:: FSCIRC_2 semantic presentation

REAL is set
NAT is non empty V2() V9() V10() V11() V36() cardinal limit_cardinal V51() V52() Element of K18(REAL)
K18(REAL) is set
COMPLEX is set
RAT is set
INT is set
K19(COMPLEX,COMPLEX) is Relation-like set
K18(K19(COMPLEX,COMPLEX)) is set
K19(K19(COMPLEX,COMPLEX),COMPLEX) is Relation-like set
K18(K19(K19(COMPLEX,COMPLEX),COMPLEX)) is set
K19(REAL,REAL) is Relation-like set
K18(K19(REAL,REAL)) is set
K19(K19(REAL,REAL),REAL) is Relation-like set
K18(K19(K19(REAL,REAL),REAL)) is set
K19(RAT,RAT) is Relation-like set
K18(K19(RAT,RAT)) is set
K19(K19(RAT,RAT),RAT) is Relation-like set
K18(K19(K19(RAT,RAT),RAT)) is set
K19(INT,INT) is Relation-like set
K18(K19(INT,INT)) is set
K19(K19(INT,INT),INT) is Relation-like set
K18(K19(K19(INT,INT),INT)) is set
K19(NAT,NAT) is V2() Relation-like V36() set
K19(K19(NAT,NAT),NAT) is V2() Relation-like V36() set
K18(K19(K19(NAT,NAT),NAT)) is V2() V36() set
NAT is non empty V2() V9() V10() V11() V36() cardinal limit_cardinal V51() V52() set
K18(NAT) is V2() V36() set
K18(NAT) is V2() V36() set
BOOLEAN is non empty set
0 is empty Relation-like non-empty empty-yielding NAT -defined V9() V10() V11() V13() V14() V15() Function-like one-to-one constant functional non pair V30() V31() V36() V37() V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V48() V49() V51() non with_pair nonpair-yielding ext-real non positive non negative Element of NAT
{} is empty Relation-like non-empty empty-yielding NAT -defined V9() V10() V11() V13() V14() V15() Function-like one-to-one constant functional non pair V30() V31() V36() V37() V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V48() V49() V51() non with_pair nonpair-yielding ext-real non positive non negative set
the empty Relation-like non-empty empty-yielding NAT -defined V9() V10() V11() V13() V14() V15() Function-like one-to-one constant functional non pair V30() V31() V36() V37() V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V48() V49() V51() non with_pair nonpair-yielding ext-real non positive non negative set is empty Relation-like non-empty empty-yielding NAT -defined V9() V10() V11() V13() V14() V15() Function-like one-to-one constant functional non pair V30() V31() V36() V37() V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V48() V49() V51() non with_pair nonpair-yielding ext-real non positive non negative set
1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
{0,1} is non empty V36() V40() V51() non with_pair set
{{},1} is non empty V36() V40() V51() non with_pair set
K348() is set
K18(K348()) is set
K349() is Element of K18(K348())
K389() is non empty V95() L10()
the carrier of K389() is non empty set
K352( the carrier of K389()) is non empty M24( the carrier of K389())
K388(K389()) is Element of K18(K352( the carrier of K389()))
K18(K352( the carrier of K389())) is set
K19(K388(K389()),NAT) is Relation-like set
K18(K19(K388(K389()),NAT)) is set
K19(NAT,K388(K389())) is Relation-like set
K18(K19(NAT,K388(K389()))) is set
2 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
2 -tuples_on BOOLEAN is non empty functional FinSequence-membered FinSequenceSet of BOOLEAN
K19((2 -tuples_on BOOLEAN),BOOLEAN) is Relation-like set
K18(K19((2 -tuples_on BOOLEAN),BOOLEAN)) is set
3 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
3 -tuples_on BOOLEAN is non empty functional FinSequence-membered FinSequenceSet of BOOLEAN
K19((3 -tuples_on BOOLEAN),BOOLEAN) is Relation-like set
K18(K19((3 -tuples_on BOOLEAN),BOOLEAN)) is set
'xor' is Relation-like Function-like V27(2 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K18(K19((2 -tuples_on BOOLEAN),BOOLEAN))
Seg 1 is non empty V2() V36() 1 -element V51() Element of K18(NAT)
or3 is Relation-like Function-like V27(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K18(K19((3 -tuples_on BOOLEAN),BOOLEAN))
and2 is Relation-like Function-like V27(2 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K18(K19((2 -tuples_on BOOLEAN),BOOLEAN))
and2a is Relation-like Function-like V27(2 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K18(K19((2 -tuples_on BOOLEAN),BOOLEAN))
K18(K19(NAT,NAT)) is V2() V36() set
f is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
g is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
0 -tuples_on BOOLEAN is non empty functional FinSequence-membered FinSequenceSet of BOOLEAN
TRUE is boolean Element of BOOLEAN
(0 -tuples_on BOOLEAN) --> TRUE is Relation-like Function-like V27(0 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K18(K19((0 -tuples_on BOOLEAN),BOOLEAN))
K19((0 -tuples_on BOOLEAN),BOOLEAN) is Relation-like set
K18(K19((0 -tuples_on BOOLEAN),BOOLEAN)) is set
1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
[{},((0 -tuples_on BOOLEAN) --> TRUE)] is non empty pair set
{{},((0 -tuples_on BOOLEAN) --> TRUE)} is non empty functional V36() V51() set
{{}} is non empty V2() functional V36() V40() 1 -element V49() V51() non with_pair set
{{{},((0 -tuples_on BOOLEAN) --> TRUE)},{{}}} is non empty V36() V40() V51() set
S0 is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
N is Relation-like NAT -defined Function-like V23( NAT ) set
N . n is set
N . 0 is set
h is Relation-like NAT -defined Function-like V23( NAT ) set
h . 0 is set
A0 is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
Sn is Relation-like NAT -defined Function-like V23( NAT ) set
Sn . n is set
Sn . 0 is set
An is Relation-like NAT -defined Function-like V23( NAT ) set
An . 0 is set
S0 is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
A0 is Relation-like NAT -defined Function-like V23( NAT ) set
A0 . n is set
A0 . 0 is set
N is Relation-like NAT -defined Function-like V23( NAT ) set
N . 0 is set
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
f is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
g is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
(n,f,g) is non empty non void V71() 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 V107( 1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) gate`2=den Boolean MSAlgebra over 1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))
Sn is non empty V71() ManySortedSign
f1 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
f1 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f . (f1 + 1) is set
g . (f1 + 1) is set
o0 is set
BitSubtracterWithBorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f1 + 1)),(g . (f1 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'] is non empty pair set
{<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (f1 + 1)),(g . (f1 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'},{<*(f . (f1 + 1)),(g . (f1 + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (f1 + 1)),o0*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (f1 + 1)),o0*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f1 + 1)),o0*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2))) +* (1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a] is non empty pair set
{<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a},{<*(f . (f1 + 1)),(g . (f1 + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (f1 + 1)),o0*>,and2] is non empty pair set
{<*(g . (f1 + 1)),o0*>,and2} is non empty functional V36() V51() set
{<*(g . (f1 + 1)),o0*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (f1 + 1)),o0*>,and2},{<*(g . (f1 + 1)),o0*>}} is non empty V36() V40() V51() set
[<*(f . (f1 + 1)),o0*>,and2a] is non empty pair set
{<*(f . (f1 + 1)),o0*>,and2a} is non empty functional V36() V51() set
{<*(f . (f1 + 1)),o0*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (f1 + 1)),o0*>,and2a},{<*(f . (f1 + 1)),o0*>}} is non empty V36() V40() V51() set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) +* (BorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
An is non-empty MSAlgebra over Sn
BitSubtracterWithBorrowCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V107( BitSubtracterWithBorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over BitSubtracterWithBorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
BitSubtracterCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V107( 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')
2GatesCircuit ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor') is strict non-empty finitely-generated V107( 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')
1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor')
1GateCircuit (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor')
1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor')
1GateCircuit (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor')
(1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),'xor')) +* (1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0,'xor')) is strict non-empty finitely-generated V107((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor'))
BorrowCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V107( BorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over BorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
BorrowICirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V107( BorrowIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over BorrowIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)
1GateCircuit (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)
1GateCircuit ((g . (f1 + 1)),o0,and2) is strict non-empty finitely-generated V107( 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 V107( 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)),and2a)) +* (1GateCircuit ((g . (f1 + 1)),o0,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2))
1GateCircuit ((f . (f1 + 1)),o0,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a)
1GateCircuit (<*(f . (f1 + 1)),o0*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a)
((1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2a)) +* (1GateCircuit ((g . (f1 + 1)),o0,and2))) +* (1GateCircuit ((f . (f1 + 1)),o0,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2))) +* (1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2))) +* (1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a))
1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3)
1GateCircuit (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3)
(BorrowICirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3))
(BitSubtracterCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (BorrowCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is strict non-empty finitely-generated V107((2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) +* (BorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) +* (BorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))
An +* (BitSubtracterWithBorrowCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is strict non-empty MSAlgebra over Sn +* (BitSubtracterWithBorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))
Sn +* (BitSubtracterWithBorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is non empty non void V71() strict ManySortedSign
Sn is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
o0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
o0 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f . (o0 + 1) is set
g . (o0 + 1) is set
An is set
BitSubtracterWithBorrowStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),An,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (o0 + 1)),(g . (o0 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (o0 + 1)),(g . (o0 + 1))*>,'xor'] is non empty pair set
{<*(f . (o0 + 1)),(g . (o0 + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (o0 + 1)),(g . (o0 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (o0 + 1)),(g . (o0 + 1))*>,'xor'},{<*(f . (o0 + 1)),(g . (o0 + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,'xor'],An*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,'xor'],An*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,'xor'],An*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (o0 + 1)),An*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (o0 + 1)),An*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (o0 + 1)),An*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (o0 + 1)),An*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,and2))) +* (1GateCircStr (<*(f . (o0 + 1)),An*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2a] is non empty pair set
{<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2a},{<*(f . (o0 + 1)),(g . (o0 + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (o0 + 1)),An*>,and2] is non empty pair set
{<*(g . (o0 + 1)),An*>,and2} is non empty functional V36() V51() set
{<*(g . (o0 + 1)),An*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (o0 + 1)),An*>,and2},{<*(g . (o0 + 1)),An*>}} is non empty V36() V40() V51() set
[<*(f . (o0 + 1)),An*>,and2a] is non empty pair set
{<*(f . (o0 + 1)),An*>,and2a} is non empty functional V36() V51() set
{<*(f . (o0 + 1)),An*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (o0 + 1)),An*>,and2a},{<*(f . (o0 + 1)),An*>}} is non empty V36() V40() V51() set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2a],[<*(g . (o0 + 1)),An*>,and2],[<*(f . (o0 + 1)),An*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2a],[<*(g . (o0 + 1)),An*>,and2],[<*(f . (o0 + 1)),An*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,and2a],[<*(g . (o0 + 1)),An*>,and2],[<*(f . (o0 + 1)),An*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),An,'xor')) +* (BorrowStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
Sn +* (BitSubtracterWithBorrowStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f1 is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h1 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
h1 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f . (h1 + 1) is set
g . (h1 + 1) is set
g1 is set
BitSubtracterWithBorrowStr ((f . (h1 + 1)),(g . (h1 + 1)),g1) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (h1 + 1)),(g . (h1 + 1)),g1,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (h1 + 1)),(g . (h1 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (h1 + 1)),(g . (h1 + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (h1 + 1)),(g . (h1 + 1))*>,'xor'] is non empty pair set
{<*(f . (h1 + 1)),(g . (h1 + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (h1 + 1)),(g . (h1 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (h1 + 1)),(g . (h1 + 1))*>,'xor'},{<*(f . (h1 + 1)),(g . (h1 + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (h1 + 1)),(g . (h1 + 1))*>,'xor'],g1*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (h1 + 1)),(g . (h1 + 1))*>,'xor'],g1*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (h1 + 1)),(g . (h1 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (h1 + 1)),(g . (h1 + 1))*>,'xor'],g1*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (h1 + 1)),(g . (h1 + 1)),g1) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (h1 + 1)),(g . (h1 + 1)),g1) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (h1 + 1)),(g . (h1 + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (h1 + 1)),g1*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (h1 + 1)),g1*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (h1 + 1)),(g . (h1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (h1 + 1)),g1*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (h1 + 1)),g1*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (h1 + 1)),g1*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (h1 + 1)),(g . (h1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (h1 + 1)),g1*>,and2))) +* (1GateCircStr (<*(f . (h1 + 1)),g1*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (h1 + 1)),(g . (h1 + 1))*>,and2a] is non empty pair set
{<*(f . (h1 + 1)),(g . (h1 + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (h1 + 1)),(g . (h1 + 1))*>,and2a},{<*(f . (h1 + 1)),(g . (h1 + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (h1 + 1)),g1*>,and2] is non empty pair set
{<*(g . (h1 + 1)),g1*>,and2} is non empty functional V36() V51() set
{<*(g . (h1 + 1)),g1*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (h1 + 1)),g1*>,and2},{<*(g . (h1 + 1)),g1*>}} is non empty V36() V40() V51() set
[<*(f . (h1 + 1)),g1*>,and2a] is non empty pair set
{<*(f . (h1 + 1)),g1*>,and2a} is non empty functional V36() V51() set
{<*(f . (h1 + 1)),g1*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (h1 + 1)),g1*>,and2a},{<*(f . (h1 + 1)),g1*>}} is non empty V36() V40() V51() set
<*[<*(f . (h1 + 1)),(g . (h1 + 1))*>,and2a],[<*(g . (h1 + 1)),g1*>,and2],[<*(f . (h1 + 1)),g1*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (h1 + 1)),(g . (h1 + 1))*>,and2a],[<*(g . (h1 + 1)),g1*>,and2],[<*(f . (h1 + 1)),g1*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (h1 + 1)),(g . (h1 + 1)),g1)) +* (1GateCircStr (<*[<*(f . (h1 + 1)),(g . (h1 + 1))*>,and2a],[<*(g . (h1 + 1)),g1*>,and2],[<*(f . (h1 + 1)),g1*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (h1 + 1)),(g . (h1 + 1)),g1,'xor')) +* (BorrowStr ((f . (h1 + 1)),(g . (h1 + 1)),g1)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f1 +* (BitSubtracterWithBorrowStr ((f . (h1 + 1)),(g . (h1 + 1)),g1)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
n is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
xx is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
xx + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f . (xx + 1) is set
g . (xx + 1) is set
x is set
BitSubtracterWithBorrowStr ((f . (xx + 1)),(g . (xx + 1)),x) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (xx + 1)),(g . (xx + 1)),x,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (xx + 1)),(g . (xx + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (xx + 1)),(g . (xx + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (xx + 1)),(g . (xx + 1))*>,'xor'] is non empty pair set
{<*(f . (xx + 1)),(g . (xx + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (xx + 1)),(g . (xx + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (xx + 1)),(g . (xx + 1))*>,'xor'},{<*(f . (xx + 1)),(g . (xx + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (xx + 1)),(g . (xx + 1))*>,'xor'],x*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (xx + 1)),(g . (xx + 1))*>,'xor'],x*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (xx + 1)),(g . (xx + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (xx + 1)),(g . (xx + 1))*>,'xor'],x*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (xx + 1)),(g . (xx + 1)),x) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (xx + 1)),(g . (xx + 1)),x) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (xx + 1)),(g . (xx + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (xx + 1)),x*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (xx + 1)),x*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (xx + 1)),(g . (xx + 1))*>,and2a)) +* (1GateCircStr (<*(g . (xx + 1)),x*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (xx + 1)),x*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (xx + 1)),x*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (xx + 1)),(g . (xx + 1))*>,and2a)) +* (1GateCircStr (<*(g . (xx + 1)),x*>,and2))) +* (1GateCircStr (<*(f . (xx + 1)),x*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (xx + 1)),(g . (xx + 1))*>,and2a] is non empty pair set
{<*(f . (xx + 1)),(g . (xx + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (xx + 1)),(g . (xx + 1))*>,and2a},{<*(f . (xx + 1)),(g . (xx + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (xx + 1)),x*>,and2] is non empty pair set
{<*(g . (xx + 1)),x*>,and2} is non empty functional V36() V51() set
{<*(g . (xx + 1)),x*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (xx + 1)),x*>,and2},{<*(g . (xx + 1)),x*>}} is non empty V36() V40() V51() set
[<*(f . (xx + 1)),x*>,and2a] is non empty pair set
{<*(f . (xx + 1)),x*>,and2a} is non empty functional V36() V51() set
{<*(f . (xx + 1)),x*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (xx + 1)),x*>,and2a},{<*(f . (xx + 1)),x*>}} is non empty V36() V40() V51() set
<*[<*(f . (xx + 1)),(g . (xx + 1))*>,and2a],[<*(g . (xx + 1)),x*>,and2],[<*(f . (xx + 1)),x*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (xx + 1)),(g . (xx + 1))*>,and2a],[<*(g . (xx + 1)),x*>,and2],[<*(f . (xx + 1)),x*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (xx + 1)),(g . (xx + 1)),x)) +* (1GateCircStr (<*[<*(f . (xx + 1)),(g . (xx + 1))*>,and2a],[<*(g . (xx + 1)),x*>,and2],[<*(f . (xx + 1)),x*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (xx + 1)),(g . (xx + 1)),x,'xor')) +* (BorrowStr ((f . (xx + 1)),(g . (xx + 1)),x)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
n +* (BitSubtracterWithBorrowStr ((f . (xx + 1)),(g . (xx + 1)),x)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
xy is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
c<sub>19</sub> is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
c<sub>19</sub> + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f . (c<sub>19</sub> + 1) is set
g . (c<sub>19</sub> + 1) is set
c<sub>18</sub> is set
BitSubtracterWithBorrowStr ((f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1)),c<sub>18</sub>) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (c₁₉ + 1)),(g . (c₁₉ + 1)),c₁₈,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,'xor'] is non empty pair set
{<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,'xor'},{<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,'xor'],c₁₈*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,'xor'],c₁₈*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>,'xor'],c<sub>18</sub>*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (c₁₉ + 1)),(g . (c₁₉ + 1)),c₁₈) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1)),c<sub>18</sub>) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (c<sub>19</sub> + 1)),c<sub>18</sub>*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,and2a)) +* (1GateCircStr (<*(g . (c₁₉ + 1)),c₁₈*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (c<sub>19</sub> + 1)),c<sub>18</sub>*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,and2a)) +* (1GateCircStr (<*(g . (c₁₉ + 1)),c₁₈*>,and2))) +* (1GateCircStr (<*(f . (c₁₉ + 1)),c₁₈*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>,and2a] is non empty pair set
{<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>,and2a},{<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2] is non empty pair set
{<*(g . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2} is non empty functional V36() V51() set
{<*(g . (c<sub>19</sub> + 1)),c<sub>18</sub>*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2},{<*(g . (c<sub>19</sub> + 1)),c<sub>18</sub>*>}} is non empty V36() V40() V51() set
[<*(f . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a] is non empty pair set
{<*(f . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a} is non empty functional V36() V51() set
{<*(f . (c<sub>19</sub> + 1)),c<sub>18</sub>*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a},{<*(f . (c<sub>19</sub> + 1)),c<sub>18</sub>*>}} is non empty V36() V40() V51() set
<*[<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>,and2a],[<*(g . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2],[<*(f . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>,and2a],[<*(g . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2],[<*(f . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (c₁₉ + 1)),(g . (c₁₉ + 1)),c₁₈)) +* (1GateCircStr (<*[<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,and2a],[<*(g . (c₁₉ + 1)),c₁₈*>,and2],[<*(f . (c₁₉ + 1)),c₁₈*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1)),c<sub>18</sub>,'xor')) +* (BorrowStr ((f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1)),c<sub>18</sub>)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
xy +* (BitSubtracterWithBorrowStr ((f . (c₁₉ + 1)),(g . (c₁₉ + 1)),c₁₈)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
c<sub>20</sub> is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
c₂₂ is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
c₂₂ + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f . (c₂₂ + 1) is set
g . (c₂₂ + 1) is set
c₂₁ is set
BitSubtracterWithBorrowStr ((f . (c₂₂ + 1)),(g . (c₂₂ + 1)),c₂₁) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1)),c<sub>21</sub>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>,'xor'] is non empty pair set
{<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>,'xor'},{<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>,'xor'],c<sub>21</sub>*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>,'xor'],c<sub>21</sub>*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,'xor'],c₂₁*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1)),c<sub>21</sub>) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (c₂₂ + 1)),(g . (c₂₂ + 1)),c₂₁) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (c₂₂ + 1)),c₂₁*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (c₂₂ + 1)),c₂₁*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>,and2a)) +* (1GateCircStr (<*(g . (c<sub>22</sub> + 1)),c<sub>21</sub>*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (c₂₂ + 1)),c₂₁*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (c₂₂ + 1)),c₂₁*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>,and2a)) +* (1GateCircStr (<*(g . (c<sub>22</sub> + 1)),c<sub>21</sub>*>,and2))) +* (1GateCircStr (<*(f . (c<sub>22</sub> + 1)),c<sub>21</sub>*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,and2a] is non empty pair set
{<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,and2a},{<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (c₂₂ + 1)),c₂₁*>,and2] is non empty pair set
{<*(g . (c₂₂ + 1)),c₂₁*>,and2} is non empty functional V36() V51() set
{<*(g . (c₂₂ + 1)),c₂₁*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (c₂₂ + 1)),c₂₁*>,and2},{<*(g . (c₂₂ + 1)),c₂₁*>}} is non empty V36() V40() V51() set
[<*(f . (c₂₂ + 1)),c₂₁*>,and2a] is non empty pair set
{<*(f . (c₂₂ + 1)),c₂₁*>,and2a} is non empty functional V36() V51() set
{<*(f . (c₂₂ + 1)),c₂₁*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (c₂₂ + 1)),c₂₁*>,and2a},{<*(f . (c₂₂ + 1)),c₂₁*>}} is non empty V36() V40() V51() set
<*[<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,and2a],[<*(g . (c₂₂ + 1)),c₂₁*>,and2],[<*(f . (c₂₂ + 1)),c₂₁*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,and2a],[<*(g . (c₂₂ + 1)),c₂₁*>,and2],[<*(f . (c₂₂ + 1)),c₂₁*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1)),c<sub>21</sub>)) +* (1GateCircStr (<*[<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>,and2a],[<*(g . (c<sub>22</sub> + 1)),c<sub>21</sub>*>,and2],[<*(f . (c<sub>22</sub> + 1)),c<sub>21</sub>*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (c₂₂ + 1)),(g . (c₂₂ + 1)),c₂₁,'xor')) +* (BorrowStr ((f . (c₂₂ + 1)),(g . (c₂₂ + 1)),c₂₁)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
c<sub>20</sub> +* (BitSubtracterWithBorrowStr ((f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1)),c<sub>21</sub>)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
Sn is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
An is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
g1 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
g1 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f . (g1 + 1) is set
g . (g1 + 1) is set
f1 is set
BitSubtracterWithBorrowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (g1 + 1)),(g . (g1 + 1)),f1,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (g1 + 1)),(g . (g1 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'] is non empty pair set
{<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (g1 + 1)),(g . (g1 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'},{<*(f . (g1 + 1)),(g . (g1 + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'],f1*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'],f1*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'],f1*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (g1 + 1)),f1*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (g1 + 1)),f1*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (g1 + 1)),f1*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (g1 + 1)),f1*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,and2))) +* (1GateCircStr (<*(f . (g1 + 1)),f1*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a] is non empty pair set
{<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a},{<*(f . (g1 + 1)),(g . (g1 + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (g1 + 1)),f1*>,and2] is non empty pair set
{<*(g . (g1 + 1)),f1*>,and2} is non empty functional V36() V51() set
{<*(g . (g1 + 1)),f1*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (g1 + 1)),f1*>,and2},{<*(g . (g1 + 1)),f1*>}} is non empty V36() V40() V51() set
[<*(f . (g1 + 1)),f1*>,and2a] is non empty pair set
{<*(f . (g1 + 1)),f1*>,and2a} is non empty functional V36() V51() set
{<*(f . (g1 + 1)),f1*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (g1 + 1)),f1*>,and2a},{<*(f . (g1 + 1)),f1*>}} is non empty V36() V40() V51() set
<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a],[<*(g . (g1 + 1)),f1*>,and2],[<*(f . (g1 + 1)),f1*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a],[<*(g . (g1 + 1)),f1*>,and2],[<*(f . (g1 + 1)),f1*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a],[<*(g . (g1 + 1)),f1*>,and2],[<*(f . (g1 + 1)),f1*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (g1 + 1)),(g . (g1 + 1)),f1,'xor')) +* (BorrowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
Sn +* (BitSubtracterWithBorrowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
o0 is strict non-empty finitely-generated V107(Sn) gate`2=den Boolean MSAlgebra over Sn
BitSubtracterWithBorrowCirc ((f . (g1 + 1)),(g . (g1 + 1)),f1) is strict non-empty finitely-generated V107( BitSubtracterWithBorrowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) gate`2=den Boolean MSAlgebra over BitSubtracterWithBorrowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)
BitSubtracterCirc ((f . (g1 + 1)),(g . (g1 + 1)),f1) is strict non-empty finitely-generated V107( 2GatesCircStr ((f . (g1 + 1)),(g . (g1 + 1)),f1,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (g1 + 1)),(g . (g1 + 1)),f1,'xor')
2GatesCircuit ((f . (g1 + 1)),(g . (g1 + 1)),f1,'xor') is strict non-empty finitely-generated V107( 2GatesCircStr ((f . (g1 + 1)),(g . (g1 + 1)),f1,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (g1 + 1)),(g . (g1 + 1)),f1,'xor')
1GateCircuit ((f . (g1 + 1)),(g . (g1 + 1)),'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor')
1GateCircuit (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor')
1GateCircuit ([<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'],f1,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'],f1*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'],f1*>,'xor')
1GateCircuit (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'],f1*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'],f1*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'],f1*>,'xor')
(1GateCircuit ((f . (g1 + 1)),(g . (g1 + 1)),'xor')) +* (1GateCircuit ([<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'],f1,'xor')) is strict non-empty finitely-generated V107((1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'],f1*>,'xor'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'],f1*>,'xor'))
BorrowCirc ((f . (g1 + 1)),(g . (g1 + 1)),f1) is strict non-empty finitely-generated V107( BorrowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) gate`2=den Boolean MSAlgebra over BorrowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)
BorrowICirc ((f . (g1 + 1)),(g . (g1 + 1)),f1) is strict non-empty finitely-generated V107( BorrowIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) gate`2=den Boolean MSAlgebra over BorrowIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)
1GateCircuit ((f . (g1 + 1)),(g . (g1 + 1)),and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a)
1GateCircuit (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a)
1GateCircuit ((g . (g1 + 1)),f1,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*(g . (g1 + 1)),f1*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (g1 + 1)),f1*>,and2)
1GateCircuit (<*(g . (g1 + 1)),f1*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*(g . (g1 + 1)),f1*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (g1 + 1)),f1*>,and2)
(1GateCircuit ((f . (g1 + 1)),(g . (g1 + 1)),and2a)) +* (1GateCircuit ((g . (g1 + 1)),f1,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,and2))
1GateCircuit ((f . (g1 + 1)),f1,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (g1 + 1)),f1*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (g1 + 1)),f1*>,and2a)
1GateCircuit (<*(f . (g1 + 1)),f1*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (g1 + 1)),f1*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (g1 + 1)),f1*>,and2a)
((1GateCircuit ((f . (g1 + 1)),(g . (g1 + 1)),and2a)) +* (1GateCircuit ((g . (g1 + 1)),f1,and2))) +* (1GateCircuit ((f . (g1 + 1)),f1,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,and2))) +* (1GateCircStr (<*(f . (g1 + 1)),f1*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,and2))) +* (1GateCircStr (<*(f . (g1 + 1)),f1*>,and2a))
1GateCircuit ([<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a],[<*(g . (g1 + 1)),f1*>,and2],[<*(f . (g1 + 1)),f1*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a],[<*(g . (g1 + 1)),f1*>,and2],[<*(f . (g1 + 1)),f1*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a],[<*(g . (g1 + 1)),f1*>,and2],[<*(f . (g1 + 1)),f1*>,and2a]*>,or3)
1GateCircuit (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a],[<*(g . (g1 + 1)),f1*>,and2],[<*(f . (g1 + 1)),f1*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a],[<*(g . (g1 + 1)),f1*>,and2],[<*(f . (g1 + 1)),f1*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a],[<*(g . (g1 + 1)),f1*>,and2],[<*(f . (g1 + 1)),f1*>,and2a]*>,or3)
(BorrowICirc ((f . (g1 + 1)),(g . (g1 + 1)),f1)) +* (1GateCircuit ([<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a],[<*(g . (g1 + 1)),f1*>,and2],[<*(f . (g1 + 1)),f1*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a],[<*(g . (g1 + 1)),f1*>,and2],[<*(f . (g1 + 1)),f1*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,and2a],[<*(g . (g1 + 1)),f1*>,and2],[<*(f . (g1 + 1)),f1*>,and2a]*>,or3))
(BitSubtracterCirc ((f . (g1 + 1)),(g . (g1 + 1)),f1)) +* (BorrowCirc ((f . (g1 + 1)),(g . (g1 + 1)),f1)) is strict non-empty finitely-generated V107((2GatesCircStr ((f . (g1 + 1)),(g . (g1 + 1)),f1,'xor')) +* (BorrowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((f . (g1 + 1)),(g . (g1 + 1)),f1,'xor')) +* (BorrowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1))
o0 +* (BitSubtracterWithBorrowCirc ((f . (g1 + 1)),(g . (g1 + 1)),f1)) is strict non-empty finitely-generated V107(Sn +* (BitSubtracterWithBorrowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1))) gate`2=den Boolean MSAlgebra over Sn +* (BitSubtracterWithBorrowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1))
Sn is non empty V71() ManySortedSign
f1 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
f1 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f . (f1 + 1) is set
g . (f1 + 1) is set
o0 is set
BitSubtracterWithBorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f1 + 1)),(g . (f1 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'] is non empty pair set
{<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (f1 + 1)),(g . (f1 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'},{<*(f . (f1 + 1)),(g . (f1 + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (f1 + 1)),o0*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (f1 + 1)),o0*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f1 + 1)),o0*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2))) +* (1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a] is non empty pair set
{<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a},{<*(f . (f1 + 1)),(g . (f1 + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (f1 + 1)),o0*>,and2] is non empty pair set
{<*(g . (f1 + 1)),o0*>,and2} is non empty functional V36() V51() set
{<*(g . (f1 + 1)),o0*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (f1 + 1)),o0*>,and2},{<*(g . (f1 + 1)),o0*>}} is non empty V36() V40() V51() set
[<*(f . (f1 + 1)),o0*>,and2a] is non empty pair set
{<*(f . (f1 + 1)),o0*>,and2a} is non empty functional V36() V51() set
{<*(f . (f1 + 1)),o0*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (f1 + 1)),o0*>,and2a},{<*(f . (f1 + 1)),o0*>}} is non empty V36() V40() V51() set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) +* (BorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
An is non-empty MSAlgebra over Sn
BitSubtracterWithBorrowCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V107( BitSubtracterWithBorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over BitSubtracterWithBorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
BitSubtracterCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V107( 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')
2GatesCircuit ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor') is strict non-empty finitely-generated V107( 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')
1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor')
1GateCircuit (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor')
1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor')
1GateCircuit (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor')
(1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),'xor')) +* (1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0,'xor')) is strict non-empty finitely-generated V107((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor'))
BorrowCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V107( BorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over BorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
BorrowICirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V107( BorrowIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over BorrowIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)
1GateCircuit (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)
1GateCircuit ((g . (f1 + 1)),o0,and2) is strict non-empty finitely-generated V107( 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 V107( 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)),and2a)) +* (1GateCircuit ((g . (f1 + 1)),o0,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2))
1GateCircuit ((f . (f1 + 1)),o0,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a)
1GateCircuit (<*(f . (f1 + 1)),o0*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a)
((1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),and2a)) +* (1GateCircuit ((g . (f1 + 1)),o0,and2))) +* (1GateCircuit ((f . (f1 + 1)),o0,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2))) +* (1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,and2))) +* (1GateCircStr (<*(f . (f1 + 1)),o0*>,and2a))
1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3)
1GateCircuit (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3)
(BorrowICirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,and2a],[<*(g . (f1 + 1)),o0*>,and2],[<*(f . (f1 + 1)),o0*>,and2a]*>,or3))
(BitSubtracterCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (BorrowCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is strict non-empty finitely-generated V107((2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) +* (BorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) +* (BorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))
An +* (BitSubtracterWithBorrowCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is strict non-empty MSAlgebra over Sn +* (BitSubtracterWithBorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))
Sn +* (BitSubtracterWithBorrowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is non empty non void V71() strict ManySortedSign
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
f is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
g is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
(n,f,g) is non empty non void V71() 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 K18( the carrier of (n,f,g))
K18( the carrier of (n,f,g)) is set
the ResultSort of (n,f,g) is Relation-like Function-like V27( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K19( the carrier' of (n,f,g), the carrier of (n,f,g)) is Relation-like set
K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g))) is set
K547( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K18( the carrier of (n,f,g))
A0 is Element of InnerVertices (n,f,g)
N is Element of InnerVertices (n,f,g)
h is Relation-like NAT -defined Function-like V23( NAT ) set
h . n is set
h . 0 is set
Sn is Relation-like NAT -defined Function-like V23( NAT ) set
Sn . n is set
Sn . 0 is set
proj1 h is set
An is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
An + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
h . (An + 1) is set
f . (An + 1) is set
g . (An + 1) is set
h . An is set
BorrowOutput ((f . (An + 1)),(g . (An + 1)),(h . An)) is Element of InnerVertices (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An)))
BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (An + 1)),(g . (An + 1)),(h . An)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (An + 1)),(g . (An + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (An + 1)),(h . An)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (An + 1)),(h . An)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2a)) +* (1GateCircStr (<*(g . (An + 1)),(h . An)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (An + 1)),(h . An)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (An + 1)),(h . An)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2a)) +* (1GateCircStr (<*(g . (An + 1)),(h . An)*>,and2))) +* (1GateCircStr (<*(f . (An + 1)),(h . An)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (An + 1)),(g . (An + 1))*>,and2a] is non empty pair set
{<*(f . (An + 1)),(g . (An + 1))*>,and2a} is non empty functional V36() V51() set
{<*(f . (An + 1)),(g . (An + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (An + 1)),(g . (An + 1))*>,and2a},{<*(f . (An + 1)),(g . (An + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (An + 1)),(h . An)*>,and2] is non empty pair set
{<*(g . (An + 1)),(h . An)*>,and2} is non empty functional V36() V51() set
{<*(g . (An + 1)),(h . An)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (An + 1)),(h . An)*>,and2},{<*(g . (An + 1)),(h . An)*>}} is non empty V36() V40() V51() set
[<*(f . (An + 1)),(h . An)*>,and2a] is non empty pair set
{<*(f . (An + 1)),(h . An)*>,and2a} is non empty functional V36() V51() set
{<*(f . (An + 1)),(h . An)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (An + 1)),(h . An)*>,and2a},{<*(f . (An + 1)),(h . An)*>}} is non empty V36() V40() V51() set
<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(h . An)*>,and2],[<*(f . (An + 1)),(h . An)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(h . An)*>,and2],[<*(f . (An + 1)),(h . An)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (An + 1)),(g . (An + 1)),(h . An))) +* (1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(h . An)*>,and2],[<*(f . (An + 1)),(h . An)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An))) is non empty set
InnerVertices (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An))) is non empty Element of K18( the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An))))
K18( the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An)))) is set
the ResultSort of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An))) is Relation-like Function-like V27( the carrier' of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An))), the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An)))) Element of K18(K19( the carrier' of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An))), the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An)))))
the carrier' of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An))) is non empty set
K19( the carrier' of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An))), the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An)))) is Relation-like set
K18(K19( the carrier' of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An))), the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An))))) is set
K547( the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An))), the ResultSort of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An)))) is Element of K18( the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(h . An))))
[<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(h . An)*>,and2],[<*(f . (An + 1)),(h . An)*>,and2a]*>,or3] is non empty pair set
{<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(h . An)*>,and2],[<*(f . (An + 1)),(h . An)*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(h . An)*>,and2],[<*(f . (An + 1)),(h . An)*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(h . An)*>,and2],[<*(f . (An + 1)),(h . An)*>,and2a]*>,or3},{<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(h . An)*>,and2],[<*(f . (An + 1)),(h . An)*>,and2a]*>}} is non empty V36() V40() V51() set
proj1 Sn is set
An is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
An + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
Sn . (An + 1) is set
f . (An + 1) is set
g . (An + 1) is set
Sn . An is set
BorrowOutput ((f . (An + 1)),(g . (An + 1)),(Sn . An)) is Element of InnerVertices (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)))
BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (An + 1)),(g . (An + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (An + 1)),(Sn . An)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (An + 1)),(Sn . An)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2a)) +* (1GateCircStr (<*(g . (An + 1)),(Sn . An)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (An + 1)),(Sn . An)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (An + 1)),(Sn . An)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,and2a)) +* (1GateCircStr (<*(g . (An + 1)),(Sn . An)*>,and2))) +* (1GateCircStr (<*(f . (An + 1)),(Sn . An)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (An + 1)),(g . (An + 1))*>,and2a] is non empty pair set
{<*(f . (An + 1)),(g . (An + 1))*>,and2a} is non empty functional V36() V51() set
{<*(f . (An + 1)),(g . (An + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (An + 1)),(g . (An + 1))*>,and2a},{<*(f . (An + 1)),(g . (An + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (An + 1)),(Sn . An)*>,and2] is non empty pair set
{<*(g . (An + 1)),(Sn . An)*>,and2} is non empty functional V36() V51() set
{<*(g . (An + 1)),(Sn . An)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (An + 1)),(Sn . An)*>,and2},{<*(g . (An + 1)),(Sn . An)*>}} is non empty V36() V40() V51() set
[<*(f . (An + 1)),(Sn . An)*>,and2a] is non empty pair set
{<*(f . (An + 1)),(Sn . An)*>,and2a} is non empty functional V36() V51() set
{<*(f . (An + 1)),(Sn . An)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (An + 1)),(Sn . An)*>,and2a},{<*(f . (An + 1)),(Sn . An)*>}} is non empty V36() V40() V51() set
<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(Sn . An)*>,and2],[<*(f . (An + 1)),(Sn . An)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(Sn . An)*>,and2],[<*(f . (An + 1)),(Sn . An)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))) +* (1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(Sn . An)*>,and2],[<*(f . (An + 1)),(Sn . An)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))) is non empty set
InnerVertices (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))) is non empty Element of K18( the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))))
K18( the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)))) is set
the ResultSort of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))) is Relation-like Function-like V27( the carrier' of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))), the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)))) Element of K18(K19( the carrier' of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))), the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)))))
the carrier' of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))) is non empty set
K19( the carrier' of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))), the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)))) is Relation-like set
K18(K19( the carrier' of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))), the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))))) is set
K547( the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))), the ResultSort of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)))) is Element of K18( the carrier of (BorrowStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))))
[<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(Sn . An)*>,and2],[<*(f . (An + 1)),(Sn . An)*>,and2a]*>,or3] is non empty pair set
{<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(Sn . An)*>,and2],[<*(f . (An + 1)),(Sn . An)*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(Sn . An)*>,and2],[<*(f . (An + 1)),(Sn . An)*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(Sn . An)*>,and2],[<*(f . (An + 1)),(Sn . An)*>,and2a]*>,or3},{<*[<*(f . (An + 1)),(g . (An + 1))*>,and2a],[<*(g . (An + 1)),(Sn . An)*>,and2],[<*(f . (An + 1)),(Sn . An)*>,and2a]*>}} is non empty V36() V40() V51() set
A0 is Relation-like NAT -defined Function-like V23( NAT ) set
A0 . n is set
A0 . 0 is set
N is Relation-like NAT -defined Function-like V23( NAT ) set
N . 0 is set
InnerVertices (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) is non empty Element of K18( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))))
the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) is non empty set
K18( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)))) is set
the ResultSort of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) is Relation-like Function-like V27( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)))) Element of K18(K19( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)))))
the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) is non empty set
K19( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)))) is Relation-like set
K18(K19( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))))) is set
K547( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))), the ResultSort of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)))) is Element of K18( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))))
{[{},((0 -tuples_on BOOLEAN) --> TRUE)]} is non empty V2() Relation-like Function-like constant V36() 1 -element V51() set
h is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
A0 . h is set
N . h is set
h + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
A0 . (h + 1) is set
N . (h + 1) is set
Sn is non empty V71() ManySortedSign
InnerVertices Sn is Element of K18( the carrier of Sn)
the carrier of Sn is non empty set
K18( the carrier of Sn) is set
the ResultSort of Sn is Relation-like Function-like V27( the carrier' of Sn, the carrier of Sn) Element of K18(K19( the carrier' of Sn, the carrier of Sn))
the carrier' of Sn is set
K19( the carrier' of Sn, the carrier of Sn) is Relation-like set
K18(K19( the carrier' of Sn, the carrier of Sn)) is set
K547( the carrier of Sn, the ResultSort of Sn) is Element of K18( the carrier of Sn)
Sn is non empty V71() ManySortedSign
InnerVertices Sn is Element of K18( the carrier of Sn)
the carrier of Sn is non empty set
K18( the carrier of Sn) is set
the ResultSort of Sn is Relation-like Function-like V27( the carrier' of Sn, the carrier of Sn) Element of K18(K19( the carrier' of Sn, the carrier of Sn))
the carrier' of Sn is set
K19( the carrier' of Sn, the carrier of Sn) is Relation-like set
K18(K19( the carrier' of Sn, the carrier of Sn)) is set
K547( the carrier of Sn, the ResultSort of Sn) is Element of K18( the carrier of Sn)
f . (h + 1) is set
g . (h + 1) is set
BorrowOutput ((f . (h + 1)),(g . (h + 1)),(N . h)) is Element of InnerVertices (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))
BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (h + 1)),(g . (h + 1)),(N . h)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (h + 1)),(g . (h + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (h + 1)),(g . (h + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (h + 1)),(N . h)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (h + 1)),(N . h)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (h + 1)),(g . (h + 1))*>,and2a)) +* (1GateCircStr (<*(g . (h + 1)),(N . h)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (h + 1)),(N . h)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (h + 1)),(N . h)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (h + 1)),(g . (h + 1))*>,and2a)) +* (1GateCircStr (<*(g . (h + 1)),(N . h)*>,and2))) +* (1GateCircStr (<*(f . (h + 1)),(N . h)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (h + 1)),(g . (h + 1))*>,and2a] is non empty pair set
{<*(f . (h + 1)),(g . (h + 1))*>,and2a} is non empty functional V36() V51() set
{<*(f . (h + 1)),(g . (h + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (h + 1)),(g . (h + 1))*>,and2a},{<*(f . (h + 1)),(g . (h + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (h + 1)),(N . h)*>,and2] is non empty pair set
{<*(g . (h + 1)),(N . h)*>,and2} is non empty functional V36() V51() set
{<*(g . (h + 1)),(N . h)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (h + 1)),(N . h)*>,and2},{<*(g . (h + 1)),(N . h)*>}} is non empty V36() V40() V51() set
[<*(f . (h + 1)),(N . h)*>,and2a] is non empty pair set
{<*(f . (h + 1)),(N . h)*>,and2a} is non empty functional V36() V51() set
{<*(f . (h + 1)),(N . h)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (h + 1)),(N . h)*>,and2a},{<*(f . (h + 1)),(N . h)*>}} is non empty V36() V40() V51() set
<*[<*(f . (h + 1)),(g . (h + 1))*>,and2a],[<*(g . (h + 1)),(N . h)*>,and2],[<*(f . (h + 1)),(N . h)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (h + 1)),(g . (h + 1))*>,and2a],[<*(g . (h + 1)),(N . h)*>,and2],[<*(f . (h + 1)),(N . h)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (h + 1)),(g . (h + 1)),(N . h))) +* (1GateCircStr (<*[<*(f . (h + 1)),(g . (h + 1))*>,and2a],[<*(g . (h + 1)),(N . h)*>,and2],[<*(f . (h + 1)),(N . h)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty set
InnerVertices (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty Element of K18( the carrier of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))
K18( the carrier of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is set
the ResultSort of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is Relation-like Function-like V27( the carrier' of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) Element of K18(K19( the carrier' of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))))
the carrier' of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty set
K19( the carrier' of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is Relation-like set
K18(K19( the carrier' of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))) is set
K547( the carrier of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the ResultSort of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is Element of K18( the carrier of (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))
[<*[<*(f . (h + 1)),(g . (h + 1))*>,and2a],[<*(g . (h + 1)),(N . h)*>,and2],[<*(f . (h + 1)),(N . h)*>,and2a]*>,or3] is non empty pair set
{<*[<*(f . (h + 1)),(g . (h + 1))*>,and2a],[<*(g . (h + 1)),(N . h)*>,and2],[<*(f . (h + 1)),(N . h)*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*(f . (h + 1)),(g . (h + 1))*>,and2a],[<*(g . (h + 1)),(N . h)*>,and2],[<*(f . (h + 1)),(N . h)*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(f . (h + 1)),(g . (h + 1))*>,and2a],[<*(g . (h + 1)),(N . h)*>,and2],[<*(f . (h + 1)),(N . h)*>,and2a]*>,or3},{<*[<*(f . (h + 1)),(g . (h + 1))*>,and2a],[<*(g . (h + 1)),(N . h)*>,and2],[<*(f . (h + 1)),(N . h)*>,and2a]*>}} is non empty V36() V40() V51() set
BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (h + 1)),(g . (h + 1)),(N . h),'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (h + 1)),(g . (h + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (h + 1)),(g . (h + 1))*>,'xor'] is non empty pair set
{<*(f . (h + 1)),(g . (h + 1))*>,'xor'} is non empty functional V36() V51() set
{{<*(f . (h + 1)),(g . (h + 1))*>,'xor'},{<*(f . (h + 1)),(g . (h + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (h + 1)),(g . (h + 1))*>,'xor'],(N . h)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (h + 1)),(g . (h + 1))*>,'xor'],(N . h)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (h + 1)),(g . (h + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (h + 1)),(g . (h + 1))*>,'xor'],(N . h)*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (h + 1)),(g . (h + 1)),(N . h),'xor')) +* (BorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty Element of K18( the carrier of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))
the carrier of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty set
K18( the carrier of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is set
the ResultSort of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))))
the carrier' of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))) is set
K547( the carrier of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the ResultSort of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))
Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty non void V71() strict ManySortedSign
InnerVertices (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is non empty Element of K18( the carrier of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))))
the carrier of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is non empty set
K18( the carrier of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))) is set
the ResultSort of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is Relation-like Function-like V27( the carrier' of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))), the carrier of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))) Element of K18(K19( the carrier' of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))), the carrier of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))))
the carrier' of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is non empty set
K19( the carrier' of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))), the carrier of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))) is Relation-like set
K18(K19( the carrier' of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))), the carrier of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))))) is set
K547( the carrier of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))), the ResultSort of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))) is Element of K18( the carrier of (Sn +* (BitSubtracterWithBorrowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))))
N . n is set
Sn is non empty V71() ManySortedSign
InnerVertices Sn is Element of K18( the carrier of Sn)
the carrier of Sn is non empty set
K18( the carrier of Sn) is set
the ResultSort of Sn is Relation-like Function-like V27( the carrier' of Sn, the carrier of Sn) Element of K18(K19( the carrier' of Sn, the carrier of Sn))
the carrier' of Sn is set
K19( the carrier' of Sn, the carrier of Sn) is Relation-like set
K18(K19( the carrier' of Sn, the carrier of Sn)) is set
K547( the carrier of Sn, the ResultSort of Sn) is Element of K18( the carrier of Sn)
h is Element of InnerVertices (n,f,g)
Sn is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
Sn + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
N . (Sn + 1) is set
f . (Sn + 1) is set
g . (Sn + 1) is set
N . Sn is set
BorrowOutput ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn)) is Element of InnerVertices (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn)))
BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (Sn + 1)),(g . (Sn + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (Sn + 1)),(N . Sn)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (Sn + 1)),(N . Sn)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) +* (1GateCircStr (<*(g . (Sn + 1)),(N . Sn)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (Sn + 1)),(N . Sn)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (Sn + 1)),(N . Sn)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) +* (1GateCircStr (<*(g . (Sn + 1)),(N . Sn)*>,and2))) +* (1GateCircStr (<*(f . (Sn + 1)),(N . Sn)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a] is non empty pair set
{<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a} is non empty functional V36() V51() set
{<*(f . (Sn + 1)),(g . (Sn + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a},{<*(f . (Sn + 1)),(g . (Sn + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (Sn + 1)),(N . Sn)*>,and2] is non empty pair set
{<*(g . (Sn + 1)),(N . Sn)*>,and2} is non empty functional V36() V51() set
{<*(g . (Sn + 1)),(N . Sn)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (Sn + 1)),(N . Sn)*>,and2},{<*(g . (Sn + 1)),(N . Sn)*>}} is non empty V36() V40() V51() set
[<*(f . (Sn + 1)),(N . Sn)*>,and2a] is non empty pair set
{<*(f . (Sn + 1)),(N . Sn)*>,and2a} is non empty functional V36() V51() set
{<*(f . (Sn + 1)),(N . Sn)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (Sn + 1)),(N . Sn)*>,and2a},{<*(f . (Sn + 1)),(N . Sn)*>}} is non empty V36() V40() V51() set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),(N . Sn)*>,and2],[<*(f . (Sn + 1)),(N . Sn)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),(N . Sn)*>,and2],[<*(f . (Sn + 1)),(N . Sn)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),(N . Sn)*>,and2],[<*(f . (Sn + 1)),(N . Sn)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))) is non empty set
InnerVertices (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))) is non empty Element of K18( the carrier of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))))
K18( the carrier of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn)))) is set
the ResultSort of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))) is Relation-like Function-like V27( the carrier' of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))), the carrier of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn)))) Element of K18(K19( the carrier' of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))), the carrier of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn)))))
the carrier' of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))) is non empty set
K19( the carrier' of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))), the carrier of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn)))) is Relation-like set
K18(K19( the carrier' of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))), the carrier of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))))) is set
K547( the carrier of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))), the ResultSort of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn)))) is Element of K18( the carrier of (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),(N . Sn))))
[<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),(N . Sn)*>,and2],[<*(f . (Sn + 1)),(N . Sn)*>,and2a]*>,or3] is non empty pair set
{<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),(N . Sn)*>,and2],[<*(f . (Sn + 1)),(N . Sn)*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),(N . Sn)*>,and2],[<*(f . (Sn + 1)),(N . Sn)*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),(N . Sn)*>,and2],[<*(f . (Sn + 1)),(N . Sn)*>,and2a]*>,or3},{<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),(N . Sn)*>,and2],[<*(f . (Sn + 1)),(N . Sn)*>,and2a]*>}} is non empty V36() V40() V51() set
o0 is non empty V71() ManySortedSign
An is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
A0 . An is set
f1 is set
N . An is set
A0 . Sn is set
An is non empty V71() ManySortedSign
n is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
f is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
g is Relation-like NAT -defined Function-like V23( NAT ) set
g . 0 is set
S0 is Relation-like NAT -defined Function-like V23( NAT ) set
S0 . 0 is set
A0 is Relation-like NAT -defined Function-like V23( NAT ) set
A0 . 0 is set
N is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
(N,n,f) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
g . N is set
(N,n,f) is strict non-empty finitely-generated V107((N,n,f)) gate`2=den Boolean MSAlgebra over (N,n,f)
S0 . N is set
(N,n,f) is Element of InnerVertices (N,n,f)
the carrier of (N,n,f) is non empty set
InnerVertices (N,n,f) is non empty Element of K18( the carrier of (N,n,f))
K18( the carrier of (N,n,f)) is set
the ResultSort of (N,n,f) is Relation-like Function-like V27( the carrier' of (N,n,f), the carrier of (N,n,f)) Element of K18(K19( the carrier' of (N,n,f), the carrier of (N,n,f)))
the carrier' of (N,n,f) is non empty set
K19( the carrier' of (N,n,f), the carrier of (N,n,f)) is Relation-like set
K18(K19( the carrier' of (N,n,f), the carrier of (N,n,f))) is set
K547( the carrier of (N,n,f), the ResultSort of (N,n,f)) is Element of K18( the carrier of (N,n,f))
A0 . N is set
h is Relation-like NAT -defined Function-like V23( NAT ) set
h . N is set
Sn is Relation-like NAT -defined Function-like V23( NAT ) set
Sn . N is set
h . 0 is set
Sn . 0 is set
An is Relation-like NAT -defined Function-like V23( NAT ) set
An . 0 is set
o0 is non empty V71() ManySortedSign
h1 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
h1 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
n . (h1 + 1) is set
f . (h1 + 1) is set
g1 is set
BitSubtracterWithBorrowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((n . (h1 + 1)),(f . (h1 + 1)),g1,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (h1 + 1)),(f . (h1 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'] is non empty pair set
{<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(n . (h1 + 1)),(f . (h1 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'},{<*(n . (h1 + 1)),(f . (h1 + 1))*>}} is non empty V36() V40() V51() set
<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'],g1*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'],g1*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'],g1*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((n . (h1 + 1)),(f . (h1 + 1)),g1) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (h1 + 1)),g1*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (h1 + 1)),g1*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (h1 + 1)),g1*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (h1 + 1)),g1*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(n . (h1 + 1)),g1*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (h1 + 1)),g1*>,and2))) +* (1GateCircStr (<*(n . (h1 + 1)),g1*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a] is non empty pair set
{<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a},{<*(n . (h1 + 1)),(f . (h1 + 1))*>}} is non empty V36() V40() V51() set
[<*(f . (h1 + 1)),g1*>,and2] is non empty pair set
{<*(f . (h1 + 1)),g1*>,and2} is non empty functional V36() V51() set
{<*(f . (h1 + 1)),g1*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (h1 + 1)),g1*>,and2},{<*(f . (h1 + 1)),g1*>}} is non empty V36() V40() V51() set
[<*(n . (h1 + 1)),g1*>,and2a] is non empty pair set
{<*(n . (h1 + 1)),g1*>,and2a} is non empty functional V36() V51() set
{<*(n . (h1 + 1)),g1*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (h1 + 1)),g1*>,and2a},{<*(n . (h1 + 1)),g1*>}} is non empty V36() V40() V51() set
<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a],[<*(f . (h1 + 1)),g1*>,and2],[<*(n . (h1 + 1)),g1*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a],[<*(f . (h1 + 1)),g1*>,and2],[<*(n . (h1 + 1)),g1*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) +* (1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a],[<*(f . (h1 + 1)),g1*>,and2],[<*(n . (h1 + 1)),g1*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((n . (h1 + 1)),(f . (h1 + 1)),g1,'xor')) +* (BorrowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f1 is non-empty MSAlgebra over o0
BitSubtracterWithBorrowCirc ((n . (h1 + 1)),(f . (h1 + 1)),g1) is strict non-empty finitely-generated V107( BitSubtracterWithBorrowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) gate`2=den Boolean MSAlgebra over BitSubtracterWithBorrowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)
BitSubtracterCirc ((n . (h1 + 1)),(f . (h1 + 1)),g1) is strict non-empty finitely-generated V107( 2GatesCircStr ((n . (h1 + 1)),(f . (h1 + 1)),g1,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((n . (h1 + 1)),(f . (h1 + 1)),g1,'xor')
2GatesCircuit ((n . (h1 + 1)),(f . (h1 + 1)),g1,'xor') is strict non-empty finitely-generated V107( 2GatesCircStr ((n . (h1 + 1)),(f . (h1 + 1)),g1,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((n . (h1 + 1)),(f . (h1 + 1)),g1,'xor')
1GateCircuit ((n . (h1 + 1)),(f . (h1 + 1)),'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor')
1GateCircuit (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor')
1GateCircuit ([<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'],g1,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'],g1*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'],g1*>,'xor')
1GateCircuit (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'],g1*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'],g1*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'],g1*>,'xor')
(1GateCircuit ((n . (h1 + 1)),(f . (h1 + 1)),'xor')) +* (1GateCircuit ([<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'],g1,'xor')) is strict non-empty finitely-generated V107((1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'],g1*>,'xor'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'],g1*>,'xor'))
BorrowCirc ((n . (h1 + 1)),(f . (h1 + 1)),g1) is strict non-empty finitely-generated V107( BorrowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) gate`2=den Boolean MSAlgebra over BorrowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)
