0,h0)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(Sn,A0,h0),(A0 . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(Sn,A0,h0),(A0 . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(h0 . (Sn + 1)),(Sn,A0,h0)*>,and2a))) +* (1GateCircStr (<*(Sn,A0,h0),(A0 . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c] is non empty pair set
[<*(h0 . (Sn + 1)),(Sn,A0,h0)*>,and2a] is non empty pair set
[<*(Sn,A0,h0),(A0 . (Sn + 1))*>,and2] is non empty pair set
<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),(Sn,A0,h0)*>,and2a],[<*(Sn,A0,h0),(A0 . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),(Sn,A0,h0)*>,and2a],[<*(Sn,A0,h0),(A0 . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0))) +* (1GateCircStr (<*[<*(A0 . (Sn + 1)),(h0 . (Sn + 1))*>,and2c],[<*(h0 . (Sn + 1)),(Sn,A0,h0)*>,and2a],[<*(Sn,A0,h0),(A0 . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0))) +* (GFA1CarryStr ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0))) is non empty set
InputVertices (BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0))) is Element of K27( the carrier of (BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0))))
K27( the carrier of (BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0)))) is set
{(Sn,A0,h0)} is Relation-like non empty V12() V28() 1 -element set
(InputVertices (BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0)))) \ {(Sn,A0,h0)} is Element of K27( the carrier of (BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0))))
(InputVertices (Sn,A0,h0)) \/ ((InputVertices (BitGFA1Str ((A0 . (Sn + 1)),(h0 . (Sn + 1)),(Sn,A0,h0)))) \ {(Sn,A0,h0)}) is set
N . Sn is set
g is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty non pair V21() V22() V23() V25() V26() V27() V28() V29() V32() cardinal 0 -element V37() FinSequence-like FinSubsequence-like FinSequence-membered non with_pair nonpair-yielding ext-real non positive non negative V115() V126() set
S0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty non pair V21() V22() V23() V25() V26() V27() V28() V29() V32() cardinal 0 -element V37() FinSequence-like FinSubsequence-like FinSequence-membered non with_pair nonpair-yielding ext-real non positive non negative V115() V126() set
(0,g,S0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (0,g,S0) is Element of K27( the carrier of (0,g,S0))
the carrier of (0,g,S0) is non empty set
K27( the carrier of (0,g,S0)) is set
proj2 g is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V12() non pair V21() V22() V23() V25() V26() V27() V28() V29() V32() cardinal {} -element V37() FinSequence-like FinSubsequence-like FinSequence-membered non with_pair nonpair-yielding ext-real non positive non negative V115() V126() set
proj2 S0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V12() non pair V21() V22() V23() V25() V26() V27() V28() V29() V32() cardinal {} -element V37() FinSequence-like FinSubsequence-like FinSequence-membered non with_pair nonpair-yielding ext-real non positive non negative V115() V126() set
(proj2 g) \/ (proj2 S0) is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty non pair V21() V22() V23() V25() V26() V27() V28() V29() V32() cardinal {} -element V37() FinSequence-like FinSubsequence-like FinSequence-membered non with_pair nonpair-yielding ext-real non positive non negative V115() V126() set
proj2 {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V12() non pair V21() V22() V23() V25() V26() V27() V28() V29() V32() cardinal {} -element V37() FinSequence-like FinSubsequence-like FinSequence-membered non with_pair nonpair-yielding ext-real non positive non negative V115() V126() set
g is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
g + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
S0 is Relation-like NAT -defined Function-like V28() g + 1 -element FinSequence-like FinSubsequence-like nonpair-yielding set
A0 is Relation-like NAT -defined Function-like V28() g + 1 -element FinSequence-like FinSubsequence-like nonpair-yielding set
((g + 1),S0,A0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices ((g + 1),S0,A0) is Element of K27( the carrier of ((g + 1),S0,A0))
the carrier of ((g + 1),S0,A0) is non empty set
K27( the carrier of ((g + 1),S0,A0)) is set
proj2 S0 is V28() non with_pair set
proj2 A0 is V28() non with_pair set
(proj2 S0) \/ (proj2 A0) is V28() non with_pair set
h0 is Relation-like NAT -defined Function-like V28() g -element FinSequence-like FinSubsequence-like nonpair-yielding set
N is non pair set
<*N*> is Relation-like NAT -defined Function-like constant non empty V12() V28() 1 -element FinSequence-like FinSubsequence-like nonpair-yielding set
h0 ^ <*N*> is Relation-like NAT -defined Function-like non empty V28() g + 1 -element FinSequence-like FinSubsequence-like set
h is Relation-like NAT -defined Function-like V28() g -element FinSequence-like FinSubsequence-like nonpair-yielding set
Sn is non pair set
<*Sn*> is Relation-like NAT -defined Function-like constant non empty V12() V28() 1 -element FinSequence-like FinSubsequence-like nonpair-yielding set
h ^ <*Sn*> is Relation-like NAT -defined Function-like non empty V28() g + 1 -element FinSequence-like FinSubsequence-like set
dom <*N*> is non empty V12() V28() 1 -element Element of K27(NAT)
len h0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
S0 . (g + 1) is non pair set
<*N*> . 1 is non pair set
dom <*Sn*> is non empty V12() V28() 1 -element Element of K27(NAT)
len h is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
A0 . (g + 1) is non pair set
<*Sn*> . 1 is non pair set
(g,S0,A0) is non empty pair Element of InnerVertices (g,S0,A0)
(g,S0,A0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (g,S0,A0) is non empty set