BorrowICirc ((n . (h1 + 1)),(f . (h1 + 1)),g1) is strict non-empty finitely-generated V107( BorrowIStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) gate`2=den Boolean MSAlgebra over BorrowIStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)
1GateCircuit ((n . (h1 + 1)),(f . (h1 + 1)),and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a)
1GateCircuit (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a)
1GateCircuit ((f . (h1 + 1)),g1,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (h1 + 1)),g1*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (h1 + 1)),g1*>,and2)
1GateCircuit (<*(f . (h1 + 1)),g1*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (h1 + 1)),g1*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (h1 + 1)),g1*>,and2)
(1GateCircuit ((n . (h1 + 1)),(f . (h1 + 1)),and2a)) +* (1GateCircuit ((f . (h1 + 1)),g1,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (h1 + 1)),g1*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (h1 + 1)),g1*>,and2))
1GateCircuit ((n . (h1 + 1)),g1,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(n . (h1 + 1)),g1*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (h1 + 1)),g1*>,and2a)
1GateCircuit (<*(n . (h1 + 1)),g1*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(n . (h1 + 1)),g1*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (h1 + 1)),g1*>,and2a)
((1GateCircuit ((n . (h1 + 1)),(f . (h1 + 1)),and2a)) +* (1GateCircuit ((f . (h1 + 1)),g1,and2))) +* (1GateCircuit ((n . (h1 + 1)),g1,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (h1 + 1)),g1*>,and2))) +* (1GateCircStr (<*(n . (h1 + 1)),g1*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (h1 + 1)),g1*>,and2))) +* (1GateCircStr (<*(n . (h1 + 1)),g1*>,and2a))
1GateCircuit ([<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a],[<*(f . (h1 + 1)),g1*>,and2],[<*(n . (h1 + 1)),g1*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a],[<*(f . (h1 + 1)),g1*>,and2],[<*(n . (h1 + 1)),g1*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a],[<*(f . (h1 + 1)),g1*>,and2],[<*(n . (h1 + 1)),g1*>,and2a]*>,or3)
1GateCircuit (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a],[<*(f . (h1 + 1)),g1*>,and2],[<*(n . (h1 + 1)),g1*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a],[<*(f . (h1 + 1)),g1*>,and2],[<*(n . (h1 + 1)),g1*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a],[<*(f . (h1 + 1)),g1*>,and2],[<*(n . (h1 + 1)),g1*>,and2a]*>,or3)
(BorrowICirc ((n . (h1 + 1)),(f . (h1 + 1)),g1)) +* (1GateCircuit ([<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a],[<*(f . (h1 + 1)),g1*>,and2],[<*(n . (h1 + 1)),g1*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) +* (1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a],[<*(f . (h1 + 1)),g1*>,and2],[<*(n . (h1 + 1)),g1*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) +* (1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,and2a],[<*(f . (h1 + 1)),g1*>,and2],[<*(n . (h1 + 1)),g1*>,and2a]*>,or3))
(BitSubtracterCirc ((n . (h1 + 1)),(f . (h1 + 1)),g1)) +* (BorrowCirc ((n . (h1 + 1)),(f . (h1 + 1)),g1)) is strict non-empty finitely-generated V107((2GatesCircStr ((n . (h1 + 1)),(f . (h1 + 1)),g1,'xor')) +* (BorrowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((n . (h1 + 1)),(f . (h1 + 1)),g1,'xor')) +* (BorrowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1))
f1 +* (BitSubtracterWithBorrowCirc ((n . (h1 + 1)),(f . (h1 + 1)),g1)) is strict non-empty MSAlgebra over o0 +* (BitSubtracterWithBorrowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1))
o0 +* (BitSubtracterWithBorrowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) is non empty non void V71() strict ManySortedSign
proj1 A0 is set
o0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
o0 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
A0 . (o0 + 1) is set
n . (o0 + 1) is set
f . (o0 + 1) is set
A0 . o0 is set
BorrowOutput ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)) is Element of InnerVertices (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)))
BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (o0 + 1)),(f . (o0 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(n . (o0 + 1)),(f . (o0 + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (o0 + 1)),(A0 . o0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (o0 + 1)),(A0 . o0)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (o0 + 1)),(f . (o0 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (o0 + 1)),(A0 . o0)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (o0 + 1)),(A0 . o0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(n . (o0 + 1)),(A0 . o0)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (o0 + 1)),(f . (o0 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (o0 + 1)),(A0 . o0)*>,and2))) +* (1GateCircStr (<*(n . (o0 + 1)),(A0 . o0)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (o0 + 1)),(f . (o0 + 1))*>,and2a] is non empty pair set
{<*(n . (o0 + 1)),(f . (o0 + 1))*>,and2a} is non empty functional V36() V51() set
{<*(n . (o0 + 1)),(f . (o0 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (o0 + 1)),(f . (o0 + 1))*>,and2a},{<*(n . (o0 + 1)),(f . (o0 + 1))*>}} is non empty V36() V40() V51() set
[<*(f . (o0 + 1)),(A0 . o0)*>,and2] is non empty pair set
{<*(f . (o0 + 1)),(A0 . o0)*>,and2} is non empty functional V36() V51() set
{<*(f . (o0 + 1)),(A0 . o0)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (o0 + 1)),(A0 . o0)*>,and2},{<*(f . (o0 + 1)),(A0 . o0)*>}} is non empty V36() V40() V51() set
[<*(n . (o0 + 1)),(A0 . o0)*>,and2a] is non empty pair set
{<*(n . (o0 + 1)),(A0 . o0)*>,and2a} is non empty functional V36() V51() set
{<*(n . (o0 + 1)),(A0 . o0)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (o0 + 1)),(A0 . o0)*>,and2a},{<*(n . (o0 + 1)),(A0 . o0)*>}} is non empty V36() V40() V51() set
<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,and2a],[<*(f . (o0 + 1)),(A0 . o0)*>,and2],[<*(n . (o0 + 1)),(A0 . o0)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,and2a],[<*(f . (o0 + 1)),(A0 . o0)*>,and2],[<*(n . (o0 + 1)),(A0 . o0)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))) +* (1GateCircStr (<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,and2a],[<*(f . (o0 + 1)),(A0 . o0)*>,and2],[<*(n . (o0 + 1)),(A0 . o0)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))) is non empty set
InnerVertices (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))) is non empty Element of K18( the carrier of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))))
K18( the carrier of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)))) is set
the ResultSort of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))) is Relation-like Function-like V27( the carrier' of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))), the carrier of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)))) Element of K18(K19( the carrier' of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))), the carrier of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)))))
the carrier' of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))) is non empty set
K19( the carrier' of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))), the carrier of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)))) is Relation-like set
K18(K19( the carrier' of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))), the carrier of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))))) is set
K547( the carrier of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))), the ResultSort of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)))) is Element of K18( the carrier of (BorrowStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))))
[<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,and2a],[<*(f . (o0 + 1)),(A0 . o0)*>,and2],[<*(n . (o0 + 1)),(A0 . o0)*>,and2a]*>,or3] is non empty pair set
{<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,and2a],[<*(f . (o0 + 1)),(A0 . o0)*>,and2],[<*(n . (o0 + 1)),(A0 . o0)*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,and2a],[<*(f . (o0 + 1)),(A0 . o0)*>,and2],[<*(n . (o0 + 1)),(A0 . o0)*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,and2a],[<*(f . (o0 + 1)),(A0 . o0)*>,and2],[<*(n . (o0 + 1)),(A0 . o0)*>,and2a]*>,or3},{<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,and2a],[<*(f . (o0 + 1)),(A0 . o0)*>,and2],[<*(n . (o0 + 1)),(A0 . o0)*>,and2a]*>}} is non empty V36() V40() V51() set
o0 is Relation-like NAT -defined Function-like V23( NAT ) set
o0 . N is set
o0 . 0 is set
proj1 o0 is set
f1 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
f1 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
o0 . (f1 + 1) is set
n . (f1 + 1) is set
f . (f1 + 1) is set
o0 . f1 is set
BorrowOutput ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)) is Element of InnerVertices (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)))
BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (f1 + 1)),(f . (f1 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(n . (f1 + 1)),(f . (f1 + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (f1 + 1)),(o0 . f1)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (f1 + 1)),(o0 . f1)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (f1 + 1)),(f . (f1 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (f1 + 1)),(o0 . f1)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (f1 + 1)),(o0 . f1)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(n . (f1 + 1)),(o0 . f1)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (f1 + 1)),(f . (f1 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (f1 + 1)),(o0 . f1)*>,and2))) +* (1GateCircStr (<*(n . (f1 + 1)),(o0 . f1)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (f1 + 1)),(f . (f1 + 1))*>,and2a] is non empty pair set
{<*(n . (f1 + 1)),(f . (f1 + 1))*>,and2a} is non empty functional V36() V51() set
{<*(n . (f1 + 1)),(f . (f1 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (f1 + 1)),(f . (f1 + 1))*>,and2a},{<*(n . (f1 + 1)),(f . (f1 + 1))*>}} is non empty V36() V40() V51() set
[<*(f . (f1 + 1)),(o0 . f1)*>,and2] is non empty pair set
{<*(f . (f1 + 1)),(o0 . f1)*>,and2} is non empty functional V36() V51() set
{<*(f . (f1 + 1)),(o0 . f1)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (f1 + 1)),(o0 . f1)*>,and2},{<*(f . (f1 + 1)),(o0 . f1)*>}} is non empty V36() V40() V51() set
[<*(n . (f1 + 1)),(o0 . f1)*>,and2a] is non empty pair set
{<*(n . (f1 + 1)),(o0 . f1)*>,and2a} is non empty functional V36() V51() set
{<*(n . (f1 + 1)),(o0 . f1)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (f1 + 1)),(o0 . f1)*>,and2a},{<*(n . (f1 + 1)),(o0 . f1)*>}} is non empty V36() V40() V51() set
<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,and2a],[<*(f . (f1 + 1)),(o0 . f1)*>,and2],[<*(n . (f1 + 1)),(o0 . f1)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,and2a],[<*(f . (f1 + 1)),(o0 . f1)*>,and2],[<*(n . (f1 + 1)),(o0 . f1)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))) +* (1GateCircStr (<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,and2a],[<*(f . (f1 + 1)),(o0 . f1)*>,and2],[<*(n . (f1 + 1)),(o0 . f1)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))) is non empty set
InnerVertices (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))) is non empty Element of K18( the carrier of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))))
K18( the carrier of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)))) is set
the ResultSort of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))) is Relation-like Function-like V27( the carrier' of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))), the carrier of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)))) Element of K18(K19( the carrier' of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))), the carrier of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)))))
the carrier' of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))) is non empty set
K19( the carrier' of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))), the carrier of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)))) is Relation-like set
K18(K19( the carrier' of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))), the carrier of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))))) is set
K547( the carrier of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))), the ResultSort of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)))) is Element of K18( the carrier of (BorrowStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))))
[<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,and2a],[<*(f . (f1 + 1)),(o0 . f1)*>,and2],[<*(n . (f1 + 1)),(o0 . f1)*>,and2a]*>,or3] is non empty pair set
{<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,and2a],[<*(f . (f1 + 1)),(o0 . f1)*>,and2],[<*(n . (f1 + 1)),(o0 . f1)*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,and2a],[<*(f . (f1 + 1)),(o0 . f1)*>,and2],[<*(n . (f1 + 1)),(o0 . f1)*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,and2a],[<*(f . (f1 + 1)),(o0 . f1)*>,and2],[<*(n . (f1 + 1)),(o0 . f1)*>,and2a]*>,or3},{<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,and2a],[<*(f . (f1 + 1)),(o0 . f1)*>,and2],[<*(n . (f1 + 1)),(o0 . f1)*>,and2a]*>}} is non empty V36() V40() V51() set
n is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
f is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
(0,n,f) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(0,n,f) is strict non-empty finitely-generated V107((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 K18( the carrier of (0,n,f))
K18( the carrier of (0,n,f)) is set
the ResultSort of (0,n,f) is Relation-like Function-like V27( the carrier' of (0,n,f), the carrier of (0,n,f)) Element of K18(K19( the carrier' of (0,n,f), the carrier of (0,n,f)))
the carrier' of (0,n,f) is non empty set
K19( the carrier' of (0,n,f), the carrier of (0,n,f)) is Relation-like set
K18(K19( the carrier' of (0,n,f), the carrier of (0,n,f))) is set
K547( the carrier of (0,n,f), the ResultSort of (0,n,f)) is Element of K18( the carrier of (0,n,f))
g is Relation-like NAT -defined Function-like V23( NAT ) set
g . 0 is set
S0 is Relation-like NAT -defined Function-like V23( NAT ) set
S0 . 0 is set
A0 is Relation-like NAT -defined Function-like V23( NAT ) set
A0 . 0 is set
g is Relation-like NAT -defined Function-like V23( NAT ) set
g . 0 is set
S0 is Relation-like NAT -defined Function-like V23( NAT ) set
S0 . 0 is set
A0 is Relation-like NAT -defined Function-like V23( NAT ) set
A0 . 0 is set
{[{},((0 -tuples_on BOOLEAN) --> TRUE)]} is non empty V2() Relation-like Function-like constant V36() 1 -element V51() set
g is Relation-like NAT -defined Function-like V23( NAT ) set
g . 0 is set
S0 is Relation-like NAT -defined Function-like V23( NAT ) set
S0 . 0 is set
A0 is Relation-like NAT -defined Function-like V23( NAT ) set
A0 . 0 is set
n is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
f is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
(1,n,f) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
n . 1 is set
f . 1 is set
(1,n,f) is strict non-empty finitely-generated V107((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 K18( the carrier of (1,n,f))
K18( the carrier of (1,n,f)) is set
the ResultSort of (1,n,f) is Relation-like Function-like V27( the carrier' of (1,n,f), the carrier of (1,n,f)) Element of K18(K19( the carrier' of (1,n,f), the carrier of (1,n,f)))
the carrier' of (1,n,f) is non empty set
K19( the carrier' of (1,n,f), the carrier of (1,n,f)) is Relation-like set
K18(K19( the carrier' of (1,n,f), the carrier of (1,n,f))) is set
K547( the carrier of (1,n,f), the ResultSort of (1,n,f)) is Element of K18( the carrier of (1,n,f))
g is set
BitSubtracterWithBorrowStr ((n . 1),(f . 1),g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((n . 1),(f . 1),g,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . 1),(f . 1)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(n . 1),(f . 1)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . 1),(f . 1)*>,'xor'] is non empty pair set
{<*(n . 1),(f . 1)*>,'xor'} is non empty functional V36() V51() set
{<*(n . 1),(f . 1)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . 1),(f . 1)*>,'xor'},{<*(n . 1),(f . 1)*>}} is non empty V36() V40() V51() set
<*[<*(n . 1),(f . 1)*>,'xor'],g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . 1),(f . 1)*>,'xor'],g*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . 1),(f . 1)*>,'xor')) +* (1GateCircStr (<*[<*(n . 1),(f . 1)*>,'xor'],g*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((n . 1),(f . 1),g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((n . 1),(f . 1),g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . 1),(f . 1)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . 1),g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . 1),g*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . 1),(f . 1)*>,and2a)) +* (1GateCircStr (<*(f . 1),g*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . 1),g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(n . 1),g*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . 1),(f . 1)*>,and2a)) +* (1GateCircStr (<*(f . 1),g*>,and2))) +* (1GateCircStr (<*(n . 1),g*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . 1),(f . 1)*>,and2a] is non empty pair set
{<*(n . 1),(f . 1)*>,and2a} is non empty functional V36() V51() set
{{<*(n . 1),(f . 1)*>,and2a},{<*(n . 1),(f . 1)*>}} is non empty V36() V40() V51() set
[<*(f . 1),g*>,and2] is non empty pair set
{<*(f . 1),g*>,and2} is non empty functional V36() V51() set
{<*(f . 1),g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . 1),g*>,and2},{<*(f . 1),g*>}} is non empty V36() V40() V51() set
[<*(n . 1),g*>,and2a] is non empty pair set
{<*(n . 1),g*>,and2a} is non empty functional V36() V51() set
{<*(n . 1),g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . 1),g*>,and2a},{<*(n . 1),g*>}} is non empty V36() V40() V51() set
<*[<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((n . 1),(f . 1),g)) +* (1GateCircStr (<*[<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((n . 1),(f . 1),g,'xor')) +* (BorrowStr ((n . 1),(f . 1),g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitSubtracterWithBorrowStr ((n . 1),(f . 1),g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitSubtracterWithBorrowCirc ((n . 1),(f . 1),g) is strict non-empty finitely-generated V107( BitSubtracterWithBorrowStr ((n . 1),(f . 1),g)) gate`2=den Boolean MSAlgebra over BitSubtracterWithBorrowStr ((n . 1),(f . 1),g)
BitSubtracterCirc ((n . 1),(f . 1),g) is strict non-empty finitely-generated V107( 2GatesCircStr ((n . 1),(f . 1),g,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((n . 1),(f . 1),g,'xor')
2GatesCircuit ((n . 1),(f . 1),g,'xor') is strict non-empty finitely-generated V107( 2GatesCircStr ((n . 1),(f . 1),g,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((n . 1),(f . 1),g,'xor')
1GateCircuit ((n . 1),(f . 1),'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(n . 1),(f . 1)*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . 1),(f . 1)*>,'xor')
1GateCircuit (<*(n . 1),(f . 1)*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(n . 1),(f . 1)*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . 1),(f . 1)*>,'xor')
1GateCircuit ([<*(n . 1),(f . 1)*>,'xor'],g,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(n . 1),(f . 1)*>,'xor'],g*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . 1),(f . 1)*>,'xor'],g*>,'xor')
1GateCircuit (<*[<*(n . 1),(f . 1)*>,'xor'],g*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(n . 1),(f . 1)*>,'xor'],g*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . 1),(f . 1)*>,'xor'],g*>,'xor')
(1GateCircuit ((n . 1),(f . 1),'xor')) +* (1GateCircuit ([<*(n . 1),(f . 1)*>,'xor'],g,'xor')) is strict non-empty finitely-generated V107((1GateCircStr (<*(n . 1),(f . 1)*>,'xor')) +* (1GateCircStr (<*[<*(n . 1),(f . 1)*>,'xor'],g*>,'xor'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(n . 1),(f . 1)*>,'xor')) +* (1GateCircStr (<*[<*(n . 1),(f . 1)*>,'xor'],g*>,'xor'))
BorrowCirc ((n . 1),(f . 1),g) is strict non-empty finitely-generated V107( BorrowStr ((n . 1),(f . 1),g)) gate`2=den Boolean MSAlgebra over BorrowStr ((n . 1),(f . 1),g)
BorrowICirc ((n . 1),(f . 1),g) is strict non-empty finitely-generated V107( BorrowIStr ((n . 1),(f . 1),g)) gate`2=den Boolean MSAlgebra over BorrowIStr ((n . 1),(f . 1),g)
1GateCircuit ((n . 1),(f . 1),and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(n . 1),(f . 1)*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . 1),(f . 1)*>,and2a)
1GateCircuit (<*(n . 1),(f . 1)*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(n . 1),(f . 1)*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . 1),(f . 1)*>,and2a)
1GateCircuit ((f . 1),g,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . 1),g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . 1),g*>,and2)
1GateCircuit (<*(f . 1),g*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . 1),g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . 1),g*>,and2)
(1GateCircuit ((n . 1),(f . 1),and2a)) +* (1GateCircuit ((f . 1),g,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*(n . 1),(f . 1)*>,and2a)) +* (1GateCircStr (<*(f . 1),g*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(n . 1),(f . 1)*>,and2a)) +* (1GateCircStr (<*(f . 1),g*>,and2))
1GateCircuit ((n . 1),g,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(n . 1),g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . 1),g*>,and2a)
1GateCircuit (<*(n . 1),g*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(n . 1),g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . 1),g*>,and2a)
((1GateCircuit ((n . 1),(f . 1),and2a)) +* (1GateCircuit ((f . 1),g,and2))) +* (1GateCircuit ((n . 1),g,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*(n . 1),(f . 1)*>,and2a)) +* (1GateCircStr (<*(f . 1),g*>,and2))) +* (1GateCircStr (<*(n . 1),g*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(n . 1),(f . 1)*>,and2a)) +* (1GateCircStr (<*(f . 1),g*>,and2))) +* (1GateCircStr (<*(n . 1),g*>,and2a))
1GateCircuit ([<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a]*>,or3)
1GateCircuit (<*[<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a]*>,or3)
(BorrowICirc ((n . 1),(f . 1),g)) +* (1GateCircuit ([<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr ((n . 1),(f . 1),g)) +* (1GateCircStr (<*[<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr ((n . 1),(f . 1),g)) +* (1GateCircStr (<*[<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a]*>,or3))
(BitSubtracterCirc ((n . 1),(f . 1),g)) +* (BorrowCirc ((n . 1),(f . 1),g)) is strict non-empty finitely-generated V107((2GatesCircStr ((n . 1),(f . 1),g,'xor')) +* (BorrowStr ((n . 1),(f . 1),g))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((n . 1),(f . 1),g,'xor')) +* (BorrowStr ((n . 1),(f . 1),g))
(1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitSubtracterWithBorrowCirc ((n . 1),(f . 1),g)) is strict non-empty finitely-generated V107((1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitSubtracterWithBorrowStr ((n . 1),(f . 1),g))) gate`2=den Boolean MSAlgebra over (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitSubtracterWithBorrowStr ((n . 1),(f . 1),g))
BorrowOutput ((n . 1),(f . 1),g) is Element of InnerVertices (BorrowStr ((n . 1),(f . 1),g))
the carrier of (BorrowStr ((n . 1),(f . 1),g)) is non empty set
InnerVertices (BorrowStr ((n . 1),(f . 1),g)) is non empty Element of K18( the carrier of (BorrowStr ((n . 1),(f . 1),g)))
K18( the carrier of (BorrowStr ((n . 1),(f . 1),g))) is set
the ResultSort of (BorrowStr ((n . 1),(f . 1),g)) is Relation-like Function-like V27( the carrier' of (BorrowStr ((n . 1),(f . 1),g)), the carrier of (BorrowStr ((n . 1),(f . 1),g))) Element of K18(K19( the carrier' of (BorrowStr ((n . 1),(f . 1),g)), the carrier of (BorrowStr ((n . 1),(f . 1),g))))
the carrier' of (BorrowStr ((n . 1),(f . 1),g)) is non empty set
K19( the carrier' of (BorrowStr ((n . 1),(f . 1),g)), the carrier of (BorrowStr ((n . 1),(f . 1),g))) is Relation-like set
K18(K19( the carrier' of (BorrowStr ((n . 1),(f . 1),g)), the carrier of (BorrowStr ((n . 1),(f . 1),g)))) is set
K547( the carrier of (BorrowStr ((n . 1),(f . 1),g)), the ResultSort of (BorrowStr ((n . 1),(f . 1),g))) is Element of K18( the carrier of (BorrowStr ((n . 1),(f . 1),g)))
[<*[<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a]*>,or3] is non empty pair set
{<*[<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a]*>,or3},{<*[<*(n . 1),(f . 1)*>,and2a],[<*(f . 1),g*>,and2],[<*(n . 1),g*>,and2a]*>}} is non empty V36() V40() V51() set
S0 is Relation-like NAT -defined Function-like V23( NAT ) set
S0 . 1 is set
A0 is Relation-like NAT -defined Function-like V23( NAT ) set
A0 . 1 is set
S0 . 0 is set
A0 . 0 is set
N is Relation-like NAT -defined Function-like V23( NAT ) set
N . 0 is set
0 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
N . (0 + 1) is set
n is set
<*n*> is non empty V2() Relation-like NAT -defined Function-like constant V36() 1 -element FinSequence-like FinSubsequence-like V51() set
f is set
<*f*> is non empty V2() Relation-like NAT -defined Function-like constant V36() 1 -element FinSequence-like FinSubsequence-like V51() set
(1,<*n*>,<*f*>) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1,<*n*>,<*f*>) is strict non-empty finitely-generated V107((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 K18( the carrier of (1,<*n*>,<*f*>))
K18( the carrier of (1,<*n*>,<*f*>)) is set
the ResultSort of (1,<*n*>,<*f*>) is Relation-like Function-like V27( the carrier' of (1,<*n*>,<*f*>), the carrier of (1,<*n*>,<*f*>)) Element of K18(K19( the carrier' of (1,<*n*>,<*f*>), the carrier of (1,<*n*>,<*f*>)))
the carrier' of (1,<*n*>,<*f*>) is non empty set
K19( the carrier' of (1,<*n*>,<*f*>), the carrier of (1,<*n*>,<*f*>)) is Relation-like set
K18(K19( the carrier' of (1,<*n*>,<*f*>), the carrier of (1,<*n*>,<*f*>))) is set
K547( the carrier of (1,<*n*>,<*f*>), the ResultSort of (1,<*n*>,<*f*>)) is Element of K18( the carrier of (1,<*n*>,<*f*>))
<*n*> . 1 is set
<*f*> . 1 is set
g is set
BitSubtracterWithBorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (n,f,g,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,f*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*n,f*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*n,f*>,'xor'] is non empty pair set
{<*n,f*>,'xor'} is non empty functional V36() V51() set
{<*n,f*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,f*>,'xor'},{<*n,f*>}} is non empty V36() V40() V51() set
<*[<*n,f*>,'xor'],g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'xor')) +* (1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*f,g*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*n,g*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*n,f*>,and2a] is non empty pair set
{<*n,f*>,and2a} is non empty functional V36() V51() set
{{<*n,f*>,and2a},{<*n,f*>}} is non empty V36() V40() V51() set
[<*f,g*>,and2] is non empty pair set
{<*f,g*>,and2} is non empty functional V36() V51() set
{<*f,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*f,g*>,and2},{<*f,g*>}} is non empty V36() V40() V51() set
[<*n,g*>,and2a] is non empty pair set
{<*n,g*>,and2a} is non empty functional V36() V51() set
{<*n,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,g*>,and2a},{<*n,g*>}} is non empty V36() V40() V51() set
<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitSubtracterWithBorrowStr (n,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitSubtracterWithBorrowCirc (n,f,g) is strict non-empty finitely-generated V107( BitSubtracterWithBorrowStr (n,f,g)) gate`2=den Boolean MSAlgebra over BitSubtracterWithBorrowStr (n,f,g)
BitSubtracterCirc (n,f,g) is strict non-empty finitely-generated V107( 2GatesCircStr (n,f,g,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr (n,f,g,'xor')
2GatesCircuit (n,f,g,'xor') is strict non-empty finitely-generated V107( 2GatesCircStr (n,f,g,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr (n,f,g,'xor')
1GateCircuit (n,f,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'xor')
1GateCircuit (<*n,f*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'xor')
1GateCircuit ([<*n,f*>,'xor'],g,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')
1GateCircuit (<*[<*n,f*>,'xor'],g*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')
(1GateCircuit (n,f,'xor')) +* (1GateCircuit ([<*n,f*>,'xor'],g,'xor')) is strict non-empty finitely-generated V107((1GateCircStr (<*n,f*>,'xor')) +* (1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,'xor')) +* (1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor'))
BorrowCirc (n,f,g) is strict non-empty finitely-generated V107( BorrowStr (n,f,g)) gate`2=den Boolean MSAlgebra over BorrowStr (n,f,g)
BorrowICirc (n,f,g) is strict non-empty finitely-generated V107( BorrowIStr (n,f,g)) gate`2=den Boolean MSAlgebra over BorrowIStr (n,f,g)
1GateCircuit (n,f,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2a)
1GateCircuit (<*n,f*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2a)
1GateCircuit (f,g,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
1GateCircuit (<*f,g*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
(1GateCircuit (n,f,and2a)) +* (1GateCircuit (f,g,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))
1GateCircuit (n,g,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,g*>,and2a)
1GateCircuit (<*n,g*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,g*>,and2a)
((1GateCircuit (n,f,and2a)) +* (1GateCircuit (f,g,and2))) +* (1GateCircuit (n,g,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a))
1GateCircuit ([<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)
1GateCircuit (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)
(BorrowICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))
(BitSubtracterCirc (n,f,g)) +* (BorrowCirc (n,f,g)) is strict non-empty finitely-generated V107((2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g))) gate`2=den Boolean MSAlgebra over (2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g))
(1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitSubtracterWithBorrowCirc (n,f,g)) is strict non-empty finitely-generated V107((1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitSubtracterWithBorrowStr (n,f,g))) gate`2=den Boolean MSAlgebra over (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) +* (BitSubtracterWithBorrowStr (n,f,g))
BorrowOutput (n,f,g) is Element of InnerVertices (BorrowStr (n,f,g))
the carrier of (BorrowStr (n,f,g)) is non empty set
InnerVertices (BorrowStr (n,f,g)) is non empty Element of K18( the carrier of (BorrowStr (n,f,g)))
K18( the carrier of (BorrowStr (n,f,g))) is set
the ResultSort of (BorrowStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) Element of K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))))
the carrier' of (BorrowStr (n,f,g)) is non empty set
K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g)))) is set
K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
[<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3] is non empty pair set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3},{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>}} is non empty V36() V40() V51() set
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
g is Relation-like NAT -defined Function-like V36() n -element FinSequence-like FinSubsequence-like V51() set
S0 is Relation-like NAT -defined Function-like V36() n -element FinSequence-like FinSubsequence-like V51() set
A0 is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
g ^ A0 is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
h is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
S0 ^ h is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
(n,(g ^ A0),(S0 ^ h)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
N is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
g ^ N is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
Sn is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
S0 ^ Sn is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
(n,(g ^ N),(S0 ^ Sn)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,(g ^ A0),(S0 ^ h)) is strict non-empty finitely-generated V107((n,(g ^ A0),(S0 ^ h))) gate`2=den Boolean MSAlgebra over (n,(g ^ A0),(S0 ^ h))
(n,(g ^ N),(S0 ^ Sn)) is strict non-empty finitely-generated V107((n,(g ^ N),(S0 ^ Sn))) gate`2=den Boolean MSAlgebra over (n,(g ^ N),(S0 ^ Sn))
(n,(g ^ A0),(S0 ^ h)) is Element of InnerVertices (n,(g ^ A0),(S0 ^ h))
the carrier of (n,(g ^ A0),(S0 ^ h)) is non empty set
InnerVertices (n,(g ^ A0),(S0 ^ h)) is non empty Element of K18( the carrier of (n,(g ^ A0),(S0 ^ h)))
K18( the carrier of (n,(g ^ A0),(S0 ^ h))) is set
the ResultSort of (n,(g ^ A0),(S0 ^ h)) is Relation-like Function-like V27( the carrier' of (n,(g ^ A0),(S0 ^ h)), the carrier of (n,(g ^ A0),(S0 ^ h))) Element of K18(K19( the carrier' of (n,(g ^ A0),(S0 ^ h)), the carrier of (n,(g ^ A0),(S0 ^ h))))
the carrier' of (n,(g ^ A0),(S0 ^ h)) is non empty set
K19( the carrier' of (n,(g ^ A0),(S0 ^ h)), the carrier of (n,(g ^ A0),(S0 ^ h))) is Relation-like set
K18(K19( the carrier' of (n,(g ^ A0),(S0 ^ h)), the carrier of (n,(g ^ A0),(S0 ^ h)))) is set
K547( the carrier of (n,(g ^ A0),(S0 ^ h)), the ResultSort of (n,(g ^ A0),(S0 ^ h))) is Element of K18( the carrier of (n,(g ^ A0),(S0 ^ h)))
(n,(g ^ N),(S0 ^ Sn)) is Element of InnerVertices (n,(g ^ N),(S0 ^ Sn))
the carrier of (n,(g ^ N),(S0 ^ Sn)) is non empty set
InnerVertices (n,(g ^ N),(S0 ^ Sn)) is non empty Element of K18( the carrier of (n,(g ^ N),(S0 ^ Sn)))
K18( the carrier of (n,(g ^ N),(S0 ^ Sn))) is set
the ResultSort of (n,(g ^ N),(S0 ^ Sn)) is Relation-like Function-like V27( the carrier' of (n,(g ^ N),(S0 ^ Sn)), the carrier of (n,(g ^ N),(S0 ^ Sn))) Element of K18(K19( the carrier' of (n,(g ^ N),(S0 ^ Sn)), the carrier of (n,(g ^ N),(S0 ^ Sn))))
the carrier' of (n,(g ^ N),(S0 ^ Sn)) is non empty set
K19( the carrier' of (n,(g ^ N),(S0 ^ Sn)), the carrier of (n,(g ^ N),(S0 ^ Sn))) is Relation-like set
K18(K19( the carrier' of (n,(g ^ N),(S0 ^ Sn)), the carrier of (n,(g ^ N),(S0 ^ Sn)))) is set
K547( the carrier of (n,(g ^ N),(S0 ^ Sn)), the ResultSort of (n,(g ^ N),(S0 ^ Sn))) is Element of K18( the carrier of (n,(g ^ N),(S0 ^ Sn)))
An is Relation-like NAT -defined Function-like V23( NAT ) set
An . n is set
o0 is Relation-like NAT -defined Function-like V23( NAT ) set
o0 . n is set
An . 0 is set
o0 . 0 is set
f1 is Relation-like NAT -defined Function-like V23( NAT ) set
f1 . 0 is set
g1 is Relation-like NAT -defined Function-like V23( NAT ) set
g1 . n is set
h1 is Relation-like NAT -defined Function-like V23( NAT ) set
h1 . n is set
g1 . 0 is set
h1 . 0 is set
n is Relation-like NAT -defined Function-like V23( NAT ) set
n . 0 is set
x is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
f1 . x is set
n . x is set
An . x is set
g1 . x is set
o0 . x is set
h1 . x is set
x + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f1 . (x + 1) is set
n . (x + 1) is set