InnerVertices (g,S0,A0) is non empty Element of K27( the carrier of (g,S0,A0))
K27( the carrier of (g,S0,A0)) is set
{N,Sn,H1(g)} is V28() set
{H1(g),N,Sn} is V28() set
proj2 h0 is V28() non with_pair set
proj2 <*N*> is non empty V12() V28() 1 -element non with_pair set
(proj2 h0) \/ (proj2 <*N*>) is non empty V28() non with_pair set
{N} is non empty V12() V28() 1 -element non with_pair set
(proj2 h0) \/ {N} is non empty V28() non with_pair set
proj2 h is V28() non with_pair set
proj2 <*Sn*> is non empty V12() V28() 1 -element non with_pair set
(proj2 h) \/ (proj2 <*Sn*>) is non empty V28() non with_pair set
{Sn} is non empty V12() V28() 1 -element non with_pair set
(proj2 h) \/ {Sn} is non empty V28() non with_pair set
<*N,Sn*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
[<*N,Sn*>,and2c] is non empty pair set
[<*N,Sn*>,xor2c] is non empty pair set
h0 ^ {} is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
h ^ {} is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(g,h0,h) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (g,h0,h) is Element of K27( the carrier of (g,h0,h))
the carrier of (g,h0,h) is non empty set
K27( the carrier of (g,h0,h)) is set
BitGFA1Str (N,Sn,H1(g)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr (N,Sn,(g,S0,A0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (N,Sn,(g,S0,A0),xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*N,Sn*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*N,Sn*>,xor2c],(g,S0,A0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*N,Sn*>,xor2c],(g,S0,A0)*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*N,Sn*>,xor2c)) +* (1GateCircStr (<*[<*N,Sn*>,xor2c],(g,S0,A0)*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr (N,Sn,(g,S0,A0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr (N,Sn,(g,S0,A0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*N,Sn*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*Sn,(g,S0,A0)*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*Sn,(g,S0,A0)*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*N,Sn*>,and2c)) +* (1GateCircStr (<*Sn,(g,S0,A0)*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g,S0,A0),N*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g,S0,A0),N*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*N,Sn*>,and2c)) +* (1GateCircStr (<*Sn,(g,S0,A0)*>,and2a))) +* (1GateCircStr (<*(g,S0,A0),N*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*Sn,(g,S0,A0)*>,and2a] is non empty pair set
[<*(g,S0,A0),N*>,and2] is non empty pair set
<*[<*N,Sn*>,and2c],[<*Sn,(g,S0,A0)*>,and2a],[<*(g,S0,A0),N*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*N,Sn*>,and2c],[<*Sn,(g,S0,A0)*>,and2a],[<*(g,S0,A0),N*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr (N,Sn,(g,S0,A0))) +* (1GateCircStr (<*[<*N,Sn*>,and2c],[<*Sn,(g,S0,A0)*>,and2a],[<*(g,S0,A0),N*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr (N,Sn,(g,S0,A0))) +* (GFA1CarryStr (N,Sn,(g,S0,A0))) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BitGFA1Str (N,Sn,H1(g))) is non empty set
InputVertices (BitGFA1Str (N,Sn,H1(g))) is Element of K27( the carrier of (BitGFA1Str (N,Sn,H1(g))))
K27( the carrier of (BitGFA1Str (N,Sn,H1(g)))) is set
{H1(g)} is Relation-like non empty V12() V28() 1 -element set
(InputVertices (BitGFA1Str (N,Sn,H1(g)))) \ {H1(g)} is Element of K27( the carrier of (BitGFA1Str (N,Sn,H1(g))))
(InputVertices (g,h0,h)) \/ ((InputVertices (BitGFA1Str (N,Sn,H1(g)))) \ {H1(g)}) is set
(proj2 h0) \/ (proj2 h) is V28() non with_pair set
((proj2 h0) \/ (proj2 h)) \/ ((InputVertices (BitGFA1Str (N,Sn,H1(g)))) \ {H1(g)}) is set
{N,Sn,H1(g)} \ {H1(g)} is V28() Element of K27({N,Sn,H1(g)})
K27({N,Sn,H1(g)}) is V28() V32() set
((proj2 h0) \/ (proj2 h)) \/ ({N,Sn,H1(g)} \ {H1(g)}) is V28() set
{N,Sn} is non empty V28() non with_pair set
((proj2 h0) \/ (proj2 h)) \/ {N,Sn} is non empty V28() non with_pair set
{N} \/ {Sn} is non empty V28() non with_pair set
((proj2 h0) \/ (proj2 h)) \/ ({N} \/ {Sn}) is non empty V28() non with_pair set
((proj2 h0) \/ (proj2 h)) \/ {N} is non empty V28() non with_pair set
(((proj2 h0) \/ (proj2 h)) \/ {N}) \/ {Sn} is non empty V28() non with_pair set
((proj2 h0) \/ {N}) \/ (proj2 h) is non empty V28() non with_pair set
(((proj2 h0) \/ {N}) \/ (proj2 h)) \/ {Sn} is non empty V28() non with_pair set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
2 * n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
1 + (2 * n) is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f is Relation-like NAT -defined Function-like V28() n -element FinSequence-like FinSubsequence-like nonpair-yielding set
g is Relation-like NAT -defined Function-like V28() n -element FinSequence-like FinSubsequence-like nonpair-yielding set
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,f,g) is strict non-empty finitely-generated V95((n,f,g)) gate`2=den Boolean MSAlgebra over (n,f,g)
the Sorts of (n,f,g) is Relation-like the carrier of (n,f,g) -defined Function-like V14( the carrier of (n,f,g)) set
the carrier of (n,f,g) is non empty set
K106( the Sorts of (n,f,g)) is set
N is Relation-like Function-like V18( NAT , NAT ) Element of K27(K28(NAT,NAT))
N . 0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
N . 1 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
N . 2 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
Sn is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
Sn + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (Sn + 1) is non pair set
g . (Sn + 1) is non pair set
h is set
BitGFA1Circ ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V95( BitGFA1Str ((f . (Sn + 1)),(g . (Sn + 1)),h)) gate`2=den Boolean MSAlgebra over BitGFA1Str ((f . (Sn + 1)),(g . (Sn + 1)),h)
BitGFA1Str ((f . (Sn + 1)),(g . (Sn + 1)),h) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),h) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (Sn + 1)),(g . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c] is non empty pair set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c],h*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c],h*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c],h*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),h) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),h) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (Sn + 1)),h*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (Sn + 1)),h*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*h,(f . (Sn + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*h,(f . (Sn + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2a))) +* (1GateCircStr (<*h,(f . (Sn + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c] is non empty pair set
[<*(g . (Sn + 1)),h*>,and2a] is non empty pair set
[<*h,(f . (Sn + 1))*>,and2] is non empty pair set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),h*>,and2a],[<*h,(f . (Sn + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),h*>,and2a],[<*h,(f . (Sn + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),h*>,and2a],[<*h,(f . (Sn + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderCirc ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V95( GFA1AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) gate`2=den Boolean MSAlgebra over GFA1AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),h)
2GatesCircuit ((f . (Sn + 1)),(g . (Sn + 1)),h,xor2c) is strict non-empty finitely-generated V95( 2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,xor2c)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,xor2c)
1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c)
1GateCircuit (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c)
1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c],h,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c],h*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c],h*>,xor2c)
1GateCircuit (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c],h*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c],h*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c],h*>,xor2c)
(1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),xor2c)) +* (1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c],h,xor2c)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c],h*>,xor2c))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,xor2c],h*>,xor2c))
GFA1CarryCirc ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V95( GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) gate`2=den Boolean MSAlgebra over GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),h)
GFA1CarryICirc ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V95( GFA1CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) gate`2=den Boolean MSAlgebra over GFA1CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)
1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)
1GateCircuit (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)
1GateCircuit ((g . (Sn + 1)),h,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (Sn + 1)),h*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (Sn + 1)),h*>,and2a)
1GateCircuit (<*(g . (Sn + 1)),h*>,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (Sn + 1)),h*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (Sn + 1)),h*>,and2a)
(1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),and2c)) +* (1GateCircuit ((g . (Sn + 1)),h,and2a)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2a))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2a))
1GateCircuit (h,(f . (Sn + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*h,(f . (Sn + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*h,(f . (Sn + 1))*>,and2)
1GateCircuit (<*h,(f . (Sn + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*h,(f . (Sn + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*h,(f . (Sn + 1))*>,and2)
((1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),and2c)) +* (1GateCircuit ((g . (Sn + 1)),h,and2a))) +* (1GateCircuit (h,(f . (Sn + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2a))) +* (1GateCircStr (<*h,(f . (Sn + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2a))) +* (1GateCircStr (<*h,(f . (Sn + 1))*>,and2))
1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),h*>,and2a],[<*h,(f . (Sn + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),h*>,and2a],[<*h,(f . (Sn + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),h*>,and2a],[<*h,(f . (Sn + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),h*>,and2a],[<*h,(f . (Sn + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),h*>,and2a],[<*h,(f . (Sn + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),h*>,and2a],[<*h,(f . (Sn + 1))*>,and2]*>,or3)
(GFA1CarryICirc ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),h*>,and2a],[<*h,(f . (Sn + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA1CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),h*>,and2a],[<*h,(f . (Sn + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA1CarryIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2c],[<*(g . (Sn + 1)),h*>,and2a],[<*h,(f . (Sn + 1))*>,and2]*>,or3))
(GFA1AdderCirc ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (GFA1CarryCirc ((f . (Sn + 1)),(g . (Sn + 1)),h)) is strict non-empty finitely-generated V95((GFA1AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),h))) gate`2=den Boolean MSAlgebra over (GFA1AdderStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (GFA1CarryStr ((f . (Sn + 1)),(g . (Sn + 1)),h))