An . (x + 1) is set
g1 . (x + 1) is set
o0 . (x + 1) is set
h1 . (x + 1) is set
len g is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
len S0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
dom g is V36() n -element V51() Element of K18(NAT)
Seg n is V36() n -element V51() Element of K18(NAT)
dom S0 is V36() n -element V51() Element of K18(NAT)
0 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
(g ^ A0) . (x + 1) is set
g . (x + 1) is set
(g ^ N) . (x + 1) is set
(S0 ^ h) . (x + 1) is set
S0 . (x + 1) is set
(S0 ^ Sn) . (x + 1) is set
xy is non empty V71() ManySortedSign
xx is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
An . xx is set
c<sub>18</sub> is non-empty MSAlgebra over xy
o0 . xx is set
c<sub>19</sub> is set
f1 . xx is set
xx is non empty V71() ManySortedSign
c<sub>19</sub> is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
c<sub>19</sub> + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
(g ^ A0) . (c<sub>19</sub> + 1) is set
(S0 ^ h) . (c<sub>19</sub> + 1) is set
c<sub>18</sub> is set
BitSubtracterWithBorrowStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor'] is non empty pair set
{<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor'} is non empty functional V36() V51() set
{<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor'},{<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>}} is non empty V36() V40() V51() set
<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor'],c₁₈*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor'],c₁₈*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'xor')) +* (1GateCircStr (<*[<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'xor'],c<sub>18</sub>*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,and2a)) +* (1GateCircStr (<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,and2a)) +* (1GateCircStr (<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,and2))) +* (1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),c₁₈*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,and2a] is non empty pair set
{<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,and2a} is non empty functional V36() V51() set
{{<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,and2a},{<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>}} is non empty V36() V40() V51() set
[<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2] is non empty pair set
{<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2} is non empty functional V36() V51() set
{<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2},{<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>}} is non empty V36() V40() V51() set
[<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a] is non empty pair set
{<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a} is non empty functional V36() V51() set
{<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a},{<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>}} is non empty V36() V40() V51() set
<*[<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,and2a],[<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2],[<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,and2a],[<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2],[<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈)) +* (1GateCircStr (<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,and2a],[<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,and2],[<*((g ^ A0) . (c₁₉ + 1)),c₁₈*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>,'xor')) +* (BorrowStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
xy is non-empty MSAlgebra over xx
BitSubtracterWithBorrowCirc (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈) is strict non-empty finitely-generated V107( BitSubtracterWithBorrowStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈)) gate`2=den Boolean MSAlgebra over BitSubtracterWithBorrowStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>)
BitSubtracterCirc (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>) is strict non-empty finitely-generated V107( 2GatesCircStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈,'xor')
2GatesCircuit (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈,'xor') is strict non-empty finitely-generated V107( 2GatesCircStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>,'xor')
1GateCircuit (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor')
1GateCircuit (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'xor')
1GateCircuit ([<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'xor'],c<sub>18</sub>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'xor'],c<sub>18</sub>*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor'],c₁₈*>,'xor')
1GateCircuit (<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor'],c₁₈*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor'],c₁₈*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'xor'],c<sub>18</sub>*>,'xor')
(1GateCircuit (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),'xor')) +* (1GateCircuit ([<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'xor'],c<sub>18</sub>,'xor')) is strict non-empty finitely-generated V107((1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'xor')) +* (1GateCircStr (<*[<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'xor'],c<sub>18</sub>*>,'xor'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor')) +* (1GateCircStr (<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor'],c₁₈*>,'xor'))
BorrowCirc (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈) is strict non-empty finitely-generated V107( BorrowStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈)) gate`2=den Boolean MSAlgebra over BorrowStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>)
BorrowICirc (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>) is strict non-empty finitely-generated V107( BorrowIStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>)) gate`2=den Boolean MSAlgebra over BorrowIStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈)
1GateCircuit (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,and2a)
1GateCircuit (<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,and2a)
1GateCircuit (((S0 ^ h) . (c₁₉ + 1)),c₁₈,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2)
1GateCircuit (<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,and2)
(1GateCircuit (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),and2a)) +* (1GateCircuit (((S0 ^ h) . (c₁₉ + 1)),c₁₈,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,and2a)) +* (1GateCircStr (<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,and2a)) +* (1GateCircStr (<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2))
1GateCircuit (((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),c₁₈*>,and2a)
1GateCircuit (<*((g ^ A0) . (c₁₉ + 1)),c₁₈*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),c₁₈*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a)
((1GateCircuit (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),and2a)) +* (1GateCircuit (((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>,and2))) +* (1GateCircuit (((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,and2a)) +* (1GateCircStr (<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2))) +* (1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,and2a)) +* (1GateCircStr (<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,and2))) +* (1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),c₁₈*>,and2a))
1GateCircuit ([<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,and2a],[<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,and2],[<*((g ^ A0) . (c₁₉ + 1)),c₁₈*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,and2a],[<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,and2],[<*((g ^ A0) . (c₁₉ + 1)),c₁₈*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,and2a],[<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2],[<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a]*>,or3)
1GateCircuit (<*[<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,and2a],[<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2],[<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,and2a],[<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2],[<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,and2a],[<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,and2],[<*((g ^ A0) . (c₁₉ + 1)),c₁₈*>,and2a]*>,or3)
(BorrowICirc (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈)) +* (1GateCircuit ([<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,and2a],[<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,and2],[<*((g ^ A0) . (c₁₉ + 1)),c₁₈*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈)) +* (1GateCircStr (<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,and2a],[<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,and2],[<*((g ^ A0) . (c₁₉ + 1)),c₁₈*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>)) +* (1GateCircStr (<*[<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,and2a],[<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2],[<*((g ^ A0) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,and2a]*>,or3))
(BitSubtracterCirc (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>)) +* (BorrowCirc (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>)) is strict non-empty finitely-generated V107((2GatesCircStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>,'xor')) +* (BorrowStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>))) gate`2=den Boolean MSAlgebra over (2GatesCircStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈,'xor')) +* (BorrowStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈))
xy +* (BitSubtracterWithBorrowCirc (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈)) is strict non-empty MSAlgebra over xx +* (BitSubtracterWithBorrowStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈))
xx +* (BitSubtracterWithBorrowStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈)) is non empty non void V71() strict ManySortedSign
xx is non empty V71() ManySortedSign
xy is non-empty MSAlgebra over xx
BorrowOutput (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is Element of InnerVertices (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))
BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((S0 ^ Sn) . (x + 1)),(n . x)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a)) +* (1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((g ^ N) . (x + 1)),(n . x)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*((g ^ N) . (x + 1)),(n . x)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a)) +* (1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2))) +* (1GateCircStr (<*((g ^ N) . (x + 1)),(n . x)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a] is non empty pair set
{<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a} is non empty functional V36() V51() set
{<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a},{<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>}} is non empty V36() V40() V51() set
[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2] is non empty pair set
{<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2} is non empty functional V36() V51() set
{<*((S0 ^ Sn) . (x + 1)),(n . x)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2},{<*((S0 ^ Sn) . (x + 1)),(n . x)*>}} is non empty V36() V40() V51() set
[<*((g ^ N) . (x + 1)),(n . x)*>,and2a] is non empty pair set
{<*((g ^ N) . (x + 1)),(n . x)*>,and2a} is non empty functional V36() V51() set
{<*((g ^ N) . (x + 1)),(n . x)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*((g ^ N) . (x + 1)),(n . x)*>,and2a},{<*((g ^ N) . (x + 1)),(n . x)*>}} is non empty V36() V40() V51() set
<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) +* (1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is non empty set
InnerVertices (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is non empty Element of K18( the carrier of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))))
K18( the carrier of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))) is set
the ResultSort of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is Relation-like Function-like V27( the carrier' of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))), the carrier of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))) Element of K18(K19( the carrier' of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))), the carrier of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))))
the carrier' of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is non empty set
K19( the carrier' of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))), the carrier of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))) is Relation-like set
K18(K19( the carrier' of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))), the carrier of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))))) is set
K547( the carrier of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))), the ResultSort of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))) is Element of K18( the carrier of (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))))
[<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a]*>,or3] is non empty pair set
{<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a]*>,or3},{<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a]*>}} is non empty V36() V40() V51() set
BitSubtracterWithBorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x),'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'] is non empty pair set
{<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'} is non empty functional V36() V51() set
{{<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'},{<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>}} is non empty V36() V40() V51() set
<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'],(n . x)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'],(n . x)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor')) +* (1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'],(n . x)*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x),'xor')) +* (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
xx +* (BitSubtracterWithBorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is non empty non void V71() strict ManySortedSign
BitSubtracterWithBorrowCirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is strict non-empty finitely-generated V107( BitSubtracterWithBorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) gate`2=den Boolean MSAlgebra over BitSubtracterWithBorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))
BitSubtracterCirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is strict non-empty finitely-generated V107( 2GatesCircStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x),'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x),'xor')
2GatesCircuit (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x),'xor') is strict non-empty finitely-generated V107( 2GatesCircStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x),'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x),'xor')
1GateCircuit (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor')
1GateCircuit (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor')
1GateCircuit ([<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'],(n . x),'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'],(n . x)*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'],(n . x)*>,'xor')
1GateCircuit (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'],(n . x)*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'],(n . x)*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'],(n . x)*>,'xor')
(1GateCircuit (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),'xor')) +* (1GateCircuit ([<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'],(n . x),'xor')) is strict non-empty finitely-generated V107((1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor')) +* (1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'],(n . x)*>,'xor'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor')) +* (1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'],(n . x)*>,'xor'))
BorrowCirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is strict non-empty finitely-generated V107( BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) gate`2=den Boolean MSAlgebra over BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))
BorrowICirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is strict non-empty finitely-generated V107( BorrowIStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) gate`2=den Boolean MSAlgebra over BorrowIStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))
1GateCircuit (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a)
1GateCircuit (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a)
1GateCircuit (((S0 ^ Sn) . (x + 1)),(n . x),and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2)
1GateCircuit (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2)
(1GateCircuit (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),and2a)) +* (1GateCircuit (((S0 ^ Sn) . (x + 1)),(n . x),and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a)) +* (1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a)) +* (1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2))
1GateCircuit (((g ^ N) . (x + 1)),(n . x),and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*((g ^ N) . (x + 1)),(n . x)*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ N) . (x + 1)),(n . x)*>,and2a)
1GateCircuit (<*((g ^ N) . (x + 1)),(n . x)*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*((g ^ N) . (x + 1)),(n . x)*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ N) . (x + 1)),(n . x)*>,and2a)
((1GateCircuit (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),and2a)) +* (1GateCircuit (((S0 ^ Sn) . (x + 1)),(n . x),and2))) +* (1GateCircuit (((g ^ N) . (x + 1)),(n . x),and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a)) +* (1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2))) +* (1GateCircStr (<*((g ^ N) . (x + 1)),(n . x)*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a)) +* (1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2))) +* (1GateCircStr (<*((g ^ N) . (x + 1)),(n . x)*>,and2a))
1GateCircuit ([<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a]*>,or3)
1GateCircuit (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a]*>,or3)
(BorrowICirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) +* (1GateCircuit ([<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) +* (1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) +* (1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,and2a],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,and2],[<*((g ^ N) . (x + 1)),(n . x)*>,and2a]*>,or3))
(BitSubtracterCirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) +* (BorrowCirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is strict non-empty finitely-generated V107((2GatesCircStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x),'xor')) +* (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))) gate`2=den Boolean MSAlgebra over (2GatesCircStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x),'xor')) +* (BorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))
xy +* (BitSubtracterWithBorrowCirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is strict non-empty MSAlgebra over xx +* (BitSubtracterWithBorrowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))
f1 . n is set
n . n is set
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
n + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
g is Relation-like NAT -defined Function-like V36() n -element FinSequence-like FinSubsequence-like V51() set
S0 is Relation-like NAT -defined Function-like V36() n -element FinSequence-like FinSubsequence-like V51() set
(n,g,S0) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,g,S0) is Element of InnerVertices (n,g,S0)
the carrier of (n,g,S0) is non empty set
InnerVertices (n,g,S0) is non empty Element of K18( the carrier of (n,g,S0))
K18( the carrier of (n,g,S0)) is set
the ResultSort of (n,g,S0) is Relation-like Function-like V27( the carrier' of (n,g,S0), the carrier of (n,g,S0)) Element of K18(K19( the carrier' of (n,g,S0), the carrier of (n,g,S0)))
the carrier' of (n,g,S0) is non empty set
K19( the carrier' of (n,g,S0), the carrier of (n,g,S0)) is Relation-like set
K18(K19( the carrier' of (n,g,S0), the carrier of (n,g,S0))) is set
K547( the carrier of (n,g,S0), the ResultSort of (n,g,S0)) is Element of K18( the carrier of (n,g,S0))
(n,g,S0) is strict non-empty finitely-generated V107((n,g,S0)) gate`2=den Boolean MSAlgebra over (n,g,S0)
A0 is set
<*A0*> is non empty V2() Relation-like NAT -defined Function-like constant V36() 1 -element FinSequence-like FinSubsequence-like V51() set
g ^ <*A0*> is non empty Relation-like NAT -defined Function-like V36() n + 1 -element FinSequence-like FinSubsequence-like V51() set
n + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
N is set
<*N*> is non empty V2() Relation-like NAT -defined Function-like constant V36() 1 -element FinSequence-like FinSubsequence-like V51() set
S0 ^ <*N*> is non empty Relation-like NAT -defined Function-like V36() n + 1 -element FinSequence-like FinSubsequence-like V51() set
((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitSubtracterWithBorrowStr (A0,N,(n,g,S0)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (A0,N,(n,g,S0),'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*A0,N*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*A0,N*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*A0,N*>,'xor'] is non empty pair set
{<*A0,N*>,'xor'} is non empty functional V36() V51() set
{<*A0,N*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*A0,N*>,'xor'},{<*A0,N*>}} is non empty V36() V40() V51() set
<*[<*A0,N*>,'xor'],(n,g,S0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*A0,N*>,'xor'],(n,g,S0)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*A0,N*>,'xor')) +* (1GateCircStr (<*[<*A0,N*>,'xor'],(n,g,S0)*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr (A0,N,(n,g,S0)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr (A0,N,(n,g,S0)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*A0,N*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*N,(n,g,S0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*N,(n,g,S0)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*A0,N*>,and2a)) +* (1GateCircStr (<*N,(n,g,S0)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*A0,(n,g,S0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*A0,(n,g,S0)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*A0,N*>,and2a)) +* (1GateCircStr (<*N,(n,g,S0)*>,and2))) +* (1GateCircStr (<*A0,(n,g,S0)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*A0,N*>,and2a] is non empty pair set
{<*A0,N*>,and2a} is non empty functional V36() V51() set
{{<*A0,N*>,and2a},{<*A0,N*>}} is non empty V36() V40() V51() set
[<*N,(n,g,S0)*>,and2] is non empty pair set
{<*N,(n,g,S0)*>,and2} is non empty functional V36() V51() set
{<*N,(n,g,S0)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*N,(n,g,S0)*>,and2},{<*N,(n,g,S0)*>}} is non empty V36() V40() V51() set
[<*A0,(n,g,S0)*>,and2a] is non empty pair set
{<*A0,(n,g,S0)*>,and2a} is non empty functional V36() V51() set
{<*A0,(n,g,S0)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*A0,(n,g,S0)*>,and2a},{<*A0,(n,g,S0)*>}} is non empty V36() V40() V51() set
<*[<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr (A0,N,(n,g,S0))) +* (1GateCircStr (<*[<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (A0,N,(n,g,S0),'xor')) +* (BorrowStr (A0,N,(n,g,S0))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,g,S0) +* (BitSubtracterWithBorrowStr (A0,N,(n,g,S0))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)) is strict non-empty finitely-generated V107(((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>))) gate`2=den Boolean MSAlgebra over ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>))
BitSubtracterWithBorrowCirc (A0,N,(n,g,S0)) is strict non-empty finitely-generated V107( BitSubtracterWithBorrowStr (A0,N,(n,g,S0))) gate`2=den Boolean MSAlgebra over BitSubtracterWithBorrowStr (A0,N,(n,g,S0))
BitSubtracterCirc (A0,N,(n,g,S0)) is strict non-empty finitely-generated V107( 2GatesCircStr (A0,N,(n,g,S0),'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr (A0,N,(n,g,S0),'xor')
2GatesCircuit (A0,N,(n,g,S0),'xor') is strict non-empty finitely-generated V107( 2GatesCircStr (A0,N,(n,g,S0),'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr (A0,N,(n,g,S0),'xor')
1GateCircuit (A0,N,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*A0,N*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*A0,N*>,'xor')
1GateCircuit (<*A0,N*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*A0,N*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*A0,N*>,'xor')
1GateCircuit ([<*A0,N*>,'xor'],(n,g,S0),'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*A0,N*>,'xor'],(n,g,S0)*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*A0,N*>,'xor'],(n,g,S0)*>,'xor')
1GateCircuit (<*[<*A0,N*>,'xor'],(n,g,S0)*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*A0,N*>,'xor'],(n,g,S0)*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*A0,N*>,'xor'],(n,g,S0)*>,'xor')
(1GateCircuit (A0,N,'xor')) +* (1GateCircuit ([<*A0,N*>,'xor'],(n,g,S0),'xor')) is strict non-empty finitely-generated V107((1GateCircStr (<*A0,N*>,'xor')) +* (1GateCircStr (<*[<*A0,N*>,'xor'],(n,g,S0)*>,'xor'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*A0,N*>,'xor')) +* (1GateCircStr (<*[<*A0,N*>,'xor'],(n,g,S0)*>,'xor'))
BorrowCirc (A0,N,(n,g,S0)) is strict non-empty finitely-generated V107( BorrowStr (A0,N,(n,g,S0))) gate`2=den Boolean MSAlgebra over BorrowStr (A0,N,(n,g,S0))
BorrowICirc (A0,N,(n,g,S0)) is strict non-empty finitely-generated V107( BorrowIStr (A0,N,(n,g,S0))) gate`2=den Boolean MSAlgebra over BorrowIStr (A0,N,(n,g,S0))
1GateCircuit (A0,N,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*A0,N*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*A0,N*>,and2a)
1GateCircuit (<*A0,N*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*A0,N*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*A0,N*>,and2a)
1GateCircuit (N,(n,g,S0),and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*N,(n,g,S0)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*N,(n,g,S0)*>,and2)
1GateCircuit (<*N,(n,g,S0)*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*N,(n,g,S0)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*N,(n,g,S0)*>,and2)
(1GateCircuit (A0,N,and2a)) +* (1GateCircuit (N,(n,g,S0),and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*A0,N*>,and2a)) +* (1GateCircStr (<*N,(n,g,S0)*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*A0,N*>,and2a)) +* (1GateCircStr (<*N,(n,g,S0)*>,and2))
1GateCircuit (A0,(n,g,S0),and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*A0,(n,g,S0)*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*A0,(n,g,S0)*>,and2a)
1GateCircuit (<*A0,(n,g,S0)*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*A0,(n,g,S0)*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*A0,(n,g,S0)*>,and2a)
((1GateCircuit (A0,N,and2a)) +* (1GateCircuit (N,(n,g,S0),and2))) +* (1GateCircuit (A0,(n,g,S0),and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*A0,N*>,and2a)) +* (1GateCircStr (<*N,(n,g,S0)*>,and2))) +* (1GateCircStr (<*A0,(n,g,S0)*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*A0,N*>,and2a)) +* (1GateCircStr (<*N,(n,g,S0)*>,and2))) +* (1GateCircStr (<*A0,(n,g,S0)*>,and2a))
1GateCircuit ([<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a]*>,or3)
1GateCircuit (<*[<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a]*>,or3)
(BorrowICirc (A0,N,(n,g,S0))) +* (1GateCircuit ([<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr (A0,N,(n,g,S0))) +* (1GateCircStr (<*[<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr (A0,N,(n,g,S0))) +* (1GateCircStr (<*[<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a]*>,or3))
(BitSubtracterCirc (A0,N,(n,g,S0))) +* (BorrowCirc (A0,N,(n,g,S0))) is strict non-empty finitely-generated V107((2GatesCircStr (A0,N,(n,g,S0),'xor')) +* (BorrowStr (A0,N,(n,g,S0)))) gate`2=den Boolean MSAlgebra over (2GatesCircStr (A0,N,(n,g,S0),'xor')) +* (BorrowStr (A0,N,(n,g,S0)))
(n,g,S0) +* (BitSubtracterWithBorrowCirc (A0,N,(n,g,S0))) is strict non-empty finitely-generated V107((n,g,S0) +* (BitSubtracterWithBorrowStr (A0,N,(n,g,S0)))) gate`2=den Boolean MSAlgebra over (n,g,S0) +* (BitSubtracterWithBorrowStr (A0,N,(n,g,S0)))
((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)) is Element of InnerVertices ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>))
the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)) is non empty set
InnerVertices ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)) is non empty Element of K18( the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)))
K18( the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>))) is set
the ResultSort of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)) is Relation-like Function-like V27( the carrier' of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)), the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>))) Element of K18(K19( the carrier' of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)), the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>))))
the carrier' of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)) is non empty set
K19( the carrier' of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)), the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>))) is Relation-like set
K18(K19( the carrier' of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)), the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)))) is set
K547( the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)), the ResultSort of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>))) is Element of K18( the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)))
BorrowOutput (A0,N,(n,g,S0)) is Element of InnerVertices (BorrowStr (A0,N,(n,g,S0)))
the carrier of (BorrowStr (A0,N,(n,g,S0))) is non empty set
InnerVertices (BorrowStr (A0,N,(n,g,S0))) is non empty Element of K18( the carrier of (BorrowStr (A0,N,(n,g,S0))))
K18( the carrier of (BorrowStr (A0,N,(n,g,S0)))) is set
the ResultSort of (BorrowStr (A0,N,(n,g,S0))) is Relation-like Function-like V27( the carrier' of (BorrowStr (A0,N,(n,g,S0))), the carrier of (BorrowStr (A0,N,(n,g,S0)))) Element of K18(K19( the carrier' of (BorrowStr (A0,N,(n,g,S0))), the carrier of (BorrowStr (A0,N,(n,g,S0)))))
the carrier' of (BorrowStr (A0,N,(n,g,S0))) is non empty set
K19( the carrier' of (BorrowStr (A0,N,(n,g,S0))), the carrier of (BorrowStr (A0,N,(n,g,S0)))) is Relation-like set
K18(K19( the carrier' of (BorrowStr (A0,N,(n,g,S0))), the carrier of (BorrowStr (A0,N,(n,g,S0))))) is set
K547( the carrier of (BorrowStr (A0,N,(n,g,S0))), the ResultSort of (BorrowStr (A0,N,(n,g,S0)))) is Element of K18( the carrier of (BorrowStr (A0,N,(n,g,S0))))
[<*[<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a]*>,or3] is non empty pair set
{<*[<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a]*>,or3},{<*[<*A0,N*>,and2a],[<*N,(n,g,S0)*>,and2],[<*A0,(n,g,S0)*>,and2a]*>}} is non empty V36() V40() V51() set
(n,(g ^ <*A0*>),(S0 ^ <*N*>)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,(g ^ <*A0*>),(S0 ^ <*N*>)) is strict non-empty finitely-generated V107((n,(g ^ <*A0*>),(S0 ^ <*N*>))) gate`2=den Boolean MSAlgebra over (n,(g ^ <*A0*>),(S0 ^ <*N*>))
An is Relation-like NAT -defined Function-like V23( NAT ) set
An . n is set
o0 is Relation-like NAT -defined Function-like V23( NAT ) set
o0 . n is set
An . 0 is set
o0 . 0 is set
f1 is Relation-like NAT -defined Function-like V23( NAT ) set
f1 . 0 is set
(n,(g ^ <*A0*>),(S0 ^ <*N*>)) is Element of InnerVertices (n,(g ^ <*A0*>),(S0 ^ <*N*>))
the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>)) is non empty set
InnerVertices (n,(g ^ <*A0*>),(S0 ^ <*N*>)) is non empty Element of K18( the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>)))
K18( the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>))) is set
the ResultSort of (n,(g ^ <*A0*>),(S0 ^ <*N*>)) is Relation-like Function-like V27( the carrier' of (n,(g ^ <*A0*>),(S0 ^ <*N*>)), the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>))) Element of K18(K19( the carrier' of (n,(g ^ <*A0*>),(S0 ^ <*N*>)), the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>))))
the carrier' of (n,(g ^ <*A0*>),(S0 ^ <*N*>)) is non empty set
K19( the carrier' of (n,(g ^ <*A0*>),(S0 ^ <*N*>)), the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>))) is Relation-like set
K18(K19( the carrier' of (n,(g ^ <*A0*>),(S0 ^ <*N*>)), the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>)))) is set
K547( the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>)), the ResultSort of (n,(g ^ <*A0*>),(S0 ^ <*N*>))) is Element of K18( the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>)))
f1 . n is set
An . (n + 1) is set
o0 . (n + 1) is set
f1 . (n + 1) is set
len g is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
len S0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
(g ^ <*A0*>) . (n + 1) is set
(S0 ^ <*N*>) . (n + 1) is set
g ^ {} is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
S0 ^ {} is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
n + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
g is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
((n + 1),f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f . (n + 1) is set
g . (n + 1) is set
(n,f,g) is Element of InnerVertices (n,f,g)
the carrier of (n,f,g) is non empty set
InnerVertices (n,f,g) is non empty Element of K18( the carrier of (n,f,g))
K18( the carrier of (n,f,g)) is set
the ResultSort of (n,f,g) is Relation-like Function-like V27( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K19( the carrier' of (n,f,g), the carrier of (n,f,g)) is Relation-like set
K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g))) is set
K547( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K18( the carrier of (n,f,g))
BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (n + 1)),(g . (n + 1)),(n,f,g),'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),(g . (n + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,'xor'] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (n + 1)),(g . (n + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'xor'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (n + 1)),(n,f,g)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),(n,f,g)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (n + 1)),(n,f,g)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2))) +* (1GateCircStr (<*(f . (n + 1)),(n,f,g)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,and2a] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (n + 1)),(g . (n + 1))*>,and2a},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (n + 1)),(n,f,g)*>,and2] is non empty pair set