the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE))) is Relation-like the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) -defined Function-like V14( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)))) set
the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) is non empty set
K106( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE)))) is set
h is Element of K106( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE))))
Following (h,1) is Element of K106( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE))))
Following h is Element of K106( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE))))
Following (h,H4( 0 )) is Element of K106( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE))))
h is Relation-like NAT -defined Function-like V14( NAT ) set
o0 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
o0 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (o0 + 1) is non pair set
g . (o0 + 1) is non pair set
h . o0 is set
f1 is set
BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),f1,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (o0 + 1)),(g . (o0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c] is non empty pair set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],f1*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],f1*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),f1) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (o0 + 1)),f1*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (o0 + 1)),f1*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),f1*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f1,(f . (o0 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f1,(f . (o0 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),f1*>,and2a))) +* (1GateCircStr (<*f1,(f . (o0 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c] is non empty pair set
[<*(g . (o0 + 1)),f1*>,and2a] is non empty pair set
[<*f1,(f . (o0 + 1))*>,and2] is non empty pair set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),f1*>,and2a],[<*f1,(f . (o0 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),f1*>,and2a],[<*f1,(f . (o0 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),f1*>,and2a],[<*f1,(f . (o0 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitGFA1Circ ((f . (o0 + 1)),(g . (o0 + 1)),f1) is strict non-empty finitely-generated V95( BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),f1)) gate`2=den Boolean MSAlgebra over BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),f1)
GFA1AdderCirc ((f . (o0 + 1)),(g . (o0 + 1)),f1) is strict non-empty finitely-generated V95( GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) gate`2=den Boolean MSAlgebra over GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)
2GatesCircuit ((f . (o0 + 1)),(g . (o0 + 1)),f1,xor2c) is strict non-empty finitely-generated V95( 2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),f1,xor2c)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),f1,xor2c)
1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)
1GateCircuit (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)
1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],f1,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],f1*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],f1*>,xor2c)
1GateCircuit (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],f1*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],f1*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],f1*>,xor2c)
(1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),xor2c)) +* (1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],f1,xor2c)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],f1*>,xor2c))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,xor2c],f1*>,xor2c))
GFA1CarryCirc ((f . (o0 + 1)),(g . (o0 + 1)),f1) is strict non-empty finitely-generated V95( GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) gate`2=den Boolean MSAlgebra over GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)
GFA1CarryICirc ((f . (o0 + 1)),(g . (o0 + 1)),f1) is strict non-empty finitely-generated V95( GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) gate`2=den Boolean MSAlgebra over GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)
1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)
1GateCircuit (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)
1GateCircuit ((g . (o0 + 1)),f1,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (o0 + 1)),f1*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (o0 + 1)),f1*>,and2a)
1GateCircuit (<*(g . (o0 + 1)),f1*>,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (o0 + 1)),f1*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (o0 + 1)),f1*>,and2a)
(1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2c)) +* (1GateCircuit ((g . (o0 + 1)),f1,and2a)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),f1*>,and2a))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),f1*>,and2a))
1GateCircuit (f1,(f . (o0 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*f1,(f . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f1,(f . (o0 + 1))*>,and2)
1GateCircuit (<*f1,(f . (o0 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*f1,(f . (o0 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f1,(f . (o0 + 1))*>,and2)
((1GateCircuit ((f . (o0 + 1)),(g . (o0 + 1)),and2c)) +* (1GateCircuit ((g . (o0 + 1)),f1,and2a))) +* (1GateCircuit (f1,(f . (o0 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),f1*>,and2a))) +* (1GateCircStr (<*f1,(f . (o0 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (o0 + 1)),f1*>,and2a))) +* (1GateCircStr (<*f1,(f . (o0 + 1))*>,and2))
1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),f1*>,and2a],[<*f1,(f . (o0 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),f1*>,and2a],[<*f1,(f . (o0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),f1*>,and2a],[<*f1,(f . (o0 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),f1*>,and2a],[<*f1,(f . (o0 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),f1*>,and2a],[<*f1,(f . (o0 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),f1*>,and2a],[<*f1,(f . (o0 + 1))*>,and2]*>,or3)
(GFA1CarryICirc ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (1GateCircuit ([<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),f1*>,and2a],[<*f1,(f . (o0 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),f1*>,and2a],[<*f1,(f . (o0 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA1CarryIStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2c],[<*(g . (o0 + 1)),f1*>,and2a],[<*f1,(f . (o0 + 1))*>,and2]*>,or3))
(GFA1AdderCirc ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (GFA1CarryCirc ((f . (o0 + 1)),(g . (o0 + 1)),f1)) is strict non-empty finitely-generated V95((GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),f1))) gate`2=den Boolean MSAlgebra over (GFA1AdderStr ((f . (o0 + 1)),(g . (o0 + 1)),f1)) +* (GFA1CarryStr ((f . (o0 + 1)),(g . (o0 + 1)),f1))
g1 is non-empty finitely-generated V95(H1(f1,o0)) MSAlgebra over H1(f1,o0)
the Sorts of g1 is Relation-like the carrier of H1(f1,o0) -defined Function-like V14( the carrier of H1(f1,o0)) set
the carrier of H1(f1,o0) is non empty set
K106( the Sorts of g1) is set
(o0,f,g) is non empty pair Element of InnerVertices (o0,f,g)
(o0,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (o0,f,g) is non empty set
InnerVertices (o0,f,g) is non empty Element of K27( the carrier of (o0,f,g))
K27( the carrier of (o0,f,g)) is set
h1 is Element of K106( the Sorts of g1)
Following (h1,(N . 1)) is Element of K106( the Sorts of g1)
the Sorts of g1 is Relation-like the carrier of (BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),f1)) -defined Function-like V14( the carrier of (BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),f1))) set
the carrier of (BitGFA1Str ((f . (o0 + 1)),(g . (o0 + 1)),f1)) is non empty set
K106( the Sorts of g1) is set
(0,f,g) is non empty pair Element of InnerVertices (0,f,g)
(0,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (0,f,g) is non empty set
InnerVertices (0,f,g) is non empty Element of K27( the carrier of (0,f,g))
K27( the carrier of (0,f,g)) is set
f1 is Relation-like NAT -defined Function-like V14( NAT ) set
f1 . n is set
g1 is Relation-like NAT -defined Function-like V14( NAT ) set
g1 . n is set
f1 . 0 is set
g1 . 0 is set
h1 is Relation-like NAT -defined Function-like V14( NAT ) set
h1 . 0 is set
f1 is set
h1 . f1 is set
f2 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
(f2,f,g) is non empty pair Element of InnerVertices (f2,f,g)
(f2,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (f2,f,g) is non empty set
InnerVertices (f2,f,g) is non empty Element of K27( the carrier of (f2,f,g))
K27( the carrier of (f2,f,g)) is set
h . f1 is set
h . 0 is set
f1 . H4(2) is set
g1 . H4(2) is set
f2 is non empty V56() ManySortedSign
f1 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f1 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (f1 + 1) is non pair set
g . (f1 + 1) is non pair set
f0 is set
BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),f0,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f1 + 1)),(g . (f1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c] is non empty pair set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],f0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],f0*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],f0*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (f1 + 1)),f0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (f1 + 1)),f0*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f1 + 1)),f0*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f0,(f . (f1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f0,(f . (f1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f1 + 1)),f0*>,and2a))) +* (1GateCircStr (<*f0,(f . (f1 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c] is non empty pair set
[<*(g . (f1 + 1)),f0*>,and2a] is non empty pair set
[<*f0,(f . (f1 + 1))*>,and2] is non empty pair set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f0*>,and2a],[<*f0,(f . (f1 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f0*>,and2a],[<*f0,(f . (f1 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f0*>,and2a],[<*f0,(f . (f1 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f1 . f1 is set
f3 is non-empty MSAlgebra over f2
g1 . f1 is set
h . f1 is set
n is non-empty MSAlgebra over BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),f0)
BitGFA1Circ ((f . (f1 + 1)),(g . (f1 + 1)),f0) is strict non-empty finitely-generated V95( BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),f0)) gate`2=den Boolean MSAlgebra over BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),f0)
GFA1AdderCirc ((f . (f1 + 1)),(g . (f1 + 1)),f0) is strict non-empty finitely-generated V95( GFA1AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) gate`2=den Boolean MSAlgebra over GFA1AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)
2GatesCircuit ((f . (f1 + 1)),(g . (f1 + 1)),f0,xor2c) is strict non-empty finitely-generated V95( 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),f0,xor2c)) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),f0,xor2c)
1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c)
1GateCircuit (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c)