{<*(g . (n + 1)),(n,f,g)*>,and2} is non empty functional V36() V51() set
{<*(g . (n + 1)),(n,f,g)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (n + 1)),(n,f,g)*>,and2},{<*(g . (n + 1)),(n,f,g)*>}} is non empty V36() V40() V51() set
[<*(f . (n + 1)),(n,f,g)*>,and2a] is non empty pair set
{<*(f . (n + 1)),(n,f,g)*>,and2a} is non empty functional V36() V51() set
{<*(f . (n + 1)),(n,f,g)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (n + 1)),(n,f,g)*>,and2a},{<*(f . (n + 1)),(n,f,g)*>}} is non empty V36() V40() V51() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (n + 1)),(g . (n + 1)),(n,f,g),'xor')) +* (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((n + 1),f,g) is strict non-empty finitely-generated V107(((n + 1),f,g)) gate`2=den Boolean MSAlgebra over ((n + 1),f,g)
(n,f,g) is strict non-empty finitely-generated V107((n,f,g)) gate`2=den Boolean MSAlgebra over (n,f,g)
BitSubtracterWithBorrowCirc ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is strict non-empty finitely-generated V107( BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) gate`2=den Boolean MSAlgebra over BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))
BitSubtracterCirc ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is strict non-empty finitely-generated V107( 2GatesCircStr ((f . (n + 1)),(g . (n + 1)),(n,f,g),'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (n + 1)),(g . (n + 1)),(n,f,g),'xor')
2GatesCircuit ((f . (n + 1)),(g . (n + 1)),(n,f,g),'xor') is strict non-empty finitely-generated V107( 2GatesCircStr ((f . (n + 1)),(g . (n + 1)),(n,f,g),'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (n + 1)),(g . (n + 1)),(n,f,g),'xor')
1GateCircuit ((f . (n + 1)),(g . (n + 1)),'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')
1GateCircuit (<*(f . (n + 1)),(g . (n + 1))*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')
1GateCircuit ([<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g),'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*>,'xor')
1GateCircuit (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*>,'xor')
(1GateCircuit ((f . (n + 1)),(g . (n + 1)),'xor')) +* (1GateCircuit ([<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g),'xor')) is strict non-empty finitely-generated V107((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*>,'xor'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*>,'xor'))
BorrowCirc ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is strict non-empty finitely-generated V107( BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) gate`2=den Boolean MSAlgebra over BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))
BorrowICirc ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is strict non-empty finitely-generated V107( BorrowIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) gate`2=den Boolean MSAlgebra over BorrowIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))
1GateCircuit ((f . (n + 1)),(g . (n + 1)),and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)
1GateCircuit (<*(f . (n + 1)),(g . (n + 1))*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)
1GateCircuit ((g . (n + 1)),(n,f,g),and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2)
1GateCircuit (<*(g . (n + 1)),(n,f,g)*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2)
(1GateCircuit ((f . (n + 1)),(g . (n + 1)),and2a)) +* (1GateCircuit ((g . (n + 1)),(n,f,g),and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2))
1GateCircuit ((f . (n + 1)),(n,f,g),and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (n + 1)),(n,f,g)*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),(n,f,g)*>,and2a)
1GateCircuit (<*(f . (n + 1)),(n,f,g)*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (n + 1)),(n,f,g)*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),(n,f,g)*>,and2a)
((1GateCircuit ((f . (n + 1)),(g . (n + 1)),and2a)) +* (1GateCircuit ((g . (n + 1)),(n,f,g),and2))) +* (1GateCircuit ((f . (n + 1)),(n,f,g),and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2))) +* (1GateCircStr (<*(f . (n + 1)),(n,f,g)*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2))) +* (1GateCircStr (<*(f . (n + 1)),(n,f,g)*>,and2a))
1GateCircuit ([<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>,or3)
1GateCircuit (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>,or3)
(BorrowICirc ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (1GateCircuit ([<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>,or3))
(BitSubtracterCirc ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (BorrowCirc ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is strict non-empty finitely-generated V107((2GatesCircStr ((f . (n + 1)),(g . (n + 1)),(n,f,g),'xor')) +* (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),(n,f,g),'xor')) +* (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))
(n,f,g) +* (BitSubtracterWithBorrowCirc ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is strict non-empty finitely-generated V107((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) gate`2=den Boolean MSAlgebra over (n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))
((n + 1),f,g) is Element of InnerVertices ((n + 1),f,g)
the carrier of ((n + 1),f,g) is non empty set
InnerVertices ((n + 1),f,g) is non empty Element of K18( the carrier of ((n + 1),f,g))
K18( the carrier of ((n + 1),f,g)) is set
the ResultSort of ((n + 1),f,g) is Relation-like Function-like V27( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) Element of K18(K19( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)))
the carrier' of ((n + 1),f,g) is non empty set
K19( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) is Relation-like set
K18(K19( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g))) is set
K547( the carrier of ((n + 1),f,g), the ResultSort of ((n + 1),f,g)) is Element of K18( the carrier of ((n + 1),f,g))
BorrowOutput ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is Element of InnerVertices (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))
the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty set
InnerVertices (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty Element of K18( the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))
K18( the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is set
the ResultSort of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is Relation-like Function-like V27( the carrier' of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) Element of K18(K19( the carrier' of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))))
the carrier' of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty set
K19( the carrier' of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is Relation-like set
K18(K19( the carrier' of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))) is set
K547( the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the ResultSort of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is Element of K18( the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))
[<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>,or3] is non empty pair set
{<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>,or3},{<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>}} is non empty V36() V40() V51() set
A0 is Relation-like NAT -defined Function-like V23( NAT ) set
A0 . n is set
N is Relation-like NAT -defined Function-like V23( NAT ) set
N . n is set
A0 . 0 is set
N . 0 is set
h is Relation-like NAT -defined Function-like V23( NAT ) set
h . 0 is set
h . n is set
A0 . (n + 1) is set
N . (n + 1) is set
h . (n + 1) is set
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
f is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
g is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
S0 is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
(n,g,S0) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (n,g,S0) is non empty Element of K18( the carrier of (n,g,S0))
the carrier of (n,g,S0) is non empty set
K18( the carrier of (n,g,S0)) is set
the ResultSort of (n,g,S0) is Relation-like Function-like V27( the carrier' of (n,g,S0), the carrier of (n,g,S0)) Element of K18(K19( the carrier' of (n,g,S0), the carrier of (n,g,S0)))
the carrier' of (n,g,S0) is non empty set
K19( the carrier' of (n,g,S0), the carrier of (n,g,S0)) is Relation-like set
K18(K19( the carrier' of (n,g,S0), the carrier of (n,g,S0))) is set
K547( the carrier of (n,g,S0), the ResultSort of (n,g,S0)) is Element of K18( the carrier of (n,g,S0))
(f,g,S0) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (f,g,S0) is non empty Element of K18( the carrier of (f,g,S0))
the carrier of (f,g,S0) is non empty set
K18( the carrier of (f,g,S0)) is set
the ResultSort of (f,g,S0) is Relation-like Function-like V27( the carrier' of (f,g,S0), the carrier of (f,g,S0)) Element of K18(K19( the carrier' of (f,g,S0), the carrier of (f,g,S0)))
the carrier' of (f,g,S0) is non empty set
K19( the carrier' of (f,g,S0), the carrier of (f,g,S0)) is Relation-like set
K18(K19( the carrier' of (f,g,S0), the carrier of (f,g,S0))) is set
K547( the carrier of (f,g,S0), the ResultSort of (f,g,S0)) is Element of K18( the carrier of (f,g,S0))
A0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
n + A0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
n + 0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
((n + 0),g,S0) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + 0),g,S0) is non empty Element of K18( the carrier of ((n + 0),g,S0))
the carrier of ((n + 0),g,S0) is non empty set
K18( the carrier of ((n + 0),g,S0)) is set
the ResultSort of ((n + 0),g,S0) is Relation-like Function-like V27( the carrier' of ((n + 0),g,S0), the carrier of ((n + 0),g,S0)) Element of K18(K19( the carrier' of ((n + 0),g,S0), the carrier of ((n + 0),g,S0)))
the carrier' of ((n + 0),g,S0) is non empty set
K19( the carrier' of ((n + 0),g,S0), the carrier of ((n + 0),g,S0)) is Relation-like set
K18(K19( the carrier' of ((n + 0),g,S0), the carrier of ((n + 0),g,S0))) is set
K547( the carrier of ((n + 0),g,S0), the ResultSort of ((n + 0),g,S0)) is Element of K18( the carrier of ((n + 0),g,S0))
h is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
n + h is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
((n + h),g,S0) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + h),g,S0) is non empty Element of K18( the carrier of ((n + h),g,S0))
the carrier of ((n + h),g,S0) is non empty set
K18( the carrier of ((n + h),g,S0)) is set
the ResultSort of ((n + h),g,S0) is Relation-like Function-like V27( the carrier' of ((n + h),g,S0), the carrier of ((n + h),g,S0)) Element of K18(K19( the carrier' of ((n + h),g,S0), the carrier of ((n + h),g,S0)))
the carrier' of ((n + h),g,S0) is non empty set
K19( the carrier' of ((n + h),g,S0), the carrier of ((n + h),g,S0)) is Relation-like set
K18(K19( the carrier' of ((n + h),g,S0), the carrier of ((n + h),g,S0))) is set
K547( the carrier of ((n + h),g,S0), the ResultSort of ((n + h),g,S0)) is Element of K18( the carrier of ((n + h),g,S0))
h + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
n + (h + 1) is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
((n + (h + 1)),g,S0) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + (h + 1)),g,S0) is non empty Element of K18( the carrier of ((n + (h + 1)),g,S0))
the carrier of ((n + (h + 1)),g,S0) is non empty set
K18( the carrier of ((n + (h + 1)),g,S0)) is set
the ResultSort of ((n + (h + 1)),g,S0) is Relation-like Function-like V27( the carrier' of ((n + (h + 1)),g,S0), the carrier of ((n + (h + 1)),g,S0)) Element of K18(K19( the carrier' of ((n + (h + 1)),g,S0), the carrier of ((n + (h + 1)),g,S0)))
the carrier' of ((n + (h + 1)),g,S0) is non empty set
K19( the carrier' of ((n + (h + 1)),g,S0), the carrier of ((n + (h + 1)),g,S0)) is Relation-like set
K18(K19( the carrier' of ((n + (h + 1)),g,S0), the carrier of ((n + (h + 1)),g,S0))) is set
K547( the carrier of ((n + (h + 1)),g,S0), the ResultSort of ((n + (h + 1)),g,S0)) is Element of K18( the carrier of ((n + (h + 1)),g,S0))
(n + h) + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
g . ((n + h) + 1) is set
S0 . ((n + h) + 1) is set
((n + h),g,S0) is Element of InnerVertices ((n + h),g,S0)
BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0),'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'xor'] is non empty pair set
{<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'xor'},{<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>}} is non empty V36() V40() V51() set
<*[<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'xor'],((n + h),g,S0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'xor'],((n + h),g,S0)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'xor')) +* (1GateCircStr (<*[<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'xor'],((n + h),g,S0)*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(S0 . ((n + h) + 1)),((n + h),g,S0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,and2a)) +* (1GateCircStr (<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . ((n + h) + 1)),((n + h),g,S0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . ((n + h) + 1)),((n + h),g,S0)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,and2a)) +* (1GateCircStr (<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,and2))) +* (1GateCircStr (<*(g . ((n + h) + 1)),((n + h),g,S0)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,and2a] is non empty pair set
{<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,and2a},{<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>}} is non empty V36() V40() V51() set
[<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,and2] is non empty pair set
{<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,and2} is non empty functional V36() V51() set
{<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,and2},{<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>}} is non empty V36() V40() V51() set
[<*(g . ((n + h) + 1)),((n + h),g,S0)*>,and2a] is non empty pair set
{<*(g . ((n + h) + 1)),((n + h),g,S0)*>,and2a} is non empty functional V36() V51() set
{<*(g . ((n + h) + 1)),((n + h),g,S0)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . ((n + h) + 1)),((n + h),g,S0)*>,and2a},{<*(g . ((n + h) + 1)),((n + h),g,S0)*>}} is non empty V36() V40() V51() set
<*[<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,and2a],[<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,and2],[<*(g . ((n + h) + 1)),((n + h),g,S0)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,and2a],[<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,and2],[<*(g . ((n + h) + 1)),((n + h),g,S0)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) +* (1GateCircStr (<*[<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,and2a],[<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,and2],[<*(g . ((n + h) + 1)),((n + h),g,S0)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0),'xor')) +* (BorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) is non empty Element of K18( the carrier of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))
the carrier of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) is non empty set
K18( the carrier of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is set
the ResultSort of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))), the carrier of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))), the carrier of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))))
the carrier' of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))), the carrier of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))), the carrier of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))) is set
K547( the carrier of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))), the ResultSort of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))
(InnerVertices (n,g,S0)) \/ (InnerVertices (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is non empty set
(InnerVertices ((n + h),g,S0)) \/ (InnerVertices (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is non empty set
((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is non empty Element of K18( the carrier of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))))
the carrier of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is non empty set
K18( the carrier of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))) is set
the ResultSort of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is Relation-like Function-like V27( the carrier' of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))), the carrier of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))) Element of K18(K19( the carrier' of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))), the carrier of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))))
the carrier' of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is non empty set
K19( the carrier' of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))), the carrier of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))) is Relation-like set
K18(K19( the carrier' of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))), the carrier of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))))) is set
K547( the carrier of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))), the ResultSort of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))) is Element of K18( the carrier of (((n + h),g,S0) +* (BitSubtracterWithBorrowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))))
N is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
n + N is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
n + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
g is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
((n + 1),f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + 1),f,g) is non empty Element of K18( the carrier of ((n + 1),f,g))
the carrier of ((n + 1),f,g) is non empty set
K18( the carrier of ((n + 1),f,g)) is set
the ResultSort of ((n + 1),f,g) is Relation-like Function-like V27( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) Element of K18(K19( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)))
the carrier' of ((n + 1),f,g) is non empty set
K19( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) is Relation-like set
K18(K19( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g))) is set
K547( the carrier of ((n + 1),f,g), the ResultSort of ((n + 1),f,g)) is Element of K18( the carrier of ((n + 1),f,g))
(n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (n,f,g) is non empty Element of K18( the carrier of (n,f,g))
the carrier of (n,f,g) is non empty set
K18( the carrier of (n,f,g)) is set
the ResultSort of (n,f,g) is Relation-like Function-like V27( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K19( the carrier' of (n,f,g), the carrier of (n,f,g)) is Relation-like set
K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g))) is set
K547( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K18( the carrier of (n,f,g))
f . (n + 1) is set
g . (n + 1) is set
(n,f,g) is Element of InnerVertices (n,f,g)
BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (n + 1)),(g . (n + 1)),(n,f,g),'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),(g . (n + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,'xor'] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (n + 1)),(g . (n + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'xor'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (n + 1)),(n,f,g)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),(n,f,g)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (n + 1)),(n,f,g)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,and2))) +* (1GateCircStr (<*(f . (n + 1)),(n,f,g)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,and2a] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (n + 1)),(g . (n + 1))*>,and2a},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (n + 1)),(n,f,g)*>,and2] is non empty pair set
{<*(g . (n + 1)),(n,f,g)*>,and2} is non empty functional V36() V51() set
{<*(g . (n + 1)),(n,f,g)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (n + 1)),(n,f,g)*>,and2},{<*(g . (n + 1)),(n,f,g)*>}} is non empty V36() V40() V51() set
[<*(f . (n + 1)),(n,f,g)*>,and2a] is non empty pair set
{<*(f . (n + 1)),(n,f,g)*>,and2a} is non empty functional V36() V51() set
{<*(f . (n + 1)),(n,f,g)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (n + 1)),(n,f,g)*>,and2a},{<*(f . (n + 1)),(n,f,g)*>}} is non empty V36() V40() V51() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),(n,f,g)*>,and2],[<*(f . (n + 1)),(n,f,g)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (n + 1)),(g . (n + 1)),(n,f,g),'xor')) +* (BorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty Element of K18( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))
the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty set
K18( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is set
the ResultSort of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))))
the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))) is set
K547( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the ResultSort of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))
(InnerVertices (n,f,g)) \/ (InnerVertices (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is non empty set
(n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is non empty Element of K18( the carrier of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))))
the carrier of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is non empty set
K18( the carrier of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))) is set
the ResultSort of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is Relation-like Function-like V27( the carrier' of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))), the carrier of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))) Element of K18(K19( the carrier' of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))), the carrier of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))))
the carrier' of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is non empty set
K19( the carrier' of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))), the carrier of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))) is Relation-like set
K18(K19( the carrier' of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))), the carrier of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))))) is set
K547( the carrier of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))), the ResultSort of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))) is Element of K18( the carrier of ((n,f,g) +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))))
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
f is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
g is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
S0 is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
(f,g,S0) is non empty non void V71() 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 K18( the carrier of (f,g,S0))
K18( the carrier of (f,g,S0)) is set
the ResultSort of (f,g,S0) is Relation-like Function-like V27( the carrier' of (f,g,S0), the carrier of (f,g,S0)) Element of K18(K19( the carrier' of (f,g,S0), the carrier of (f,g,S0)))
the carrier' of (f,g,S0) is non empty set
K19( the carrier' of (f,g,S0), the carrier of (f,g,S0)) is Relation-like set
K18(K19( the carrier' of (f,g,S0), the carrier of (f,g,S0))) is set
K547( the carrier of (f,g,S0), the ResultSort of (f,g,S0)) is Element of K18( the carrier of (f,g,S0))
g . n is set
S0 . n is set
h is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
h + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
A0 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 V71() 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 K18( the carrier of (h,g,S0))
K18( the carrier of (h,g,S0)) is set
the ResultSort of (h,g,S0) is Relation-like Function-like V27( the carrier' of (h,g,S0), the carrier of (h,g,S0)) Element of K18(K19( the carrier' of (h,g,S0), the carrier of (h,g,S0)))
the carrier' of (h,g,S0) is non empty set
K19( the carrier' of (h,g,S0), the carrier of (h,g,S0)) is Relation-like set
K18(K19( the carrier' of (h,g,S0), the carrier of (h,g,S0))) is set
K547( the carrier of (h,g,S0), the ResultSort of (h,g,S0)) is Element of K18( the carrier of (h,g,S0))
BitSubtracterOutput ((g . n),(S0 . n),(h,g,S0)) is Element of InnerVertices (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor'))
2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . n),(S0 . n)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . n),(S0 . n)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . n),(S0 . n)*>,'xor'] is non empty pair set
{<*(g . n),(S0 . n)*>,'xor'} is non empty functional V36() V51() set
{<*(g . n),(S0 . n)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . n),(S0 . n)*>,'xor'},{<*(g . n),(S0 . n)*>}} is non empty V36() V40() V51() set
<*[<*(g . n),(S0 . n)*>,'xor'],(h,g,S0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(g . n),(S0 . n)*>,'xor'],(h,g,S0)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . n),(S0 . n)*>,'xor')) +* (1GateCircStr (<*[<*(g . n),(S0 . n)*>,'xor'],(h,g,S0)*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')) is non empty set
InnerVertices (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')) is non empty Element of K18( the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')))
K18( the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor'))) is set
the ResultSort of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')) is Relation-like Function-like V27( the carrier' of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')), the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor'))) Element of K18(K19( the carrier' of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')), the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor'))))
the carrier' of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')) is non empty set
K19( the carrier' of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')), the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor'))) is Relation-like set
K18(K19( the carrier' of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')), the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')))) is set
K547( the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')), the ResultSort of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor'))) is Element of K18( the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')))
2GatesCircOutput ((g . n),(S0 . n),(h,g,S0),'xor') is non empty pair Element of InnerVertices (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor'))
[<*[<*(g . n),(S0 . n)*>,'xor'],(h,g,S0)*>,'xor'] is non empty pair set
{<*[<*(g . n),(S0 . n)*>,'xor'],(h,g,S0)*>,'xor'} is non empty functional V36() V51() set
{<*[<*(g . n),(S0 . n)*>,'xor'],(h,g,S0)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(g . n),(S0 . n)*>,'xor'],(h,g,S0)*>,'xor'},{<*[<*(g . n),(S0 . n)*>,'xor'],(h,g,S0)*>}} is non empty V36() V40() V51() set
Sn is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
Sn + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
N is Element of InnerVertices (f,g,S0)
(Sn,g,S0) is Element of InnerVertices (Sn,g,S0)
(Sn,g,S0) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (Sn,g,S0) is non empty set
InnerVertices (Sn,g,S0) is non empty Element of K18( the carrier of (Sn,g,S0))
K18( the carrier of (Sn,g,S0)) is set
the ResultSort of (Sn,g,S0) is Relation-like Function-like V27( the carrier' of (Sn,g,S0), the carrier of (Sn,g,S0)) Element of K18(K19( the carrier' of (Sn,g,S0), the carrier of (Sn,g,S0)))
the carrier' of (Sn,g,S0) is non empty set
K19( the carrier' of (Sn,g,S0), the carrier of (Sn,g,S0)) is Relation-like set
K18(K19( the carrier' of (Sn,g,S0), the carrier of (Sn,g,S0))) is set
K547( the carrier of (Sn,g,S0), the ResultSort of (Sn,g,S0)) is Element of K18( the carrier of (Sn,g,S0))
BitSubtracterOutput ((g . n),(S0 . n),(Sn,g,S0)) is Element of InnerVertices (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor'))
2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . n),(S0 . n)*>,'xor')) +* (1GateCircStr (<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')) is non empty set
InnerVertices (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')) is non empty Element of K18( the carrier of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')))
K18( the carrier of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor'))) is set
the ResultSort of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')) is Relation-like Function-like V27( the carrier' of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')), the carrier of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor'))) Element of K18(K19( the carrier' of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')), the carrier of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor'))))
the carrier' of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')) is non empty set
K19( the carrier' of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')), the carrier of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor'))) is Relation-like set
K18(K19( the carrier' of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')), the carrier of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')))) is set
K547( the carrier of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')), the ResultSort of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor'))) is Element of K18( the carrier of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')))
2GatesCircOutput ((g . n),(S0 . n),(Sn,g,S0),'xor') is non empty pair Element of InnerVertices (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor'))
[<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*>,'xor'] is non empty pair set
{<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*>,'xor'} is non empty functional V36() V51() set
{<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*>,'xor'},{<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*>}} is non empty V36() V40() V51() set
A0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
1 + A0 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
N is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
(N,g,S0) is Element of InnerVertices (N,g,S0)
(N,g,S0) is non empty non void V71() 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 K18( the carrier of (N,g,S0))
K18( the carrier of (N,g,S0)) is set
the ResultSort of (N,g,S0) is Relation-like Function-like V27( the carrier' of (N,g,S0), the carrier of (N,g,S0)) Element of K18(K19( the carrier' of (N,g,S0), the carrier of (N,g,S0)))
the carrier' of (N,g,S0) is non empty set
K19( the carrier' of (N,g,S0), the carrier of (N,g,S0)) is Relation-like set
K18(K19( the carrier' of (N,g,S0), the carrier of (N,g,S0))) is set
K547( the carrier of (N,g,S0), the ResultSort of (N,g,S0)) is Element of K18( the carrier of (N,g,S0))
BitSubtracterOutput ((g . n),(S0 . n),(N,g,S0)) is Element of InnerVertices (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor'))
2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . n),(S0 . n)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . n),(S0 . n)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . n),(S0 . n)*>,'xor'] is non empty pair set
{<*(g . n),(S0 . n)*>,'xor'} is non empty functional V36() V51() set
{<*(g . n),(S0 . n)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . n),(S0 . n)*>,'xor'},{<*(g . n),(S0 . n)*>}} is non empty V36() V40() V51() set
<*[<*(g . n),(S0 . n)*>,'xor'],(N,g,S0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(g . n),(S0 . n)*>,'xor'],(N,g,S0)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . n),(S0 . n)*>,'xor')) +* (1GateCircStr (<*[<*(g . n),(S0 . n)*>,'xor'],(N,g,S0)*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor')) is non empty set
InnerVertices (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor')) is non empty Element of K18( the carrier of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor')))
K18( the carrier of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor'))) is set
the ResultSort of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor')) is Relation-like Function-like V27( the carrier' of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor')), the carrier of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor'))) Element of K18(K19( the carrier' of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor')), the carrier of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor'))))
the carrier' of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor')) is non empty set
K19( the carrier' of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor')), the carrier of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor'))) is Relation-like set
K18(K19( the carrier' of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor')), the carrier of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor')))) is set
K547( the carrier of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor')), the ResultSort of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor'))) is Element of K18( the carrier of (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor')))
2GatesCircOutput ((g . n),(S0 . n),(N,g,S0),'xor') is non empty pair Element of InnerVertices (2GatesCircStr ((g . n),(S0 . n),(N,g,S0),'xor'))
[<*[<*(g . n),(S0 . n)*>,'xor'],(N,g,S0)*>,'xor'] is non empty pair set
{<*[<*(g . n),(S0 . n)*>,'xor'],(N,g,S0)*>,'xor'} is non empty functional V36() V51() set
{<*[<*(g . n),(S0 . n)*>,'xor'],(N,g,S0)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(g . n),(S0 . n)*>,'xor'],(N,g,S0)*>,'xor'},{<*[<*(g . n),(S0 . n)*>,'xor'],(N,g,S0)*>}} is non empty V36() V40() V51() set
(n,g,S0) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (n,g,S0) is non empty Element of K18( the carrier of (n,g,S0))
the carrier of (n,g,S0) is non empty set
K18( the carrier of (n,g,S0)) is set
the ResultSort of (n,g,S0) is Relation-like Function-like V27( the carrier' of (n,g,S0), the carrier of (n,g,S0)) Element of K18(K19( the carrier' of (n,g,S0), the carrier of (n,g,S0)))
the carrier' of (n,g,S0) is non empty set
K19( the carrier' of (n,g,S0), the carrier of (n,g,S0)) is Relation-like set
K18(K19( the carrier' of (n,g,S0), the carrier of (n,g,S0))) is set
K547( the carrier of (n,g,S0), the ResultSort of (n,g,S0)) is Element of K18( the carrier of (n,g,S0))
N + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
g . (N + 1) is set
S0 . (N + 1) is set
BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0),'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (N + 1)),(S0 . (N + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (N + 1)),(S0 . (N + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . (N + 1)),(S0 . (N + 1))*>,'xor'] is non empty pair set