1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],f0,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],f0*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],f0*>,xor2c)
1GateCircuit (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],f0*>,xor2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],f0*>,xor2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],f0*>,xor2c)
(1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),xor2c)) +* (1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],f0,xor2c)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],f0*>,xor2c))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],f0*>,xor2c))
GFA1CarryCirc ((f . (f1 + 1)),(g . (f1 + 1)),f0) is strict non-empty finitely-generated V95( GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) gate`2=den Boolean MSAlgebra over GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)
GFA1CarryICirc ((f . (f1 + 1)),(g . (f1 + 1)),f0) is strict non-empty finitely-generated V95( GFA1CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) gate`2=den Boolean MSAlgebra over GFA1CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)
1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)
1GateCircuit (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c) is strict non-empty finitely-generated V95( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)
1GateCircuit ((g . (f1 + 1)),f0,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (f1 + 1)),f0*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (f1 + 1)),f0*>,and2a)
1GateCircuit (<*(g . (f1 + 1)),f0*>,and2a) is strict non-empty finitely-generated V95( 1GateCircStr (<*(g . (f1 + 1)),f0*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (f1 + 1)),f0*>,and2a)
(1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2c)) +* (1GateCircuit ((g . (f1 + 1)),f0,and2a)) is strict non-empty finitely-generated V95((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f1 + 1)),f0*>,and2a))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f1 + 1)),f0*>,and2a))
1GateCircuit (f0,(f . (f1 + 1)),and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*f0,(f . (f1 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f0,(f . (f1 + 1))*>,and2)
1GateCircuit (<*f0,(f . (f1 + 1))*>,and2) is strict non-empty finitely-generated V95( 1GateCircStr (<*f0,(f . (f1 + 1))*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f0,(f . (f1 + 1))*>,and2)
((1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2c)) +* (1GateCircuit ((g . (f1 + 1)),f0,and2a))) +* (1GateCircuit (f0,(f . (f1 + 1)),and2)) is strict non-empty finitely-generated V95(((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f1 + 1)),f0*>,and2a))) +* (1GateCircStr (<*f0,(f . (f1 + 1))*>,and2))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f1 + 1)),f0*>,and2a))) +* (1GateCircStr (<*f0,(f . (f1 + 1))*>,and2))
1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f0*>,and2a],[<*f0,(f . (f1 + 1))*>,and2],or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f0*>,and2a],[<*f0,(f . (f1 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f0*>,and2a],[<*f0,(f . (f1 + 1))*>,and2]*>,or3)
1GateCircuit (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f0*>,and2a],[<*f0,(f . (f1 + 1))*>,and2]*>,or3) is strict non-empty finitely-generated V95( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f0*>,and2a],[<*f0,(f . (f1 + 1))*>,and2]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f0*>,and2a],[<*f0,(f . (f1 + 1))*>,and2]*>,or3)
(GFA1CarryICirc ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f0*>,and2a],[<*f0,(f . (f1 + 1))*>,and2],or3)) is strict non-empty finitely-generated V95((GFA1CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f0*>,and2a],[<*f0,(f . (f1 + 1))*>,and2]*>,or3))) gate`2=den Boolean MSAlgebra over (GFA1CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f0*>,and2a],[<*f0,(f . (f1 + 1))*>,and2]*>,or3))
(GFA1AdderCirc ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (GFA1CarryCirc ((f . (f1 + 1)),(g . (f1 + 1)),f0)) is strict non-empty finitely-generated V95((GFA1AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0))) gate`2=den Boolean MSAlgebra over (GFA1AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) +* (GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0))
f1 . (f1 + 1) is set
f2 +* (BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),f0)) is non empty non void V56() strict ManySortedSign
g1 . (f1 + 1) is set
f3 +* n is strict non-empty MSAlgebra over f2 +* (BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),f0))
h . (f1 + 1) is set
GFA1CarryOutput ((f . (f1 + 1)),(g . (f1 + 1)),f0) is Element of InnerVertices (GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0))
the carrier of (GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) is non empty set
InnerVertices (GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)) is non empty Element of K27( the carrier of (GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0)))
K27( the carrier of (GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f0))) is set
[<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f0*>,and2a],[<*f0,(f . (f1 + 1))*>,and2]*>,or3] is non empty pair set
InnerVertices (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) is non empty Element of K27( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))))
K27( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)))) is set
InputVertices (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) is Element of K27( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))))
{[{},((0 -tuples_on BOOLEAN) --> TRUE)]} is Relation-like Function-like constant non empty V12() V28() 1 -element set
f1 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
f1 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (f1 + 1) is non pair set
g . (f1 + 1) is non pair set
f2 is set
BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),f2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),f2,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f1 + 1)),(g . (f1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c] is non empty pair set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],f2*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],f2*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,xor2c],f2*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (f1 + 1)),f2*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (f1 + 1)),f2*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f1 + 1)),f2*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f2,(f . (f1 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f2,(f . (f1 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f1 + 1)),f2*>,and2a))) +* (1GateCircStr (<*f2,(f . (f1 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c] is non empty pair set
[<*(g . (f1 + 1)),f2*>,and2a] is non empty pair set
[<*f2,(f . (f1 + 1))*>,and2] is non empty pair set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f2*>,and2a],[<*f2,(f . (f1 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f2*>,and2a],[<*f2,(f . (f1 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (f1 + 1)),(g . (f1 + 1)),f2)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2c],[<*(g . (f1 + 1)),f2*>,and2a],[<*f2,(f . (f1 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (f1 + 1)),(g . (f1 + 1)),f2)) +* (GFA1CarryStr ((f . (f1 + 1)),(g . (f1 + 1)),f2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),f2)) is non empty Element of K27( the carrier of (BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),f2)))
the carrier of (BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),f2)) is non empty set
K27( the carrier of (BitGFA1Str ((f . (f1 + 1)),(g . (f1 + 1)),f2))) is set
f3 is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
h . f3 is set
f3 + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
f . (f3 + 1) is non pair set
g . (f3 + 1) is non pair set
f0 is set
BitGFA1Str ((f . (f3 + 1)),(g . (f3 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (f3 + 1)),(g . (f3 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (f3 + 1)),(g . (f3 + 1)),f0,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f3 + 1)),(g . (f3 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(f . (f3 + 1)),(g . (f3 + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f3 + 1)),(g . (f3 + 1))*>,xor2c] is non empty pair set
<*[<*(f . (f3 + 1)),(g . (f3 + 1))*>,xor2c],f0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f3 + 1)),(g . (f3 + 1))*>,xor2c],f0*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f3 + 1)),(g . (f3 + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (f3 + 1)),(g . (f3 + 1))*>,xor2c],f0*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryStr ((f . (f3 + 1)),(g . (f3 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (f3 + 1)),(g . (f3 + 1)),f0) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (f3 + 1)),(g . (f3 + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (f3 + 1)),f0*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (f3 + 1)),f0*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f3 + 1)),(g . (f3 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f3 + 1)),f0*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f0,(f . (f3 + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*f0,(f . (f3 + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (f3 + 1)),(g . (f3 + 1))*>,and2c)) +* (1GateCircStr (<*(g . (f3 + 1)),f0*>,and2a))) +* (1GateCircStr (<*f0,(f . (f3 + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f3 + 1)),(g . (f3 + 1))*>,and2c] is non empty pair set
[<*(g . (f3 + 1)),f0*>,and2a] is non empty pair set
[<*f0,(f . (f3 + 1))*>,and2] is non empty pair set
<*[<*(f . (f3 + 1)),(g . (f3 + 1))*>,and2c],[<*(g . (f3 + 1)),f0*>,and2a],[<*f0,(f . (f3 + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (f3 + 1)),(g . (f3 + 1))*>,and2c],[<*(g . (f3 + 1)),f0*>,and2a],[<*f0,(f . (f3 + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (f3 + 1)),(g . (f3 + 1)),f0)) +* (1GateCircStr (<*[<*(f . (f3 + 1)),(g . (f3 + 1))*>,and2c],[<*(g . (f3 + 1)),f0*>,and2a],[<*f0,(f . (f3 + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (f3 + 1)),(g . (f3 + 1)),f0)) +* (GFA1CarryStr ((f . (f3 + 1)),(g . (f3 + 1)),f0)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of H1(f0,f3) is non empty set
InputVertices H1(f0,f3) is Element of K27( the carrier of H1(f0,f3))
K27( the carrier of H1(f0,f3)) is set
{f0} is non empty V12() V28() 1 -element set
(InputVertices H1(f0,f3)) \ {f0} is Element of K27( the carrier of H1(f0,f3))
(f3,f,g) is non empty pair Element of InnerVertices (f3,f,g)
(f3,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (f3,f,g) is non empty set
InnerVertices (f3,f,g) is non empty Element of K27( the carrier of (f3,f,g))
K27( the carrier of (f3,f,g)) is set
{(f . (f3 + 1)),(g . (f3 + 1)),f0} is V28() set
n is non empty pair set
n is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() set
h . n is set
n + 1 is non empty non pair V21() V22() V23() V27() V28() cardinal ext-real positive non negative V115() V126() Element of NAT
h . (n + 1) is set
f . (n + 1) is non pair set
g . (n + 1) is non pair set
x is set
GFA1CarryOutput ((f . (n + 1)),(g . (n + 1)),x) is Element of InnerVertices (GFA1CarryStr ((f . (n + 1)),(g . (n + 1)),x))