{<*(g . (N + 1)),(S0 . (N + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(g . (N + 1)),(S0 . (N + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (N + 1)),(S0 . (N + 1))*>,'xor'},{<*(g . (N + 1)),(S0 . (N + 1))*>}} is non empty V36() V40() V51() set
<*[<*(g . (N + 1)),(S0 . (N + 1))*>,'xor'],(N,g,S0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(g . (N + 1)),(S0 . (N + 1))*>,'xor'],(N,g,S0)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . (N + 1)),(S0 . (N + 1))*>,'xor')) +* (1GateCircStr (<*[<*(g . (N + 1)),(S0 . (N + 1))*>,'xor'],(N,g,S0)*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(g . (N + 1)),(S0 . (N + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(S0 . (N + 1)),(N,g,S0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(S0 . (N + 1)),(N,g,S0)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . (N + 1)),(S0 . (N + 1))*>,and2a)) +* (1GateCircStr (<*(S0 . (N + 1)),(N,g,S0)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (N + 1)),(N,g,S0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (N + 1)),(N,g,S0)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(g . (N + 1)),(S0 . (N + 1))*>,and2a)) +* (1GateCircStr (<*(S0 . (N + 1)),(N,g,S0)*>,and2))) +* (1GateCircStr (<*(g . (N + 1)),(N,g,S0)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . (N + 1)),(S0 . (N + 1))*>,and2a] is non empty pair set
{<*(g . (N + 1)),(S0 . (N + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(g . (N + 1)),(S0 . (N + 1))*>,and2a},{<*(g . (N + 1)),(S0 . (N + 1))*>}} is non empty V36() V40() V51() set
[<*(S0 . (N + 1)),(N,g,S0)*>,and2] is non empty pair set
{<*(S0 . (N + 1)),(N,g,S0)*>,and2} is non empty functional V36() V51() set
{<*(S0 . (N + 1)),(N,g,S0)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(S0 . (N + 1)),(N,g,S0)*>,and2},{<*(S0 . (N + 1)),(N,g,S0)*>}} is non empty V36() V40() V51() set
[<*(g . (N + 1)),(N,g,S0)*>,and2a] is non empty pair set
{<*(g . (N + 1)),(N,g,S0)*>,and2a} is non empty functional V36() V51() set
{<*(g . (N + 1)),(N,g,S0)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (N + 1)),(N,g,S0)*>,and2a},{<*(g . (N + 1)),(N,g,S0)*>}} is non empty V36() V40() V51() set
<*[<*(g . (N + 1)),(S0 . (N + 1))*>,and2a],[<*(S0 . (N + 1)),(N,g,S0)*>,and2],[<*(g . (N + 1)),(N,g,S0)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(g . (N + 1)),(S0 . (N + 1))*>,and2a],[<*(S0 . (N + 1)),(N,g,S0)*>,and2],[<*(g . (N + 1)),(N,g,S0)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))) +* (1GateCircStr (<*[<*(g . (N + 1)),(S0 . (N + 1))*>,and2a],[<*(S0 . (N + 1)),(N,g,S0)*>,and2],[<*(g . (N + 1)),(N,g,S0)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0),'xor')) +* (BorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))) is non empty Element of K18( the carrier of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))))
the carrier of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))) is non empty set
K18( the carrier of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0)))) is set
the ResultSort of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))), the carrier of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0)))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))), the carrier of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0)))))
the carrier' of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))), the carrier of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0)))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))), the carrier of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))))) is set
K547( the carrier of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))), the ResultSort of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0)))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))))
(N,g,S0) +* (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0))) \/ the carrier of (N,g,S0) is non empty set
Sn is Element of the carrier of (BitSubtracterWithBorrowStr ((g . (N + 1)),(S0 . (N + 1)),(N,g,S0)))
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
f is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
f + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
g is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
S0 is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
((f + 1),n,g,S0) is Element of InnerVertices (n,g,S0)
(n,g,S0) is non empty non void V71() 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 K18( the carrier of (n,g,S0))
K18( the carrier of (n,g,S0)) is set
the ResultSort of (n,g,S0) is Relation-like Function-like V27( the carrier' of (n,g,S0), the carrier of (n,g,S0)) Element of K18(K19( the carrier' of (n,g,S0), the carrier of (n,g,S0)))
the carrier' of (n,g,S0) is non empty set
K19( the carrier' of (n,g,S0), the carrier of (n,g,S0)) is Relation-like set
K18(K19( the carrier' of (n,g,S0), the carrier of (n,g,S0))) is set
K547( the carrier of (n,g,S0), the ResultSort of (n,g,S0)) is Element of K18( the carrier of (n,g,S0))
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 V71() 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 K18( the carrier of (f,g,S0))
K18( the carrier of (f,g,S0)) is set
the ResultSort of (f,g,S0) is Relation-like Function-like V27( the carrier' of (f,g,S0), the carrier of (f,g,S0)) Element of K18(K19( the carrier' of (f,g,S0), the carrier of (f,g,S0)))
the carrier' of (f,g,S0) is non empty set
K19( the carrier' of (f,g,S0), the carrier of (f,g,S0)) is Relation-like set
K18(K19( the carrier' of (f,g,S0), the carrier of (f,g,S0))) is set
K547( the carrier of (f,g,S0), the ResultSort of (f,g,S0)) is Element of K18( the carrier of (f,g,S0))
BitSubtracterOutput ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0)) is Element of InnerVertices (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor'))
2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (f + 1)),(S0 . (f + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (f + 1)),(S0 . (f + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'] is non empty pair set
{<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(g . (f + 1)),(S0 . (f + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'},{<*(g . (f + 1)),(S0 . (f + 1))*>}} is non empty V36() V40() V51() set
<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(f,g,S0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(f,g,S0)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . (f + 1)),(S0 . (f + 1))*>,'xor')) +* (1GateCircStr (<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(f,g,S0)*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')) is non empty set
InnerVertices (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')) is non empty Element of K18( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')))
K18( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor'))) is set
the ResultSort of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')) is Relation-like Function-like V27( the carrier' of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')), the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor'))) Element of K18(K19( the carrier' of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')), the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor'))))
the carrier' of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')) is non empty set
K19( the carrier' of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')), the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor'))) is Relation-like set
K18(K19( the carrier' of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')), the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')))) is set
K547( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')), the ResultSort of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor'))) is Element of K18( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')))
2GatesCircOutput ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor') is non empty pair Element of InnerVertices (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor'))
[<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(f,g,S0)*>,'xor'] is non empty pair set
{<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(f,g,S0)*>,'xor'} is non empty functional V36() V51() set
{<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(f,g,S0)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(f,g,S0)*>,'xor'},{<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(f,g,S0)*>}} is non empty V36() V40() V51() set
A0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
A0 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
(A0,g,S0) is Element of InnerVertices (A0,g,S0)
(A0,g,S0) is non empty non void V71() 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 K18( the carrier of (A0,g,S0))
K18( the carrier of (A0,g,S0)) is set
the ResultSort of (A0,g,S0) is Relation-like Function-like V27( the carrier' of (A0,g,S0), the carrier of (A0,g,S0)) Element of K18(K19( the carrier' of (A0,g,S0), the carrier of (A0,g,S0)))
the carrier' of (A0,g,S0) is non empty set
K19( the carrier' of (A0,g,S0), the carrier of (A0,g,S0)) is Relation-like set
K18(K19( the carrier' of (A0,g,S0), the carrier of (A0,g,S0))) is set
K547( the carrier of (A0,g,S0), the ResultSort of (A0,g,S0)) is Element of K18( the carrier of (A0,g,S0))
BitSubtracterOutput ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0)) is Element of InnerVertices (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor'))
2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(A0,g,S0)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(A0,g,S0)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . (f + 1)),(S0 . (f + 1))*>,'xor')) +* (1GateCircStr (<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(A0,g,S0)*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')) is non empty set
InnerVertices (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')) is non empty Element of K18( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')))
K18( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor'))) is set
the ResultSort of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')) is Relation-like Function-like V27( the carrier' of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')), the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor'))) Element of K18(K19( the carrier' of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')), the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor'))))
the carrier' of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')) is non empty set
K19( the carrier' of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')), the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor'))) is Relation-like set
K18(K19( the carrier' of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')), the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')))) is set
K547( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')), the ResultSort of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor'))) is Element of K18( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')))
2GatesCircOutput ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor') is non empty pair Element of InnerVertices (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor'))
[<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(A0,g,S0)*>,'xor'] is non empty pair set
{<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(A0,g,S0)*>,'xor'} is non empty functional V36() V51() set
{<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(A0,g,S0)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(A0,g,S0)*>,'xor'},{<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(A0,g,S0)*>}} is non empty V36() V40() V51() set
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
f is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
g is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
(n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (n,f,g) is non empty Element of K18( the carrier of (n,f,g))
the carrier of (n,f,g) is non empty set
K18( the carrier of (n,f,g)) is set
the ResultSort of (n,f,g) is Relation-like Function-like V27( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K19( the carrier' of (n,f,g), the carrier of (n,f,g)) is Relation-like set
K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g))) is set
K547( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K18( the carrier of (n,f,g))
(0,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (0,f,g) is non empty Element of K18( the carrier of (0,f,g))
the carrier of (0,f,g) is non empty set
K18( the carrier of (0,f,g)) is set
the ResultSort of (0,f,g) is Relation-like Function-like V27( the carrier' of (0,f,g), the carrier of (0,f,g)) Element of K18(K19( the carrier' of (0,f,g), the carrier of (0,f,g)))
the carrier' of (0,f,g) is non empty set
K19( the carrier' of (0,f,g), the carrier of (0,f,g)) is Relation-like set
K18(K19( the carrier' of (0,f,g), the carrier of (0,f,g))) is set
K547( the carrier of (0,f,g), the ResultSort of (0,f,g)) is Element of K18( the carrier of (0,f,g))
S0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
(S0,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (S0,f,g) is non empty Element of K18( the carrier of (S0,f,g))
the carrier of (S0,f,g) is non empty set
K18( the carrier of (S0,f,g)) is set
the ResultSort of (S0,f,g) is Relation-like Function-like V27( the carrier' of (S0,f,g), the carrier of (S0,f,g)) Element of K18(K19( the carrier' of (S0,f,g), the carrier of (S0,f,g)))
the carrier' of (S0,f,g) is non empty set
K19( the carrier' of (S0,f,g), the carrier of (S0,f,g)) is Relation-like set
K18(K19( the carrier' of (S0,f,g), the carrier of (S0,f,g))) is set
K547( the carrier of (S0,f,g), the ResultSort of (S0,f,g)) is Element of K18( the carrier of (S0,f,g))
S0 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
((S0 + 1),f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f . (S0 + 1) is set
g . (S0 + 1) is set
(S0,f,g) is Element of InnerVertices (S0,f,g)
BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g),'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (S0 + 1)),(g . (S0 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (S0 + 1)),(g . (S0 + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'xor'] is non empty pair set
{<*(f . (S0 + 1)),(g . (S0 + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (S0 + 1)),(g . (S0 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (S0 + 1)),(g . (S0 + 1))*>,'xor'},{<*(f . (S0 + 1)),(g . (S0 + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'xor'],(S0,f,g)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'xor'],(S0,f,g)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (S0 + 1)),(g . (S0 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'xor'],(S0,f,g)*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (S0 + 1)),(S0,f,g)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (S0 + 1)),(S0,f,g)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (S0 + 1)),(S0,f,g)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (S0 + 1)),(S0,f,g)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (S0 + 1)),(S0,f,g)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (S0 + 1)),(S0,f,g)*>,and2))) +* (1GateCircStr (<*(f . (S0 + 1)),(S0,f,g)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a] is non empty pair set
{<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a},{<*(f . (S0 + 1)),(g . (S0 + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (S0 + 1)),(S0,f,g)*>,and2] is non empty pair set
{<*(g . (S0 + 1)),(S0,f,g)*>,and2} is non empty functional V36() V51() set
{<*(g . (S0 + 1)),(S0,f,g)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (S0 + 1)),(S0,f,g)*>,and2},{<*(g . (S0 + 1)),(S0,f,g)*>}} is non empty V36() V40() V51() set
[<*(f . (S0 + 1)),(S0,f,g)*>,and2a] is non empty pair set
{<*(f . (S0 + 1)),(S0,f,g)*>,and2a} is non empty functional V36() V51() set
{<*(f . (S0 + 1)),(S0,f,g)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (S0 + 1)),(S0,f,g)*>,and2a},{<*(f . (S0 + 1)),(S0,f,g)*>}} is non empty V36() V40() V51() set
<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a],[<*(g . (S0 + 1)),(S0,f,g)*>,and2],[<*(f . (S0 + 1)),(S0,f,g)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a],[<*(g . (S0 + 1)),(S0,f,g)*>,and2],[<*(f . (S0 + 1)),(S0,f,g)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) +* (1GateCircStr (<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a],[<*(g . (S0 + 1)),(S0,f,g)*>,and2],[<*(f . (S0 + 1)),(S0,f,g)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g),'xor')) +* (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(S0,f,g) +* (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty Element of K18( the carrier of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))))
the carrier of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty set
K18( the carrier of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) is set
the ResultSort of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))))
the carrier' of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))))) is set
K547( the carrier of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the ResultSort of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))))
InnerVertices ((S0 + 1),f,g) is non empty Element of K18( the carrier of ((S0 + 1),f,g))
the carrier of ((S0 + 1),f,g) is non empty set
K18( the carrier of ((S0 + 1),f,g)) is set
the ResultSort of ((S0 + 1),f,g) is Relation-like Function-like V27( the carrier' of ((S0 + 1),f,g), the carrier of ((S0 + 1),f,g)) Element of K18(K19( the carrier' of ((S0 + 1),f,g), the carrier of ((S0 + 1),f,g)))
the carrier' of ((S0 + 1),f,g) is non empty set
K19( the carrier' of ((S0 + 1),f,g), the carrier of ((S0 + 1),f,g)) is Relation-like set
K18(K19( the carrier' of ((S0 + 1),f,g), the carrier of ((S0 + 1),f,g))) is set
K547( the carrier of ((S0 + 1),f,g), the ResultSort of ((S0 + 1),f,g)) is Element of K18( the carrier of ((S0 + 1),f,g))
n is set
f is set
g is set
BorrowIStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,f*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*n,f*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*f,g*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*n,g*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BorrowIStr (n,f,g)) is non empty Element of K18( the carrier of (BorrowIStr (n,f,g)))
the carrier of (BorrowIStr (n,f,g)) is non empty set
K18( the carrier of (BorrowIStr (n,f,g))) is set
the ResultSort of (BorrowIStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BorrowIStr (n,f,g)), the carrier of (BorrowIStr (n,f,g))) Element of K18(K19( the carrier' of (BorrowIStr (n,f,g)), the carrier of (BorrowIStr (n,f,g))))
the carrier' of (BorrowIStr (n,f,g)) is non empty set
K19( the carrier' of (BorrowIStr (n,f,g)), the carrier of (BorrowIStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BorrowIStr (n,f,g)), the carrier of (BorrowIStr (n,f,g)))) is set
K547( the carrier of (BorrowIStr (n,f,g)), the ResultSort of (BorrowIStr (n,f,g))) is Element of K18( the carrier of (BorrowIStr (n,f,g)))
[<*n,f*>,and2a] is non empty pair set
{<*n,f*>,and2a} is non empty functional V36() V51() set
{<*n,f*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,f*>,and2a},{<*n,f*>}} is non empty V36() V40() V51() set
[<*f,g*>,and2] is non empty pair set
{<*f,g*>,and2} is non empty functional V36() V51() set
{<*f,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*f,g*>,and2},{<*f,g*>}} is non empty V36() V40() V51() set
[<*n,g*>,and2a] is non empty pair set
{<*n,g*>,and2a} is non empty functional V36() V51() set
{<*n,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,g*>,and2a},{<*n,g*>}} is non empty V36() V40() V51() set
{[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]} is Relation-like V36() V51() set
InnerVertices ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) is non empty Element of K18( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))))
the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) is non empty set
K18( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)))) is set
the ResultSort of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) is Relation-like Function-like V27( the carrier' of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))), the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)))) Element of K18(K19( the carrier' of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))), the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)))))
the carrier' of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) is non empty set
K19( the carrier' of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))), the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)))) is Relation-like set
K18(K19( the carrier' of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))), the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))))) is set
K547( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))), the ResultSort of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)))) is Element of K18( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))))
InnerVertices (1GateCircStr (<*n,g*>,and2a)) is non empty Element of K18( the carrier of (1GateCircStr (<*n,g*>,and2a)))
the carrier of (1GateCircStr (<*n,g*>,and2a)) is non empty set
K18( the carrier of (1GateCircStr (<*n,g*>,and2a))) is set
the ResultSort of (1GateCircStr (<*n,g*>,and2a)) is Relation-like Function-like V27( the carrier' of (1GateCircStr (<*n,g*>,and2a)), the carrier of (1GateCircStr (<*n,g*>,and2a))) Element of K18(K19( the carrier' of (1GateCircStr (<*n,g*>,and2a)), the carrier of (1GateCircStr (<*n,g*>,and2a))))
the carrier' of (1GateCircStr (<*n,g*>,and2a)) is non empty set
K19( the carrier' of (1GateCircStr (<*n,g*>,and2a)), the carrier of (1GateCircStr (<*n,g*>,and2a))) is Relation-like set
K18(K19( the carrier' of (1GateCircStr (<*n,g*>,and2a)), the carrier of (1GateCircStr (<*n,g*>,and2a)))) is set
K547( the carrier of (1GateCircStr (<*n,g*>,and2a)), the ResultSort of (1GateCircStr (<*n,g*>,and2a))) is Element of K18( the carrier of (1GateCircStr (<*n,g*>,and2a)))
(InnerVertices ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)))) \/ (InnerVertices (1GateCircStr (<*n,g*>,and2a))) is non empty set
InnerVertices (1GateCircStr (<*n,f*>,and2a)) is non empty Element of K18( the carrier of (1GateCircStr (<*n,f*>,and2a)))
the carrier of (1GateCircStr (<*n,f*>,and2a)) is non empty set
K18( the carrier of (1GateCircStr (<*n,f*>,and2a))) is set
the ResultSort of (1GateCircStr (<*n,f*>,and2a)) is Relation-like Function-like V27( the carrier' of (1GateCircStr (<*n,f*>,and2a)), the carrier of (1GateCircStr (<*n,f*>,and2a))) Element of K18(K19( the carrier' of (1GateCircStr (<*n,f*>,and2a)), the carrier of (1GateCircStr (<*n,f*>,and2a))))
the carrier' of (1GateCircStr (<*n,f*>,and2a)) is non empty set
K19( the carrier' of (1GateCircStr (<*n,f*>,and2a)), the carrier of (1GateCircStr (<*n,f*>,and2a))) is Relation-like set
K18(K19( the carrier' of (1GateCircStr (<*n,f*>,and2a)), the carrier of (1GateCircStr (<*n,f*>,and2a)))) is set
K547( the carrier of (1GateCircStr (<*n,f*>,and2a)), the ResultSort of (1GateCircStr (<*n,f*>,and2a))) is Element of K18( the carrier of (1GateCircStr (<*n,f*>,and2a)))
InnerVertices (1GateCircStr (<*f,g*>,and2)) is non empty Element of K18( the carrier of (1GateCircStr (<*f,g*>,and2)))
the carrier of (1GateCircStr (<*f,g*>,and2)) is non empty set
K18( the carrier of (1GateCircStr (<*f,g*>,and2))) is set
the ResultSort of (1GateCircStr (<*f,g*>,and2)) is Relation-like Function-like V27( the carrier' of (1GateCircStr (<*f,g*>,and2)), the carrier of (1GateCircStr (<*f,g*>,and2))) Element of K18(K19( the carrier' of (1GateCircStr (<*f,g*>,and2)), the carrier of (1GateCircStr (<*f,g*>,and2))))
the carrier' of (1GateCircStr (<*f,g*>,and2)) is non empty set
K19( the carrier' of (1GateCircStr (<*f,g*>,and2)), the carrier of (1GateCircStr (<*f,g*>,and2))) is Relation-like set
K18(K19( the carrier' of (1GateCircStr (<*f,g*>,and2)), the carrier of (1GateCircStr (<*f,g*>,and2)))) is set
K547( the carrier of (1GateCircStr (<*f,g*>,and2)), the ResultSort of (1GateCircStr (<*f,g*>,and2))) is Element of K18( the carrier of (1GateCircStr (<*f,g*>,and2)))
(InnerVertices (1GateCircStr (<*n,f*>,and2a))) \/ (InnerVertices (1GateCircStr (<*f,g*>,and2))) is non empty set
((InnerVertices (1GateCircStr (<*n,f*>,and2a))) \/ (InnerVertices (1GateCircStr (<*f,g*>,and2)))) \/ (InnerVertices (1GateCircStr (<*n,g*>,and2a))) is non empty set
{[<*n,f*>,and2a]} is non empty V2() Relation-like Function-like constant V36() 1 -element V51() set
{[<*n,f*>,and2a]} \/ (InnerVertices (1GateCircStr (<*f,g*>,and2))) is non empty set
({[<*n,f*>,and2a]} \/ (InnerVertices (1GateCircStr (<*f,g*>,and2)))) \/ (InnerVertices (1GateCircStr (<*n,g*>,and2a))) is non empty set
{[<*f,g*>,and2]} is non empty V2() Relation-like Function-like constant V36() 1 -element V51() set
{[<*n,f*>,and2a]} \/ {[<*f,g*>,and2]} is non empty Relation-like V36() V51() set
({[<*n,f*>,and2a]} \/ {[<*f,g*>,and2]}) \/ (InnerVertices (1GateCircStr (<*n,g*>,and2a))) is non empty set
{[<*n,g*>,and2a]} is non empty V2() Relation-like Function-like constant V36() 1 -element V51() set
({[<*n,f*>,and2a]} \/ {[<*f,g*>,and2]}) \/ {[<*n,g*>,and2a]} is non empty Relation-like V36() V51() set
{[<*n,f*>,and2a],[<*f,g*>,and2]} is non empty Relation-like V36() V51() set
{[<*n,f*>,and2a],[<*f,g*>,and2]} \/ {[<*n,g*>,and2a]} is non empty Relation-like V36() V51() set
n is set
f is set
g is set
<*f,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*f,g*>,and2] is non empty pair set
{<*f,g*>,and2} is non empty functional V36() V51() set
{<*f,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*f,g*>,and2},{<*f,g*>}} is non empty V36() V40() V51() set
<*n,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*n,g*>,and2a] is non empty pair set
{<*n,g*>,and2a} is non empty functional V36() V51() set
{<*n,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,g*>,and2a},{<*n,g*>}} is non empty V36() V40() V51() set
<*n,f*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*n,f*>,and2a] is non empty pair set
{<*n,f*>,and2a} is non empty functional V36() V51() set
{<*n,f*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,f*>,and2a},{<*n,f*>}} is non empty V36() V40() V51() set
BorrowIStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*f,g*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,g*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (BorrowIStr (n,f,g)) is Element of K18( the carrier of (BorrowIStr (n,f,g)))
the carrier of (BorrowIStr (n,f,g)) is non empty set
K18( the carrier of (BorrowIStr (n,f,g))) is set
the ResultSort of (BorrowIStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BorrowIStr (n,f,g)), the carrier of (BorrowIStr (n,f,g))) Element of K18(K19( the carrier' of (BorrowIStr (n,f,g)), the carrier of (BorrowIStr (n,f,g))))
the carrier' of (BorrowIStr (n,f,g)) is non empty set
K19( the carrier' of (BorrowIStr (n,f,g)), the carrier of (BorrowIStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BorrowIStr (n,f,g)), the carrier of (BorrowIStr (n,f,g)))) is set
K547( the carrier of (BorrowIStr (n,f,g)), the ResultSort of (BorrowIStr (n,f,g))) is Element of K18( the carrier of (BorrowIStr (n,f,g)))
the carrier of (BorrowIStr (n,f,g)) \ K547( the carrier of (BorrowIStr (n,f,g)), the ResultSort of (BorrowIStr (n,f,g))) is Element of K18( the carrier of (BorrowIStr (n,f,g)))
{n,f,g} is V36() V51() set
{1,f} is non empty V36() V51() set
{2,f} is non empty V36() V51() set
[1,f] is non empty pair set
{1} is non empty V2() V36() V40() 1 -element V51() non with_pair set
{{1,f},{1}} is non empty V36() V40() V51() set
[2,f] is non empty pair set
{2} is non empty V2() V36() V40() 1 -element V51() non with_pair set
{{2,f},{2}} is non empty V36() V40() V51() set
<*f*> is non empty V2() Relation-like NAT -defined Function-like constant V36() 1 -element FinSequence-like FinSubsequence-like V51() set
<*g*> is non empty V2() Relation-like NAT -defined Function-like constant V36() 1 -element FinSequence-like FinSubsequence-like V51() set
<*f*> ^ <*g*> is non empty Relation-like NAT -defined Function-like V36() 1 + 1 -element FinSequence-like FinSubsequence-like V51() set
1 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
{[1,f]} is non empty V2() Relation-like Function-like constant V36() 1 -element V51() set
{2,g} is non empty V36() V51() set
[2,g] is non empty pair set
{{2,g},{2}} is non empty V36() V40() V51() set
dom <*f,g*> is non empty V36() 2 -element V51() Element of K18(NAT)
Seg 2 is non empty V36() 2 -element V51() Element of K18(NAT)
<*f,g*> . 2 is set
dom <*n,f*> is non empty V36() 2 -element V51() Element of K18(NAT)
<*n,f*> . 2 is set
{f,g} is non empty V36() V51() set
{1,n} is non empty V36() V51() set
[1,n] is non empty pair set
{{1,n},{1}} is non empty V36() V40() V51() set
<*n*> is non empty V2() Relation-like NAT -defined Function-like constant V36() 1 -element FinSequence-like FinSubsequence-like V51() set
<*n*> ^ <*f*> is non empty Relation-like NAT -defined Function-like V36() 1 + 1 -element FinSequence-like FinSubsequence-like V51() set
{[1,n]} is non empty V2() Relation-like Function-like constant V36() 1 -element V51() set
{[<*n,f*>,and2a],[<*f,g*>,and2]} is non empty Relation-like V36() V51() set
dom <*n,g*> is non empty V36() 2 -element V51() Element of K18(NAT)
<*n,g*> . 2 is set
<*n*> ^ <*g*> is non empty Relation-like NAT -defined Function-like V36() 1 + 1 -element FinSequence-like FinSubsequence-like V51() set
the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) is non empty set
InputVertices ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) is Element of K18( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))))
K18( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)))) is set
the ResultSort of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) is Relation-like Function-like V27( the carrier' of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))), the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)))) Element of K18(K19( the carrier' of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))), the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)))))
the carrier' of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) is non empty set
K19( the carrier' of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))), the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)))) is Relation-like set
K18(K19( the carrier' of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))), the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))))) is set
K547( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))), the ResultSort of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)))) is Element of K18( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))))
the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) \ K547( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))), the ResultSort of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)))) is Element of K18( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))))
InnerVertices (1GateCircStr (<*n,g*>,and2a)) is non empty Element of K18( the carrier of (1GateCircStr (<*n,g*>,and2a)))
the carrier of (1GateCircStr (<*n,g*>,and2a)) is non empty set
K18( the carrier of (1GateCircStr (<*n,g*>,and2a))) is set
the ResultSort of (1GateCircStr (<*n,g*>,and2a)) is Relation-like Function-like V27( the carrier' of (1GateCircStr (<*n,g*>,and2a)), the carrier of (1GateCircStr (<*n,g*>,and2a))) Element of K18(K19( the carrier' of (1GateCircStr (<*n,g*>,and2a)), the carrier of (1GateCircStr (<*n,g*>,and2a))))
the carrier' of (1GateCircStr (<*n,g*>,and2a)) is non empty set
K19( the carrier' of (1GateCircStr (<*n,g*>,and2a)), the carrier of (1GateCircStr (<*n,g*>,and2a))) is Relation-like set
K18(K19( the carrier' of (1GateCircStr (<*n,g*>,and2a)), the carrier of (1GateCircStr (<*n,g*>,and2a)))) is set
K547( the carrier of (1GateCircStr (<*n,g*>,and2a)), the ResultSort of (1GateCircStr (<*n,g*>,and2a))) is Element of K18( the carrier of (1GateCircStr (<*n,g*>,and2a)))
(InputVertices ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)))) \ (InnerVertices (1GateCircStr (<*n,g*>,and2a))) is Element of K18( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))))
InputVertices (1GateCircStr (<*n,g*>,and2a)) is Element of K18( the carrier of (1GateCircStr (<*n,g*>,and2a)))
the carrier of (1GateCircStr (<*n,g*>,and2a)) \ K547( the carrier of (1GateCircStr (<*n,g*>,and2a)), the ResultSort of (1GateCircStr (<*n,g*>,and2a))) is Element of K18( the carrier of (1GateCircStr (<*n,g*>,and2a)))
InnerVertices ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) is non empty Element of K18( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))))
(InputVertices (1GateCircStr (<*n,g*>,and2a))) \ (InnerVertices ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)))) is Element of K18( the carrier of (1GateCircStr (<*n,g*>,and2a)))
((InputVertices ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)))) \ (InnerVertices (1GateCircStr (<*n,g*>,and2a)))) \/ ((InputVertices (1GateCircStr (<*n,g*>,and2a))) \ (InnerVertices ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))))) is set
the carrier of (1GateCircStr (<*n,f*>,and2a)) is non empty set
InputVertices (1GateCircStr (<*n,f*>,and2a)) is Element of K18( the carrier of (1GateCircStr (<*n,f*>,and2a)))
K18( the carrier of (1GateCircStr (<*n,f*>,and2a))) is set
the ResultSort of (1GateCircStr (<*n,f*>,and2a)) is Relation-like Function-like V27( the carrier' of (1GateCircStr (<*n,f*>,and2a)), the carrier of (1GateCircStr (<*n,f*>,and2a))) Element of K18(K19( the carrier' of (1GateCircStr (<*n,f*>,and2a)), the carrier of (1GateCircStr (<*n,f*>,and2a))))
the carrier' of (1GateCircStr (<*n,f*>,and2a)) is non empty set
K19( the carrier' of (1GateCircStr (<*n,f*>,and2a)), the carrier of (1GateCircStr (<*n,f*>,and2a))) is Relation-like set
K18(K19( the carrier' of (1GateCircStr (<*n,f*>,and2a)), the carrier of (1GateCircStr (<*n,f*>,and2a)))) is set
K547( the carrier of (1GateCircStr (<*n,f*>,and2a)), the ResultSort of (1GateCircStr (<*n,f*>,and2a))) is Element of K18( the carrier of (1GateCircStr (<*n,f*>,and2a)))
the carrier of (1GateCircStr (<*n,f*>,and2a)) \ K547( the carrier of (1GateCircStr (<*n,f*>,and2a)), the ResultSort of (1GateCircStr (<*n,f*>,and2a))) is Element of K18( the carrier of (1GateCircStr (<*n,f*>,and2a)))
InnerVertices (1GateCircStr (<*f,g*>,and2)) is non empty Element of K18( the carrier of (1GateCircStr (<*f,g*>,and2)))
the carrier of (1GateCircStr (<*f,g*>,and2)) is non empty set
K18( the carrier of (1GateCircStr (<*f,g*>,and2))) is set
the ResultSort of (1GateCircStr (<*f,g*>,and2)) is Relation-like Function-like V27( the carrier' of (1GateCircStr (<*f,g*>,and2)), the carrier of (1GateCircStr (<*f,g*>,and2))) Element of K18(K19( the carrier' of (1GateCircStr (<*f,g*>,and2)), the carrier of (1GateCircStr (<*f,g*>,and2))))
the carrier' of (1GateCircStr (<*f,g*>,and2)) is non empty set
K19( the carrier' of (1GateCircStr (<*f,g*>,and2)), the carrier of (1GateCircStr (<*f,g*>,and2))) is Relation-like set