GFA1CarryStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1CarryIStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),(g . (n + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like nonpair-yielding set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (n + 1)),x*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*(g . (n + 1)),x*>,and2a) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2c)) +* (1GateCircStr (<*(g . (n + 1)),x*>,and2a)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*x,(f . (n + 1))*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*x,(f . (n + 1))*>,and2) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2c)) +* (1GateCircStr (<*(g . (n + 1)),x*>,and2a))) +* (1GateCircStr (<*x,(f . (n + 1))*>,and2)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,and2c] is non empty pair set
[<*(g . (n + 1)),x*>,and2a] is non empty pair set
[<*x,(f . (n + 1))*>,and2] is non empty pair set
<*[<*(f . (n + 1)),(g . (n + 1))*>,and2c],[<*(g . (n + 1)),x*>,and2a],[<*x,(f . (n + 1))*>,and2]*> is Relation-like NAT -defined Function-like non empty V28() 3 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2c],[<*(g . (n + 1)),x*>,and2a],[<*x,(f . (n + 1))*>,and2]*>,or3) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1CarryIStr ((f . (n + 1)),(g . (n + 1)),x)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2c],[<*(g . (n + 1)),x*>,and2a],[<*x,(f . (n + 1))*>,and2]*>,or3)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (GFA1CarryStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
InnerVertices (GFA1CarryStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty Element of K27( the carrier of (GFA1CarryStr ((f . (n + 1)),(g . (n + 1)),x)))
K27( the carrier of (GFA1CarryStr ((f . (n + 1)),(g . (n + 1)),x))) is set
[<*[<*(f . (n + 1)),(g . (n + 1))*>,and2c],[<*(g . (n + 1)),x*>,and2a],[<*x,(f . (n + 1))*>,and2]*>,or3] is non empty pair set
BitGFA1Str ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
GFA1AdderStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,xor2c] is non empty pair set
<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2c],x*> is Relation-like NAT -defined Function-like non empty V28() 2 -element FinSequence-like FinSubsequence-like set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2c],x*>,xor2c) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,xor2c)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2c],x*>,xor2c)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(GFA1AdderStr ((f . (n + 1)),(g . (n + 1)),x)) +* (GFA1CarryStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices H1(x,n) is Element of K27( the carrier of H1(x,n))
the carrier of H1(x,n) is non empty set
K27( the carrier of H1(x,n)) is set
InnerVertices H1(x,n) is non empty Element of K27( the carrier of H1(x,n))
(n,f,g) is non empty pair Element of InnerVertices (n,f,g)
(n,f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (n,f,g) is non empty set
InnerVertices (n,f,g) is non empty Element of K27( the carrier of (n,f,g))
K27( the carrier of (n,f,g)) is set
((n + 1),f,g) is non empty pair Element of InnerVertices ((n + 1),f,g)
((n + 1),f,g) is non empty non void V56() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of ((n + 1),f,g) is non empty set
InnerVertices ((n + 1),f,g) is non empty Element of K27( the carrier of ((n + 1),f,g))
K27( the carrier of ((n + 1),f,g)) is set
{(f . (n + 1)),(g . (n + 1)),x} is V28() set
{[<*(f . (n + 1)),(g . (n + 1))*>,xor2c]} is Relation-like Function-like constant non empty V12() V28() 1 -element set
GFA1AdderOutput ((f . (n + 1)),(g . (n + 1)),x) is Element of InnerVertices (GFA1AdderStr ((f . (n + 1)),(g . (n + 1)),x))
the carrier of (GFA1AdderStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
InnerVertices (GFA1AdderStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty Element of K27( the carrier of (GFA1AdderStr ((f . (n + 1)),(g . (n + 1)),x)))
K27( the carrier of (GFA1AdderStr ((f . (n + 1)),(g . (n + 1)),x))) is set
2GatesCircOutput ((f . (n + 1)),(g . (n + 1)),x,xor2c) is non empty pair Element of InnerVertices (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,xor2c))
the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,xor2c)) is non empty set
InnerVertices (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,xor2c)) is non empty Element of K27( the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,xor2c)))
K27( the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,xor2c))) is set
[<*[<*(f . (n + 1)),(g . (n + 1))*>,xor2c],x*>,xor2c] is non empty pair set
{(GFA1AdderOutput ((f . (n + 1)),(g . (n + 1)),x))} is non empty V12() V28() 1 -element set
{[<*(f . (n + 1)),(g . (n + 1))*>,xor2c]} \/ {(GFA1AdderOutput ((f . (n + 1)),(g . (n + 1)),x))} is non empty V28() set
{[<*(f . (n + 1)),(g . (n + 1))*>,and2c],[<*(g . (n + 1)),x*>,and2a],[<*x,(f . (n + 1))*>,and2]} is Relation-like V28() set
({[<*(f . (n + 1)),(g . (n + 1))*>,xor2c]} \/ {(GFA1AdderOutput ((f . (n + 1)),(g . (n + 1)),x))}) \/ {[<*(f . (n + 1)),(g . (n + 1))*>,and2c],[<*(g . (n + 1)),x*>,and2a],[<*x,(f . (n + 1))*>,and2]} is non empty V28() set
{(GFA1CarryOutput ((f . (n + 1)),(g . (n + 1)),x))} is non empty V12() V28() 1 -element set
(({[<*(f . (n + 1)),(g . (n + 1))*>,xor2c]} \/ {(GFA1AdderOutput ((f . (n + 1)),(g . (n + 1)),x))}) \/ {[<*(f . (n + 1)),(g . (n + 1))*>,and2c],[<*(g . (n + 1)),x*>,and2a],[<*x,(f . (n + 1))*>,and2]}) \/ {(GFA1CarryOutput ((f . (n + 1)),(g . (n + 1)),x))} is non empty V28() set
{H3(x,n)} is non empty V12() V28() 1 -element set
H4(2) * H4(1) is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
H4( 0 ) + (H4(2) * H4(1)) is non pair V21() V22() V23() V27() V28() cardinal ext-real non negative V115() V126() Element of NAT
f1 is Element of K106( the Sorts of (n,f,g))
Following (f1,(1 + (2 * n))) is Element of K106( the Sorts of (n,f,g))