K18(K19( the carrier' of (1GateCircStr (<*f,g*>,and2)), the carrier of (1GateCircStr (<*f,g*>,and2)))) is set
K547( the carrier of (1GateCircStr (<*f,g*>,and2)), the ResultSort of (1GateCircStr (<*f,g*>,and2))) is Element of K18( the carrier of (1GateCircStr (<*f,g*>,and2)))
(InputVertices (1GateCircStr (<*n,f*>,and2a))) \ (InnerVertices (1GateCircStr (<*f,g*>,and2))) is Element of K18( the carrier of (1GateCircStr (<*n,f*>,and2a)))
InputVertices (1GateCircStr (<*f,g*>,and2)) is Element of K18( the carrier of (1GateCircStr (<*f,g*>,and2)))
the carrier of (1GateCircStr (<*f,g*>,and2)) \ K547( the carrier of (1GateCircStr (<*f,g*>,and2)), the ResultSort of (1GateCircStr (<*f,g*>,and2))) is Element of K18( the carrier of (1GateCircStr (<*f,g*>,and2)))
InnerVertices (1GateCircStr (<*n,f*>,and2a)) is non empty Element of K18( the carrier of (1GateCircStr (<*n,f*>,and2a)))
(InputVertices (1GateCircStr (<*f,g*>,and2))) \ (InnerVertices (1GateCircStr (<*n,f*>,and2a))) is Element of K18( the carrier of (1GateCircStr (<*f,g*>,and2)))
((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ (InnerVertices (1GateCircStr (<*f,g*>,and2)))) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ (InnerVertices (1GateCircStr (<*n,f*>,and2a)))) is set
(((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ (InnerVertices (1GateCircStr (<*f,g*>,and2)))) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ (InnerVertices (1GateCircStr (<*n,f*>,and2a))))) \ (InnerVertices (1GateCircStr (<*n,g*>,and2a))) is Element of K18((((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ (InnerVertices (1GateCircStr (<*f,g*>,and2)))) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ (InnerVertices (1GateCircStr (<*n,f*>,and2a))))))
K18((((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ (InnerVertices (1GateCircStr (<*f,g*>,and2)))) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ (InnerVertices (1GateCircStr (<*n,f*>,and2a)))))) is set
((((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ (InnerVertices (1GateCircStr (<*f,g*>,and2)))) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ (InnerVertices (1GateCircStr (<*n,f*>,and2a))))) \ (InnerVertices (1GateCircStr (<*n,g*>,and2a)))) \/ ((InputVertices (1GateCircStr (<*n,g*>,and2a))) \ (InnerVertices ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))))) is set
(InnerVertices (1GateCircStr (<*n,f*>,and2a))) \/ (InnerVertices (1GateCircStr (<*f,g*>,and2))) is non empty set
(InputVertices (1GateCircStr (<*n,g*>,and2a))) \ ((InnerVertices (1GateCircStr (<*n,f*>,and2a))) \/ (InnerVertices (1GateCircStr (<*f,g*>,and2)))) is Element of K18( the carrier of (1GateCircStr (<*n,g*>,and2a)))
((((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ (InnerVertices (1GateCircStr (<*f,g*>,and2)))) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ (InnerVertices (1GateCircStr (<*n,f*>,and2a))))) \ (InnerVertices (1GateCircStr (<*n,g*>,and2a)))) \/ ((InputVertices (1GateCircStr (<*n,g*>,and2a))) \ ((InnerVertices (1GateCircStr (<*n,f*>,and2a))) \/ (InnerVertices (1GateCircStr (<*f,g*>,and2))))) is set
{[<*f,g*>,and2]} is non empty V2() Relation-like Function-like constant V36() 1 -element V51() set
(InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]} is Element of K18( the carrier of (1GateCircStr (<*n,f*>,and2a)))
((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ (InnerVertices (1GateCircStr (<*n,f*>,and2a)))) is set
(((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ (InnerVertices (1GateCircStr (<*n,f*>,and2a))))) \ (InnerVertices (1GateCircStr (<*n,g*>,and2a))) is Element of K18((((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ (InnerVertices (1GateCircStr (<*n,f*>,and2a))))))
K18((((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ (InnerVertices (1GateCircStr (<*n,f*>,and2a)))))) is set
((((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ (InnerVertices (1GateCircStr (<*n,f*>,and2a))))) \ (InnerVertices (1GateCircStr (<*n,g*>,and2a)))) \/ ((InputVertices (1GateCircStr (<*n,g*>,and2a))) \ ((InnerVertices (1GateCircStr (<*n,f*>,and2a))) \/ (InnerVertices (1GateCircStr (<*f,g*>,and2))))) is set
{[<*n,f*>,and2a]} is non empty V2() Relation-like Function-like constant V36() 1 -element V51() set
(InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]} is Element of K18( the carrier of (1GateCircStr (<*f,g*>,and2)))
((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]}) is set
(((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]})) \ (InnerVertices (1GateCircStr (<*n,g*>,and2a))) is Element of K18((((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]})))
K18((((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]}))) is set
((((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]})) \ (InnerVertices (1GateCircStr (<*n,g*>,and2a)))) \/ ((InputVertices (1GateCircStr (<*n,g*>,and2a))) \ ((InnerVertices (1GateCircStr (<*n,f*>,and2a))) \/ (InnerVertices (1GateCircStr (<*f,g*>,and2))))) is set
{[<*n,g*>,and2a]} is non empty V2() Relation-like Function-like constant V36() 1 -element V51() set
(((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]})) \ {[<*n,g*>,and2a]} is Element of K18((((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]})))
((((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]})) \ {[<*n,g*>,and2a]}) \/ ((InputVertices (1GateCircStr (<*n,g*>,and2a))) \ ((InnerVertices (1GateCircStr (<*n,f*>,and2a))) \/ (InnerVertices (1GateCircStr (<*f,g*>,and2))))) is set
{[<*n,f*>,and2a]} \/ (InnerVertices (1GateCircStr (<*f,g*>,and2))) is non empty set
(InputVertices (1GateCircStr (<*n,g*>,and2a))) \ ({[<*n,f*>,and2a]} \/ (InnerVertices (1GateCircStr (<*f,g*>,and2)))) is Element of K18( the carrier of (1GateCircStr (<*n,g*>,and2a)))
((((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]})) \ {[<*n,g*>,and2a]}) \/ ((InputVertices (1GateCircStr (<*n,g*>,and2a))) \ ({[<*n,f*>,and2a]} \/ (InnerVertices (1GateCircStr (<*f,g*>,and2))))) is set
{[<*n,f*>,and2a]} \/ {[<*f,g*>,and2]} is non empty Relation-like V36() V51() set
(InputVertices (1GateCircStr (<*n,g*>,and2a))) \ ({[<*n,f*>,and2a]} \/ {[<*f,g*>,and2]}) is Element of K18( the carrier of (1GateCircStr (<*n,g*>,and2a)))
((((InputVertices (1GateCircStr (<*n,f*>,and2a))) \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]})) \ {[<*n,g*>,and2a]}) \/ ((InputVertices (1GateCircStr (<*n,g*>,and2a))) \ ({[<*n,f*>,and2a]} \/ {[<*f,g*>,and2]})) is set
{n,f} is non empty V36() V51() set
{n,f} \ {[<*f,g*>,and2]} is V36() V51() Element of K18({n,f})
K18({n,f}) is V36() V40() V51() set
({n,f} \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]}) is set
(({n,f} \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]})) \ {[<*n,g*>,and2a]} is Element of K18((({n,f} \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]})))
K18((({n,f} \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]}))) is set
((({n,f} \ {[<*f,g*>,and2]}) \/ ((InputVertices (1GateCircStr (<*f,g*>,and2))) \ {[<*n,f*>,and2a]})) \ {[<*n,g*>,and2a]}) \/ ((InputVertices (1GateCircStr (<*n,g*>,and2a))) \ ({[<*n,f*>,and2a]} \/ {[<*f,g*>,and2]})) is set
{f,g} \ {[<*n,f*>,and2a]} is V36() V51() Element of K18({f,g})
K18({f,g}) is V36() V40() V51() set
({n,f} \ {[<*f,g*>,and2]}) \/ ({f,g} \ {[<*n,f*>,and2a]}) is V36() V51() set
(({n,f} \ {[<*f,g*>,and2]}) \/ ({f,g} \ {[<*n,f*>,and2a]})) \ {[<*n,g*>,and2a]} is V36() V51() Element of K18((({n,f} \ {[<*f,g*>,and2]}) \/ ({f,g} \ {[<*n,f*>,and2a]})))
K18((({n,f} \ {[<*f,g*>,and2]}) \/ ({f,g} \ {[<*n,f*>,and2a]}))) is V36() V40() V51() set
((({n,f} \ {[<*f,g*>,and2]}) \/ ({f,g} \ {[<*n,f*>,and2a]})) \ {[<*n,g*>,and2a]}) \/ ((InputVertices (1GateCircStr (<*n,g*>,and2a))) \ ({[<*n,f*>,and2a]} \/ {[<*f,g*>,and2]})) is set
{n,g} is non empty V36() V51() set
{n,g} \ ({[<*n,f*>,and2a]} \/ {[<*f,g*>,and2]}) is V36() V51() Element of K18({n,g})
K18({n,g}) is V36() V40() V51() set
((({n,f} \ {[<*f,g*>,and2]}) \/ ({f,g} \ {[<*n,f*>,and2a]})) \ {[<*n,g*>,and2a]}) \/ ({n,g} \ ({[<*n,f*>,and2a]} \/ {[<*f,g*>,and2]})) is V36() V51() set
{n,g} \ {[<*n,f*>,and2a],[<*f,g*>,and2]} is V36() V51() Element of K18({n,g})
((({n,f} \ {[<*f,g*>,and2]}) \/ ({f,g} \ {[<*n,f*>,and2a]})) \ {[<*n,g*>,and2a]}) \/ ({n,g} \ {[<*n,f*>,and2a],[<*f,g*>,and2]}) is V36() V51() set
{n,f} \/ ({f,g} \ {[<*n,f*>,and2a]}) is non empty V36() V51() set
({n,f} \/ ({f,g} \ {[<*n,f*>,and2a]})) \ {[<*n,g*>,and2a]} is V36() V51() Element of K18(({n,f} \/ ({f,g} \ {[<*n,f*>,and2a]})))
K18(({n,f} \/ ({f,g} \ {[<*n,f*>,and2a]}))) is V36() V40() V51() set
(({n,f} \/ ({f,g} \ {[<*n,f*>,and2a]})) \ {[<*n,g*>,and2a]}) \/ ({n,g} \ {[<*n,f*>,and2a],[<*f,g*>,and2]}) is V36() V51() set
{n,f} \/ {f,g} is non empty V36() V51() set
({n,f} \/ {f,g}) \ {[<*n,g*>,and2a]} is V36() V51() Element of K18(({n,f} \/ {f,g}))
K18(({n,f} \/ {f,g})) is V36() V40() V51() set
(({n,f} \/ {f,g}) \ {[<*n,g*>,and2a]}) \/ ({n,g} \ {[<*n,f*>,and2a],[<*f,g*>,and2]}) is V36() V51() set
(({n,f} \/ {f,g}) \ {[<*n,g*>,and2a]}) \/ {n,g} is non empty V36() V51() set
{n,f,f,g} is V36() V51() set
{n,f,f,g} \ {[<*n,g*>,and2a]} is V36() V51() Element of K18({n,f,f,g})
K18({n,f,f,g}) is V36() V40() V51() set
({n,f,f,g} \ {[<*n,g*>,and2a]}) \/ {n,g} is non empty V36() V51() set
{f,f,n,g} is V36() V51() set
{f,f,n,g} \ {[<*n,g*>,and2a]} is V36() V51() Element of K18({f,f,n,g})
K18({f,f,n,g}) is V36() V40() V51() set
({f,f,n,g} \ {[<*n,g*>,and2a]}) \/ {n,g} is non empty V36() V51() set
{f,n,g} is V36() V51() set
{f,n,g} \ {[<*n,g*>,and2a]} is V36() V51() Element of K18({f,n,g})
K18({f,n,g}) is V36() V40() V51() set
({f,n,g} \ {[<*n,g*>,and2a]}) \/ {n,g} is non empty V36() V51() set
{n,f,g} \ {[<*n,g*>,and2a]} is V36() V51() Element of K18({n,f,g})
K18({n,f,g}) is V36() V40() V51() set
({n,f,g} \ {[<*n,g*>,and2a]}) \/ {n,g} is non empty V36() V51() set
{n,f,g} \/ {n,g} is non empty V36() V51() set
{n,f,g,g,n} is V36() V51() set
{n,f,g,g} is V36() V51() set
{n} is non empty V2() V36() 1 -element V51() set
{n,f,g,g} \/ {n} is non empty V36() V51() set
{g,g,n,f} is V36() V51() set
{g,g,n,f} \/ {n} is non empty V36() V51() set
{g,n,f} is V36() V51() set
{g,n,f} \/ {n} is non empty V36() V51() set
{g,n,f,n} is V36() V51() set
{n,n,f,g} is V36() V51() set
n is set
f is set
g is set
BorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,f*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*n,f*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*f,g*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*n,g*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*n,f*>,and2a] is non empty pair set
{<*n,f*>,and2a} is non empty functional V36() V51() set
{<*n,f*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,f*>,and2a},{<*n,f*>}} is non empty V36() V40() V51() set
[<*f,g*>,and2] is non empty pair set
{<*f,g*>,and2} is non empty functional V36() V51() set
{<*f,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*f,g*>,and2},{<*f,g*>}} is non empty V36() V40() V51() set
[<*n,g*>,and2a] is non empty pair set
{<*n,g*>,and2a} is non empty functional V36() V51() set
{<*n,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,g*>,and2a},{<*n,g*>}} is non empty V36() V40() V51() set
<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BorrowStr (n,f,g)) is non empty Element of K18( the carrier of (BorrowStr (n,f,g)))
the carrier of (BorrowStr (n,f,g)) is non empty set
K18( the carrier of (BorrowStr (n,f,g))) is set
the ResultSort of (BorrowStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) Element of K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))))
the carrier' of (BorrowStr (n,f,g)) is non empty set
K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g)))) is set
K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
{[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]} is Relation-like V36() V51() set
BorrowOutput (n,f,g) is Element of InnerVertices (BorrowStr (n,f,g))
[<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3] is non empty pair set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3},{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>}} is non empty V36() V40() V51() set
{(BorrowOutput (n,f,g))} is non empty V2() V36() 1 -element V51() set
{[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]} \/ {(BorrowOutput (n,f,g))} is non empty V36() V51() set
(1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is non empty Element of K18( the carrier of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))))
the carrier of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is non empty set
K18( the carrier of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))) is set
the ResultSort of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is Relation-like Function-like V27( the carrier' of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))), the carrier of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))) Element of K18(K19( the carrier' of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))), the carrier of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))))
the carrier' of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is non empty set
K19( the carrier' of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))), the carrier of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))) is Relation-like set
K18(K19( the carrier' of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))), the carrier of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))))) is set
K547( the carrier of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))), the ResultSort of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))) is Element of K18( the carrier of ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))))
InnerVertices (1GateCircStr (<*f,g*>,and2)) is non empty Element of K18( the carrier of (1GateCircStr (<*f,g*>,and2)))
the carrier of (1GateCircStr (<*f,g*>,and2)) is non empty set
K18( the carrier of (1GateCircStr (<*f,g*>,and2))) is set
the ResultSort of (1GateCircStr (<*f,g*>,and2)) is Relation-like Function-like V27( the carrier' of (1GateCircStr (<*f,g*>,and2)), the carrier of (1GateCircStr (<*f,g*>,and2))) Element of K18(K19( the carrier' of (1GateCircStr (<*f,g*>,and2)), the carrier of (1GateCircStr (<*f,g*>,and2))))
the carrier' of (1GateCircStr (<*f,g*>,and2)) is non empty set
K19( the carrier' of (1GateCircStr (<*f,g*>,and2)), the carrier of (1GateCircStr (<*f,g*>,and2))) is Relation-like set
K18(K19( the carrier' of (1GateCircStr (<*f,g*>,and2)), the carrier of (1GateCircStr (<*f,g*>,and2)))) is set
K547( the carrier of (1GateCircStr (<*f,g*>,and2)), the ResultSort of (1GateCircStr (<*f,g*>,and2))) is Element of K18( the carrier of (1GateCircStr (<*f,g*>,and2)))
InnerVertices ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty Element of K18( the carrier of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))
the carrier of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty set
K18( the carrier of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is set
the ResultSort of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is Relation-like Function-like V27( the carrier' of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))), the carrier of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) Element of K18(K19( the carrier' of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))), the carrier of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))))
the carrier' of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty set
K19( the carrier' of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))), the carrier of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is Relation-like set
K18(K19( the carrier' of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))), the carrier of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))) is set
K547( the carrier of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))), the ResultSort of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is Element of K18( the carrier of ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))
(InnerVertices (1GateCircStr (<*f,g*>,and2))) \/ (InnerVertices ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is non empty set
InnerVertices (1GateCircStr (<*n,g*>,and2a)) is non empty Element of K18( the carrier of (1GateCircStr (<*n,g*>,and2a)))
the carrier of (1GateCircStr (<*n,g*>,and2a)) is non empty set
K18( the carrier of (1GateCircStr (<*n,g*>,and2a))) is set
the ResultSort of (1GateCircStr (<*n,g*>,and2a)) is Relation-like Function-like V27( the carrier' of (1GateCircStr (<*n,g*>,and2a)), the carrier of (1GateCircStr (<*n,g*>,and2a))) Element of K18(K19( the carrier' of (1GateCircStr (<*n,g*>,and2a)), the carrier of (1GateCircStr (<*n,g*>,and2a))))
the carrier' of (1GateCircStr (<*n,g*>,and2a)) is non empty set
K19( the carrier' of (1GateCircStr (<*n,g*>,and2a)), the carrier of (1GateCircStr (<*n,g*>,and2a))) is Relation-like set
K18(K19( the carrier' of (1GateCircStr (<*n,g*>,and2a)), the carrier of (1GateCircStr (<*n,g*>,and2a)))) is set
K547( the carrier of (1GateCircStr (<*n,g*>,and2a)), the ResultSort of (1GateCircStr (<*n,g*>,and2a))) is Element of K18( the carrier of (1GateCircStr (<*n,g*>,and2a)))
InnerVertices (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty Element of K18( the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))
the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty set
K18( the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is set
the ResultSort of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is Relation-like Function-like V27( the carrier' of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) Element of K18(K19( the carrier' of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))
the carrier' of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty set
K19( the carrier' of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is Relation-like set
K18(K19( the carrier' of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is set
K547( the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)), the ResultSort of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is Element of K18( the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))
(InnerVertices (1GateCircStr (<*n,g*>,and2a))) \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty set
(1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty Element of K18( the carrier of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))
the carrier of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty set
K18( the carrier of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is set
the ResultSort of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is Relation-like Function-like V27( the carrier' of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))), the carrier of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) Element of K18(K19( the carrier' of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))), the carrier of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))))
the carrier' of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty set
K19( the carrier' of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))), the carrier of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is Relation-like set
K18(K19( the carrier' of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))), the carrier of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))) is set
K547( the carrier of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))), the ResultSort of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is Element of K18( the carrier of (((1GateCircStr (<*n,f*>,and2a)) +* ((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a)))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))
(1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is non empty Element of K18( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))))
the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is non empty set
K18( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))) is set
the ResultSort of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is Relation-like Function-like V27( the carrier' of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))), the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))) Element of K18(K19( the carrier' of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))), the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))))
the carrier' of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is non empty set
K19( the carrier' of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))), the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))) is Relation-like set
K18(K19( the carrier' of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))), the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))))) is set
K547( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))), the ResultSort of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))) is Element of K18( the carrier of ((1GateCircStr (<*n,f*>,and2a)) +* (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))))
InnerVertices (1GateCircStr (<*n,f*>,and2a)) is non empty Element of K18( the carrier of (1GateCircStr (<*n,f*>,and2a)))
the carrier of (1GateCircStr (<*n,f*>,and2a)) is non empty set
K18( the carrier of (1GateCircStr (<*n,f*>,and2a))) is set
the ResultSort of (1GateCircStr (<*n,f*>,and2a)) is Relation-like Function-like V27( the carrier' of (1GateCircStr (<*n,f*>,and2a)), the carrier of (1GateCircStr (<*n,f*>,and2a))) Element of K18(K19( the carrier' of (1GateCircStr (<*n,f*>,and2a)), the carrier of (1GateCircStr (<*n,f*>,and2a))))
the carrier' of (1GateCircStr (<*n,f*>,and2a)) is non empty set
K19( the carrier' of (1GateCircStr (<*n,f*>,and2a)), the carrier of (1GateCircStr (<*n,f*>,and2a))) is Relation-like set
K18(K19( the carrier' of (1GateCircStr (<*n,f*>,and2a)), the carrier of (1GateCircStr (<*n,f*>,and2a)))) is set
K547( the carrier of (1GateCircStr (<*n,f*>,and2a)), the ResultSort of (1GateCircStr (<*n,f*>,and2a))) is Element of K18( the carrier of (1GateCircStr (<*n,f*>,and2a)))
InnerVertices (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty Element of K18( the carrier of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))
the carrier of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty set
K18( the carrier of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is set
the ResultSort of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is Relation-like Function-like V27( the carrier' of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))), the carrier of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) Element of K18(K19( the carrier' of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))), the carrier of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))))
the carrier' of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty set
K19( the carrier' of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))), the carrier of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is Relation-like set
K18(K19( the carrier' of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))), the carrier of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))) is set
K547( the carrier of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))), the ResultSort of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is Element of K18( the carrier of (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))
(InnerVertices (1GateCircStr (<*n,f*>,and2a))) \/ (InnerVertices (((1GateCircStr (<*f,g*>,and2)) +* (1GateCircStr (<*n,g*>,and2a))) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is non empty set
(InnerVertices (1GateCircStr (<*n,f*>,and2a))) \/ (InnerVertices ((1GateCircStr (<*f,g*>,and2)) +* ((1GateCircStr (<*n,g*>,and2a)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))) is non empty set
(InnerVertices (1GateCircStr (<*n,f*>,and2a))) \/ (InnerVertices (1GateCircStr (<*f,g*>,and2))) is non empty set
((InnerVertices (1GateCircStr (<*n,f*>,and2a))) \/ (InnerVertices (1GateCircStr (<*f,g*>,and2)))) \/ ((InnerVertices (1GateCircStr (<*n,g*>,and2a))) \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is non empty set
((InnerVertices (1GateCircStr (<*n,f*>,and2a))) \/ (InnerVertices (1GateCircStr (<*f,g*>,and2)))) \/ (InnerVertices (1GateCircStr (<*n,g*>,and2a))) is non empty set
(((InnerVertices (1GateCircStr (<*n,f*>,and2a))) \/ (InnerVertices (1GateCircStr (<*f,g*>,and2)))) \/ (InnerVertices (1GateCircStr (<*n,g*>,and2a)))) \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty set
{[<*n,f*>,and2a]} is non empty V2() Relation-like Function-like constant V36() 1 -element V51() set
{[<*n,f*>,and2a]} \/ (InnerVertices (1GateCircStr (<*f,g*>,and2))) is non empty set
({[<*n,f*>,and2a]} \/ (InnerVertices (1GateCircStr (<*f,g*>,and2)))) \/ (InnerVertices (1GateCircStr (<*n,g*>,and2a))) is non empty set
(({[<*n,f*>,and2a]} \/ (InnerVertices (1GateCircStr (<*f,g*>,and2)))) \/ (InnerVertices (1GateCircStr (<*n,g*>,and2a)))) \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty set
{[<*f,g*>,and2]} is non empty V2() Relation-like Function-like constant V36() 1 -element V51() set
{[<*n,f*>,and2a]} \/ {[<*f,g*>,and2]} is non empty Relation-like V36() V51() set
({[<*n,f*>,and2a]} \/ {[<*f,g*>,and2]}) \/ (InnerVertices (1GateCircStr (<*n,g*>,and2a))) is non empty set
(({[<*n,f*>,and2a]} \/ {[<*f,g*>,and2]}) \/ (InnerVertices (1GateCircStr (<*n,g*>,and2a)))) \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty set
{[<*n,g*>,and2a]} is non empty V2() Relation-like Function-like constant V36() 1 -element V51() set
({[<*n,f*>,and2a]} \/ {[<*f,g*>,and2]}) \/ {[<*n,g*>,and2a]} is non empty Relation-like V36() V51() set
(({[<*n,f*>,and2a]} \/ {[<*f,g*>,and2]}) \/ {[<*n,g*>,and2a]}) \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty set
{[<*n,f*>,and2a],[<*f,g*>,and2]} is non empty Relation-like V36() V51() set
{[<*n,f*>,and2a],[<*f,g*>,and2]} \/ {[<*n,g*>,and2a]} is non empty Relation-like V36() V51() set
({[<*n,f*>,and2a],[<*f,g*>,and2]} \/ {[<*n,g*>,and2a]}) \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty set
{[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]} \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is non empty set
n is set
f is set
g is set
<*f,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*f,g*>,and2] is non empty pair set
{<*f,g*>,and2} is non empty functional V36() V51() set
{<*f,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*f,g*>,and2},{<*f,g*>}} is non empty V36() V40() V51() set
<*n,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*n,g*>,and2a] is non empty pair set
{<*n,g*>,and2a} is non empty functional V36() V51() set
{<*n,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,g*>,and2a},{<*n,g*>}} is non empty V36() V40() V51() set
<*n,f*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*n,f*>,and2a] is non empty pair set
{<*n,f*>,and2a} is non empty functional V36() V51() set
{<*n,f*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,f*>,and2a},{<*n,f*>}} is non empty V36() V40() V51() set
BorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*f,g*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,g*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (BorrowStr (n,f,g)) is Element of K18( the carrier of (BorrowStr (n,f,g)))
the carrier of (BorrowStr (n,f,g)) is non empty set
K18( the carrier of (BorrowStr (n,f,g))) is set
the ResultSort of (BorrowStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) Element of K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))))
the carrier' of (BorrowStr (n,f,g)) is non empty set
K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g)))) is set
K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
the carrier of (BorrowStr (n,f,g)) \ K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
{n,f,g} is V36() V51() set
InnerVertices (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty Element of K18( the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))
the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty set
K18( the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is set
the ResultSort of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is Relation-like Function-like V27( the carrier' of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) Element of K18(K19( the carrier' of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))))
the carrier' of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty set
K19( the carrier' of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is Relation-like set
K18(K19( the carrier' of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) is set
K547( the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)), the ResultSort of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is Element of K18( the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))
[<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3] is non empty pair set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3},{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>}} is non empty V36() V40() V51() set
{[<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3]} is non empty V2() Relation-like Function-like constant V36() 1 -element V51() set
InputVertices (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is Element of K18( the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))
the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) \ K547( the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)), the ResultSort of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is Element of K18( the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))
proj2 <*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> is non empty V36() V51() set
{[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]} is Relation-like V36() V51() set
proj2 <*n,g*> is non empty V36() V51() set
{n,g} is non empty V36() V51() set
len <*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
Seg 3 is non empty V36() 3 -element V51() Element of K18(NAT)
dom <*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> is non empty V36() 3 -element V51() Element of K18(NAT)
<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> . 3 is set
[3,[<*n,g*>,and2a]] is non empty pair set
{3,[<*n,g*>,and2a]} is non empty V36() V51() set
{3} is non empty V2() V36() V40() 1 -element V51() non with_pair set
{{3,[<*n,g*>,and2a]},{3}} is non empty V36() V40() V51() set
the_rank_of [<*n,g*>,and2a] is V9() V10() V11() set
the_rank_of [<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3] is V9() V10() V11() set
proj2 <*n,f*> is non empty V36() V51() set
{n,f} is non empty V36() V51() set
<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> . 1 is set
[1,[<*n,f*>,and2a]] is non empty pair set
{1,[<*n,f*>,and2a]} is non empty V36() V51() set
{1} is non empty V2() V36() V40() 1 -element V51() non with_pair set
{{1,[<*n,f*>,and2a]},{1}} is non empty V36() V40() V51() set
the_rank_of [<*n,f*>,and2a] is V9() V10() V11() set
proj2 <*f,g*> is non empty V36() V51() set
{f,g} is non empty V36() V51() set
<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> . 2 is set
[2,[<*f,g*>,and2]] is non empty pair set
{2,[<*f,g*>,and2]} is non empty V36() V51() set
{2} is non empty V2() V36() V40() 1 -element V51() non with_pair set
{{2,[<*f,g*>,and2]},{2}} is non empty V36() V40() V51() set
the_rank_of [<*f,g*>,and2] is V9() V10() V11() set
{[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]} \ {[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]} is Relation-like V36() V51() Element of K18({[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]})
K18({[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]}) is V36() V40() V51() set
{n,f,g} \ {[<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3]} is V36() V51() Element of K18({n,f,g})
K18({n,f,g}) is V36() V40() V51() set
An is set
the carrier of (BorrowIStr (n,f,g)) is non empty set
InputVertices (BorrowIStr (n,f,g)) is Element of K18( the carrier of (BorrowIStr (n,f,g)))
K18( the carrier of (BorrowIStr (n,f,g))) is set
the ResultSort of (BorrowIStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BorrowIStr (n,f,g)), the carrier of (BorrowIStr (n,f,g))) Element of K18(K19( the carrier' of (BorrowIStr (n,f,g)), the carrier of (BorrowIStr (n,f,g))))
the carrier' of (BorrowIStr (n,f,g)) is non empty set
K19( the carrier' of (BorrowIStr (n,f,g)), the carrier of (BorrowIStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BorrowIStr (n,f,g)), the carrier of (BorrowIStr (n,f,g)))) is set
K547( the carrier of (BorrowIStr (n,f,g)), the ResultSort of (BorrowIStr (n,f,g))) is Element of K18( the carrier of (BorrowIStr (n,f,g)))
the carrier of (BorrowIStr (n,f,g)) \ K547( the carrier of (BorrowIStr (n,f,g)), the ResultSort of (BorrowIStr (n,f,g))) is Element of K18( the carrier of (BorrowIStr (n,f,g)))
(InputVertices (BorrowIStr (n,f,g))) \ (InnerVertices (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) is Element of K18( the carrier of (BorrowIStr (n,f,g)))
InnerVertices (BorrowIStr (n,f,g)) is non empty Element of K18( the carrier of (BorrowIStr (n,f,g)))
(InputVertices (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) \ (InnerVertices (BorrowIStr (n,f,g))) is Element of K18( the carrier of (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))
((InputVertices (BorrowIStr (n,f,g))) \ (InnerVertices (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)))) \/ ((InputVertices (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) \ (InnerVertices (BorrowIStr (n,f,g)))) is set
{[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]} \ (InnerVertices (BorrowIStr (n,f,g))) is Relation-like V36() V51() Element of K18({[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]})
{n,f,g} \/ ({[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]} \ (InnerVertices (BorrowIStr (n,f,g)))) is V36() V51() set
{n,f,g} \/ {} is V36() V51() set
n is set
f is set
g is set
<*f,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*f,g*>,and2] is non empty pair set
{<*f,g*>,and2} is non empty functional V36() V51() set
{<*f,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*f,g*>,and2},{<*f,g*>}} is non empty V36() V40() V51() set
<*n,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*n,g*>,and2a] is non empty pair set
{<*n,g*>,and2a} is non empty functional V36() V51() set
{<*n,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,g*>,and2a},{<*n,g*>}} is non empty V36() V40() V51() set
<*n,f*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*n,f*>,and2a] is non empty pair set
{<*n,f*>,and2a} is non empty functional V36() V51() set
{<*n,f*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,f*>,and2a},{<*n,f*>}} is non empty V36() V40() V51() set
[<*n,f*>,'xor'] is non empty pair set
{<*n,f*>,'xor'} is non empty functional V36() V51() set
{{<*n,f*>,'xor'},{<*n,f*>}} is non empty V36() V40() V51() set
BitSubtracterWithBorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (n,f,g,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*n,f*>,'xor'],g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'xor')) +* (1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*f,g*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,g*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (BitSubtracterWithBorrowStr (n,f,g)) is Element of K18( the carrier of (BitSubtracterWithBorrowStr (n,f,g)))
the carrier of (BitSubtracterWithBorrowStr (n,f,g)) is non empty set
K18( the carrier of (BitSubtracterWithBorrowStr (n,f,g))) is set
the ResultSort of (BitSubtracterWithBorrowStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr (n,f,g)), the carrier of (BitSubtracterWithBorrowStr (n,f,g))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr (n,f,g)), the carrier of (BitSubtracterWithBorrowStr (n,f,g))))
the carrier' of (BitSubtracterWithBorrowStr (n,f,g)) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr (n,f,g)), the carrier of (BitSubtracterWithBorrowStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr (n,f,g)), the carrier of (BitSubtracterWithBorrowStr (n,f,g)))) is set
K547( the carrier of (BitSubtracterWithBorrowStr (n,f,g)), the ResultSort of (BitSubtracterWithBorrowStr (n,f,g))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr (n,f,g)))
the carrier of (BitSubtracterWithBorrowStr (n,f,g)) \ K547( the carrier of (BitSubtracterWithBorrowStr (n,f,g)), the ResultSort of (BitSubtracterWithBorrowStr (n,f,g))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr (n,f,g)))
{n,f,g} is V36() V51() set
InputVertices (2GatesCircStr (n,f,g,'xor')) is Element of K18( the carrier of (2GatesCircStr (n,f,g,'xor')))
the carrier of (2GatesCircStr (n,f,g,'xor')) is non empty set
K18( the carrier of (2GatesCircStr (n,f,g,'xor'))) is set
the ResultSort of (2GatesCircStr (n,f,g,'xor')) is Relation-like Function-like V27( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) Element of K18(K19( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))))
the carrier' of (2GatesCircStr (n,f,g,'xor')) is non empty set
K19( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) is Relation-like set
K18(K19( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor')))) is set
K547( the carrier of (2GatesCircStr (n,f,g,'xor')), the ResultSort of (2GatesCircStr (n,f,g,'xor'))) is Element of K18( the carrier of (2GatesCircStr (n,f,g,'xor')))
the carrier of (2GatesCircStr (n,f,g,'xor')) \ K547( the carrier of (2GatesCircStr (n,f,g,'xor')), the ResultSort of (2GatesCircStr (n,f,g,'xor'))) is Element of K18( the carrier of (2GatesCircStr (n,f,g,'xor')))
InputVertices (BorrowStr (n,f,g)) is Element of K18( the carrier of (BorrowStr (n,f,g)))
the carrier of (BorrowStr (n,f,g)) is non empty set
K18( the carrier of (BorrowStr (n,f,g))) is set
the ResultSort of (BorrowStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) Element of K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))))
the carrier' of (BorrowStr (n,f,g)) is non empty set
K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g)))) is set
K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
the carrier of (BorrowStr (n,f,g)) \ K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
n is set
f is set
g is set
BitSubtracterWithBorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (n,f,g,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,f*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*n,f*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*n,f*>,'xor'] is non empty pair set
{<*n,f*>,'xor'} is non empty functional V36() V51() set
{<*n,f*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,f*>,'xor'},{<*n,f*>}} is non empty V36() V40() V51() set
<*[<*n,f*>,'xor'],g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'xor')) +* (1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*f,g*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*n,g*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*n,f*>,and2a] is non empty pair set
{<*n,f*>,and2a} is non empty functional V36() V51() set
{{<*n,f*>,and2a},{<*n,f*>}} is non empty V36() V40() V51() set
[<*f,g*>,and2] is non empty pair set
{<*f,g*>,and2} is non empty functional V36() V51() set
{<*f,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*f,g*>,and2},{<*f,g*>}} is non empty V36() V40() V51() set
[<*n,g*>,and2a] is non empty pair set
{<*n,g*>,and2a} is non empty functional V36() V51() set
{<*n,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,g*>,and2a},{<*n,g*>}} is non empty V36() V40() V51() set
<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitSubtracterWithBorrowStr (n,f,g)) is non empty Element of K18( the carrier of (BitSubtracterWithBorrowStr (n,f,g)))
the carrier of (BitSubtracterWithBorrowStr (n,f,g)) is non empty set
K18( the carrier of (BitSubtracterWithBorrowStr (n,f,g))) is set
the ResultSort of (BitSubtracterWithBorrowStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr (n,f,g)), the carrier of (BitSubtracterWithBorrowStr (n,f,g))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr (n,f,g)), the carrier of (BitSubtracterWithBorrowStr (n,f,g))))
the carrier' of (BitSubtracterWithBorrowStr (n,f,g)) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr (n,f,g)), the carrier of (BitSubtracterWithBorrowStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr (n,f,g)), the carrier of (BitSubtracterWithBorrowStr (n,f,g)))) is set
K547( the carrier of (BitSubtracterWithBorrowStr (n,f,g)), the ResultSort of (BitSubtracterWithBorrowStr (n,f,g))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr (n,f,g)))
2GatesCircOutput (n,f,g,'xor') is non empty pair Element of InnerVertices (2GatesCircStr (n,f,g,'xor'))
the carrier of (2GatesCircStr (n,f,g,'xor')) is non empty set
InnerVertices (2GatesCircStr (n,f,g,'xor')) is non empty Element of K18( the carrier of (2GatesCircStr (n,f,g,'xor')))
K18( the carrier of (2GatesCircStr (n,f,g,'xor'))) is set
the ResultSort of (2GatesCircStr (n,f,g,'xor')) is Relation-like Function-like V27( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) Element of K18(K19( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))))
the carrier' of (2GatesCircStr (n,f,g,'xor')) is non empty set
K19( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) is Relation-like set
K18(K19( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor')))) is set
K547( the carrier of (2GatesCircStr (n,f,g,'xor')), the ResultSort of (2GatesCircStr (n,f,g,'xor'))) is Element of K18( the carrier of (2GatesCircStr (n,f,g,'xor')))
[<*[<*n,f*>,'xor'],g*>,'xor'] is non empty pair set
{<*[<*n,f*>,'xor'],g*>,'xor'} is non empty functional V36() V51() set
{<*[<*n,f*>,'xor'],g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*n,f*>,'xor'],g*>,'xor'},{<*[<*n,f*>,'xor'],g*>}} is non empty V36() V40() V51() set
{[<*n,f*>,'xor'],(2GatesCircOutput (n,f,g,'xor'))} is non empty Relation-like V36() V51() set
{[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]} is Relation-like V36() V51() set
{[<*n,f*>,'xor'],(2GatesCircOutput (n,f,g,'xor'))} \/ {[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]} is non empty Relation-like V36() V51() set
BorrowOutput (n,f,g) is Element of InnerVertices (BorrowStr (n,f,g))
the carrier of (BorrowStr (n,f,g)) is non empty set
InnerVertices (BorrowStr (n,f,g)) is non empty Element of K18( the carrier of (BorrowStr (n,f,g)))
K18( the carrier of (BorrowStr (n,f,g))) is set
the ResultSort of (BorrowStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) Element of K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))))
the carrier' of (BorrowStr (n,f,g)) is non empty set
K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g)))) is set
K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
[<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3] is non empty pair set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3},{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>}} is non empty V36() V40() V51() set
{(BorrowOutput (n,f,g))} is non empty V2() V36() 1 -element V51() set
({[<*n,f*>,'xor'],(2GatesCircOutput (n,f,g,'xor'))} \/ {[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]}) \/ {(BorrowOutput (n,f,g))} is non empty V36() V51() set
(InnerVertices (2GatesCircStr (n,f,g,'xor'))) \/ (InnerVertices (BorrowStr (n,f,g))) is non empty set
{[<*n,f*>,'xor'],(2GatesCircOutput (n,f,g,'xor'))} \/ (InnerVertices (BorrowStr (n,f,g))) is non empty set
{[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]} \/ {(BorrowOutput (n,f,g))} is non empty V36() V51() set
{[<*n,f*>,'xor'],(2GatesCircOutput (n,f,g,'xor'))} \/ ({[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]} \/ {(BorrowOutput (n,f,g))}) is non empty V36() V51() set
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
f is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
g is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
(n,f,g) is Element of InnerVertices (n,f,g)
(n,f,g) is non empty non void V71() 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 K18( the carrier of (n,f,g))
K18( the carrier of (n,f,g)) is set
the ResultSort of (n,f,g) is Relation-like Function-like V27( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K19( the carrier' of (n,f,g), the carrier of (n,f,g)) is Relation-like set
K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g))) is set
K547( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K18( the carrier of (n,f,g))
(0,f,g) is Element of InnerVertices (0,f,g)
(0,f,g) is non empty non void V71() 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 K18( the carrier of (0,f,g))
K18( the carrier of (0,f,g)) is set
the ResultSort of (0,f,g) is Relation-like Function-like V27( the carrier' of (0,f,g), the carrier of (0,f,g)) Element of K18(K19( the carrier' of (0,f,g), the carrier of (0,f,g)))
the carrier' of (0,f,g) is non empty set
K19( the carrier' of (0,f,g), the carrier of (0,f,g)) is Relation-like set
K18(K19( the carrier' of (0,f,g), the carrier of (0,f,g))) is set
K547( the carrier of (0,f,g), the ResultSort of (0,f,g)) is Element of K18( the carrier of (0,f,g))
S0 is Relation-like NAT -defined Function-like V23( NAT ) set
S0 . 0 is set
S0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
(S0,f,g) is Element of InnerVertices (S0,f,g)
(S0,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (S0,f,g) is non empty set
InnerVertices (S0,f,g) is non empty Element of K18( the carrier of (S0,f,g))
K18( the carrier of (S0,f,g)) is set
the ResultSort of (S0,f,g) is Relation-like Function-like V27( the carrier' of (S0,f,g), the carrier of (S0,f,g)) Element of K18(K19( the carrier' of (S0,f,g), the carrier of (S0,f,g)))
the carrier' of (S0,f,g) is non empty set
K19( the carrier' of (S0,f,g), the carrier of (S0,f,g)) is Relation-like set
K18(K19( the carrier' of (S0,f,g), the carrier of (S0,f,g))) is set
K547( the carrier of (S0,f,g), the ResultSort of (S0,f,g)) is Element of K18( the carrier of (S0,f,g))
S0 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
((S0 + 1),f,g) is Element of InnerVertices ((S0 + 1),f,g)
((S0 + 1),f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of ((S0 + 1),f,g) is non empty set
InnerVertices ((S0 + 1),f,g) is non empty Element of K18( the carrier of ((S0 + 1),f,g))
K18( the carrier of ((S0 + 1),f,g)) is set
the ResultSort of ((S0 + 1),f,g) is Relation-like Function-like V27( the carrier' of ((S0 + 1),f,g), the carrier of ((S0 + 1),f,g)) Element of K18(K19( the carrier' of ((S0 + 1),f,g), the carrier of ((S0 + 1),f,g)))
the carrier' of ((S0 + 1),f,g) is non empty set
K19( the carrier' of ((S0 + 1),f,g), the carrier of ((S0 + 1),f,g)) is Relation-like set
K18(K19( the carrier' of ((S0 + 1),f,g), the carrier of ((S0 + 1),f,g))) is set
K547( the carrier of ((S0 + 1),f,g), the ResultSort of ((S0 + 1),f,g)) is Element of K18( the carrier of ((S0 + 1),f,g))
f . (S0 + 1) is set
g . (S0 + 1) is set
BorrowOutput ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)) is Element of InnerVertices (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))
BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (S0 + 1)),(g . (S0 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (S0 + 1)),(S0,f,g)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (S0 + 1)),(S0,f,g)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (S0 + 1)),(S0,f,g)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (S0 + 1)),(S0,f,g)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (S0 + 1)),(S0,f,g)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a)) +* (1GateCircStr (<*(g . (S0 + 1)),(S0,f,g)*>,and2))) +* (1GateCircStr (<*(f . (S0 + 1)),(S0,f,g)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a] is non empty pair set
{<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a} is non empty functional V36() V51() set
{<*(f . (S0 + 1)),(g . (S0 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a},{<*(f . (S0 + 1)),(g . (S0 + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (S0 + 1)),(S0,f,g)*>,and2] is non empty pair set
{<*(g . (S0 + 1)),(S0,f,g)*>,and2} is non empty functional V36() V51() set
{<*(g . (S0 + 1)),(S0,f,g)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (S0 + 1)),(S0,f,g)*>,and2},{<*(g . (S0 + 1)),(S0,f,g)*>}} is non empty V36() V40() V51() set
[<*(f . (S0 + 1)),(S0,f,g)*>,and2a] is non empty pair set
{<*(f . (S0 + 1)),(S0,f,g)*>,and2a} is non empty functional V36() V51() set
{<*(f . (S0 + 1)),(S0,f,g)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (S0 + 1)),(S0,f,g)*>,and2a},{<*(f . (S0 + 1)),(S0,f,g)*>}} is non empty V36() V40() V51() set
<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a],[<*(g . (S0 + 1)),(S0,f,g)*>,and2],[<*(f . (S0 + 1)),(S0,f,g)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a],[<*(g . (S0 + 1)),(S0,f,g)*>,and2],[<*(f . (S0 + 1)),(S0,f,g)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) +* (1GateCircStr (<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a],[<*(g . (S0 + 1)),(S0,f,g)*>,and2],[<*(f . (S0 + 1)),(S0,f,g)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty set
InnerVertices (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty Element of K18( the carrier of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))))
K18( the carrier of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) is set
the ResultSort of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is Relation-like Function-like V27( the carrier' of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) Element of K18(K19( the carrier' of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))))
the carrier' of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty set
K19( the carrier' of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) is Relation-like set
K18(K19( the carrier' of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))))) is set
K547( the carrier of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the ResultSort of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) is Element of K18( the carrier of (BorrowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))))
[<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a],[<*(g . (S0 + 1)),(S0,f,g)*>,and2],[<*(f . (S0 + 1)),(S0,f,g)*>,and2a]*>,or3] is non empty pair set
{<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a],[<*(g . (S0 + 1)),(S0,f,g)*>,and2],[<*(f . (S0 + 1)),(S0,f,g)*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a],[<*(g . (S0 + 1)),(S0,f,g)*>,and2],[<*(f . (S0 + 1)),(S0,f,g)*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a],[<*(g . (S0 + 1)),(S0,f,g)*>,and2],[<*(f . (S0 + 1)),(S0,f,g)*>,and2a]*>,or3},{<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,and2a],[<*(g . (S0 + 1)),(S0,f,g)*>,and2],[<*(f . (S0 + 1)),(S0,f,g)*>,and2a]*>}} is non empty V36() V40() V51() set
n is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
f is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
proj1 ((0 -tuples_on BOOLEAN) --> TRUE) is set
(0,n,f) is non empty pair Element of InnerVertices (0,n,f)
(0,n,f) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (0,n,f) is non empty set
InnerVertices (0,n,f) is non empty Element of K18( the carrier of (0,n,f))
K18( the carrier of (0,n,f)) is set
the ResultSort of (0,n,f) is Relation-like Function-like V27( the carrier' of (0,n,f), the carrier of (0,n,f)) Element of K18(K19( the carrier' of (0,n,f), the carrier of (0,n,f)))
the carrier' of (0,n,f) is non empty set
K19( the carrier' of (0,n,f), the carrier of (0,n,f)) is Relation-like set
K18(K19( the carrier' of (0,n,f), the carrier of (0,n,f))) is set
K547( the carrier of (0,n,f), the ResultSort of (0,n,f)) is Element of K18( the carrier of (0,n,f))
(0,n,f) `1 is set
(0,n,f) `2 is set
proj1 ((0,n,f) `2) is set
card ((0,n,f) `1) is V9() V10() V11() cardinal set
g is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
(g,n,f) is non empty pair Element of InnerVertices (g,n,f)
(g,n,f) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (g,n,f) is non empty set
InnerVertices (g,n,f) is non empty Element of K18( the carrier of (g,n,f))
K18( the carrier of (g,n,f)) is set
the ResultSort of (g,n,f) is Relation-like Function-like V27( the carrier' of (g,n,f), the carrier of (g,n,f)) Element of K18(K19( the carrier' of (g,n,f), the carrier of (g,n,f)))
the carrier' of (g,n,f) is non empty set
K19( the carrier' of (g,n,f), the carrier of (g,n,f)) is Relation-like set
K18(K19( the carrier' of (g,n,f), the carrier of (g,n,f))) is set
K547( the carrier of (g,n,f), the ResultSort of (g,n,f)) is Element of K18( the carrier of (g,n,f))
(g,n,f) `1 is set
(g,n,f) `2 is set
proj1 ((g,n,f) `2) is set
card ((g,n,f) `1) is V9() V10() V11() cardinal set
g + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
((g + 1),n,f) is non empty pair Element of InnerVertices ((g + 1),n,f)
((g + 1),n,f) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of ((g + 1),n,f) is non empty set
InnerVertices ((g + 1),n,f) is non empty Element of K18( the carrier of ((g + 1),n,f))
K18( the carrier of ((g + 1),n,f)) is set
the ResultSort of ((g + 1),n,f) is Relation-like Function-like V27( the carrier' of ((g + 1),n,f), the carrier of ((g + 1),n,f)) Element of K18(K19( the carrier' of ((g + 1),n,f), the carrier of ((g + 1),n,f)))
the carrier' of ((g + 1),n,f) is non empty set
K19( the carrier' of ((g + 1),n,f), the carrier of ((g + 1),n,f)) is Relation-like set
K18(K19( the carrier' of ((g + 1),n,f), the carrier of ((g + 1),n,f))) is set
K547( the carrier of ((g + 1),n,f), the ResultSort of ((g + 1),n,f)) is Element of K18( the carrier of ((g + 1),n,f))
n . (g + 1) is set
f . (g + 1) is set
BorrowOutput ((n . (g + 1)),(f . (g + 1)),(g,n,f)) is Element of InnerVertices (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)))
BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (g + 1)),(f . (g + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(n . (g + 1)),(f . (g + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (g + 1)),(g,n,f)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (g + 1)),(g,n,f)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (g + 1)),(f . (g + 1))*>,and2a)) +* (1GateCircStr (<*(f . (g + 1)),(g,n,f)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (g + 1)),(g,n,f)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(n . (g + 1)),(g,n,f)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (g + 1)),(f . (g + 1))*>,and2a)) +* (1GateCircStr (<*(f . (g + 1)),(g,n,f)*>,and2))) +* (1GateCircStr (<*(n . (g + 1)),(g,n,f)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (g + 1)),(f . (g + 1))*>,and2a] is non empty pair set
{<*(n . (g + 1)),(f . (g + 1))*>,and2a} is non empty functional V36() V51() set
{<*(n . (g + 1)),(f . (g + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (g + 1)),(f . (g + 1))*>,and2a},{<*(n . (g + 1)),(f . (g + 1))*>}} is non empty V36() V40() V51() set
[<*(f . (g + 1)),(g,n,f)*>,and2] is non empty pair set
{<*(f . (g + 1)),(g,n,f)*>,and2} is non empty functional V36() V51() set
{<*(f . (g + 1)),(g,n,f)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (g + 1)),(g,n,f)*>,and2},{<*(f . (g + 1)),(g,n,f)*>}} is non empty V36() V40() V51() set
[<*(n . (g + 1)),(g,n,f)*>,and2a] is non empty pair set
{<*(n . (g + 1)),(g,n,f)*>,and2a} is non empty functional V36() V51() set
{<*(n . (g + 1)),(g,n,f)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (g + 1)),(g,n,f)*>,and2a},{<*(n . (g + 1)),(g,n,f)*>}} is non empty V36() V40() V51() set
<*[<*(n . (g + 1)),(f . (g + 1))*>,and2a],[<*(f . (g + 1)),(g,n,f)*>,and2],[<*(n . (g + 1)),(g,n,f)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . (g + 1)),(f . (g + 1))*>,and2a],[<*(f . (g + 1)),(g,n,f)*>,and2],[<*(n . (g + 1)),(g,n,f)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))) +* (1GateCircStr (<*[<*(n . (g + 1)),(f . (g + 1))*>,and2a],[<*(f . (g + 1)),(g,n,f)*>,and2],[<*(n . (g + 1)),(g,n,f)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))) is non empty set
InnerVertices (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))) is non empty Element of K18( the carrier of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))))
K18( the carrier of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)))) is set
the ResultSort of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))) is Relation-like Function-like V27( the carrier' of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))), the carrier of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)))) Element of K18(K19( the carrier' of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))), the carrier of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)))))
the carrier' of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))) is non empty set
K19( the carrier' of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))), the carrier of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)))) is Relation-like set
K18(K19( the carrier' of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))), the carrier of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))))) is set
K547( the carrier of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))), the ResultSort of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)))) is Element of K18( the carrier of (BorrowStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))))
[<*[<*(n . (g + 1)),(f . (g + 1))*>,and2a],[<*(f . (g + 1)),(g,n,f)*>,and2],[<*(n . (g + 1)),(g,n,f)*>,and2a]*>,or3] is non empty pair set
{<*[<*(n . (g + 1)),(f . (g + 1))*>,and2a],[<*(f . (g + 1)),(g,n,f)*>,and2],[<*(n . (g + 1)),(g,n,f)*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*(n . (g + 1)),(f . (g + 1))*>,and2a],[<*(f . (g + 1)),(g,n,f)*>,and2],[<*(n . (g + 1)),(g,n,f)*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(n . (g + 1)),(f . (g + 1))*>,and2a],[<*(f . (g + 1)),(g,n,f)*>,and2],[<*(n . (g + 1)),(g,n,f)*>,and2a]*>,or3},{<*[<*(n . (g + 1)),(f . (g + 1))*>,and2a],[<*(f . (g + 1)),(g,n,f)*>,and2],[<*(n . (g + 1)),(g,n,f)*>,and2a]*>}} is non empty V36() V40() V51() set
proj1 or3 is set
((g + 1),n,f) `1 is set
((g + 1),n,f) `2 is set
proj1 (((g + 1),n,f) `2) is set
card (((g + 1),n,f) `1) is V9() V10() V11() cardinal set
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
f is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
g is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
(n,f,g) is non empty pair Element of InnerVertices (n,f,g)
(n,f,g) is non empty non void V71() 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 K18( the carrier of (n,f,g))
K18( the carrier of (n,f,g)) is set
the ResultSort of (n,f,g) is Relation-like Function-like V27( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K19( the carrier' of (n,f,g), the carrier of (n,f,g)) is Relation-like set
K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g))) is set
K547( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K18( the carrier of (n,f,g))
S0 is set
[S0,and2] is non empty pair set
{S0,and2} is non empty V36() V51() set
{S0} is non empty V2() V36() 1 -element V51() set
{{S0,and2},{S0}} is non empty V36() V40() V51() set
[S0,and2a] is non empty pair set
{S0,and2a} is non empty V36() V51() set
{{S0,and2a},{S0}} is non empty V36() V40() V51() set
[S0,'xor'] is non empty pair set
{S0,'xor'} is non empty V36() V51() set
{{S0,'xor'},{S0}} is non empty V36() V40() V51() set
proj1 and2 is set
proj1 and2a is set
proj1 'xor' is set
[S0,and2] `2 is set
proj1 ([S0,and2] `2) is set
[S0,and2a] `2 is set
proj1 ([S0,and2a] `2) is set
[S0,'xor'] `2 is set
proj1 ([S0,'xor'] `2) is set
(n,f,g) `2 is set
proj1 ((n,f,g) `2) is set
n is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() nonpair-yielding set
f is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() nonpair-yielding set
g is Relation-like NAT -defined Function-like V23( NAT ) set
(0,n,f) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices H₁( 0 ) is non empty Element of K18( the carrier of H₁( 0 ))
the carrier of H₁( 0 ) is non empty set
K18( the carrier of H₁( 0 )) is set
the carrier of (0,n,f) is non empty set
the ResultSort of (0,n,f) is Relation-like Function-like V27( the carrier' of (0,n,f), the carrier of (0,n,f)) Element of K18(K19( the carrier' of (0,n,f), the carrier of (0,n,f)))
the carrier' of (0,n,f) is non empty set
K19( the carrier' of (0,n,f), the carrier of (0,n,f)) is Relation-like set
K18(K19( the carrier' of (0,n,f), the carrier of (0,n,f))) is set
K547( the carrier of (0,n,f), the ResultSort of (0,n,f)) is Element of K18( the carrier of (0,n,f))
K18( the carrier of (0,n,f)) is set
InputVertices H₁( 0 ) is Element of K18( the carrier of H₁( 0 ))
the carrier of (0,n,f) \ K547( the carrier of (0,n,f), the ResultSort of (0,n,f)) is Element of K18( the carrier of (0,n,f))
g . 0 is set
(0,n,f) is non empty pair Element of InnerVertices (0,n,f)
InnerVertices (0,n,f) is non empty Element of K18( the carrier of (0,n,f))
A0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
A0 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
n . (A0 + 1) is non pair set
f . (A0 + 1) is non pair set
N is set
BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),N,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (A0 + 1)),(f . (A0 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V36() V40() V51() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],N*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],N*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],N*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (A0 + 1)),N*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (A0 + 1)),N*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (A0 + 1)),N*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (A0 + 1)),N*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(n . (A0 + 1)),N*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (A0 + 1)),N*>,and2))) +* (1GateCircStr (<*(n . (A0 + 1)),N*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V36() V40() V51() set
[<*(f . (A0 + 1)),N*>,and2] is non empty pair set
{<*(f . (A0 + 1)),N*>,and2} is non empty functional V36() V51() set
{<*(f . (A0 + 1)),N*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (A0 + 1)),N*>,and2},{<*(f . (A0 + 1)),N*>}} is non empty V36() V40() V51() set
[<*(n . (A0 + 1)),N*>,and2a] is non empty pair set
{<*(n . (A0 + 1)),N*>,and2a} is non empty functional V36() V51() set
{<*(n . (A0 + 1)),N*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (A0 + 1)),N*>,and2a},{<*(n . (A0 + 1)),N*>}} is non empty V36() V40() V51() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),N*>,and2],[<*(n . (A0 + 1)),N*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),N*>,and2],[<*(n . (A0 + 1)),N*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) +* (1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),N*>,and2],[<*(n . (A0 + 1)),N*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),N,'xor')) +* (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty Element of K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))
the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty set
K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is set
the ResultSort of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))))
the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))) is set
K547( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the ResultSort of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))
N is set
A0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
g . A0 is set
(A0,n,f) is non empty pair Element of InnerVertices (A0,n,f)
(A0,n,f) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (A0,n,f) is non empty set
InnerVertices (A0,n,f) is non empty Element of K18( the carrier of (A0,n,f))
K18( the carrier of (A0,n,f)) is set
the ResultSort of (A0,n,f) is Relation-like Function-like V27( the carrier' of (A0,n,f), the carrier of (A0,n,f)) Element of K18(K19( the carrier' of (A0,n,f), the carrier of (A0,n,f)))
the carrier' of (A0,n,f) is non empty set
K19( the carrier' of (A0,n,f), the carrier of (A0,n,f)) is Relation-like set
K18(K19( the carrier' of (A0,n,f), the carrier of (A0,n,f))) is set
K547( the carrier of (A0,n,f), the ResultSort of (A0,n,f)) is Element of K18( the carrier of (A0,n,f))
A0 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
n . (A0 + 1) is non pair set
f . (A0 + 1) is non pair set
<*(n . (A0 + 1)),(f . (A0 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a} is non empty functional V36() V51() set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V36() V40() V51() set
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'} is non empty functional V36() V51() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V36() V40() V51() set
A0 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
n . (A0 + 1) is non pair set
f . (A0 + 1) is non pair set
BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),N,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (A0 + 1)),(f . (A0 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V36() V40() V51() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],N*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],N*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],N*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (A0 + 1)),N*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (A0 + 1)),N*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (A0 + 1)),N*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (A0 + 1)),N*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(n . (A0 + 1)),N*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (A0 + 1)),N*>,and2))) +* (1GateCircStr (<*(n . (A0 + 1)),N*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V36() V40() V51() set
[<*(f . (A0 + 1)),N*>,and2] is non empty pair set
{<*(f . (A0 + 1)),N*>,and2} is non empty functional V36() V51() set
{<*(f . (A0 + 1)),N*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (A0 + 1)),N*>,and2},{<*(f . (A0 + 1)),N*>}} is non empty V36() V40() V51() set
[<*(n . (A0 + 1)),N*>,and2a] is non empty pair set
{<*(n . (A0 + 1)),N*>,and2a} is non empty functional V36() V51() set
{<*(n . (A0 + 1)),N*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (A0 + 1)),N*>,and2a},{<*(n . (A0 + 1)),N*>}} is non empty V36() V40() V51() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),N*>,and2],[<*(n . (A0 + 1)),N*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),N*>,and2],[<*(n . (A0 + 1)),N*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) +* (1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),N*>,and2],[<*(n . (A0 + 1)),N*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),N,'xor')) +* (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices H<sub>2</sub>(N,A0) is Element of K18( the carrier of H<sub>2</sub>(N,A0))
the carrier of H<sub>2</sub>(N,A0) is non empty set
K18( the carrier of H<sub>2</sub>(N,A0)) is set
the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty set
the ResultSort of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))))
the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))) is set
K547( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the ResultSort of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))
K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is set
the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) \ K547( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the ResultSort of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))
{(n . (A0 + 1)),(f . (A0 + 1)),N} is V36() V51() set
A0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
g . A0 is set
A0 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
n . (A0 + 1) is non pair set
f . (A0 + 1) is non pair set
N is set
BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),N,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (A0 + 1)),(f . (A0 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V36() V40() V51() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],N*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],N*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],N*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (A0 + 1)),N*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (A0 + 1)),N*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (A0 + 1)),N*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (A0 + 1)),N*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(n . (A0 + 1)),N*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (A0 + 1)),N*>,and2))) +* (1GateCircStr (<*(n . (A0 + 1)),N*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V36() V40() V51() set
[<*(f . (A0 + 1)),N*>,and2] is non empty pair set
{<*(f . (A0 + 1)),N*>,and2} is non empty functional V36() V51() set
{<*(f . (A0 + 1)),N*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (A0 + 1)),N*>,and2},{<*(f . (A0 + 1)),N*>}} is non empty V36() V40() V51() set
[<*(n . (A0 + 1)),N*>,and2a] is non empty pair set
{<*(n . (A0 + 1)),N*>,and2a} is non empty functional V36() V51() set
{<*(n . (A0 + 1)),N*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (A0 + 1)),N*>,and2a},{<*(n . (A0 + 1)),N*>}} is non empty V36() V40() V51() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),N*>,and2],[<*(n . (A0 + 1)),N*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),N*>,and2],[<*(n . (A0 + 1)),N*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) +* (1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),N*>,and2],[<*(n . (A0 + 1)),N*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),N,'xor')) +* (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of H₂(N,A0) is non empty set
InputVertices H₂(N,A0) is Element of K18( the carrier of H₂(N,A0))
K18( the carrier of H₂(N,A0)) is set
the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty set
the ResultSort of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))))
the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))) is set
K547( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the ResultSort of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))
K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is set
the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) \ K547( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the ResultSort of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))
{N} is non empty V2() V36() 1 -element V51() set
(InputVertices H₂(N,A0)) \ {N} is Element of K18( the carrier of H₂(N,A0))
{(n . (A0 + 1)),(f . (A0 + 1)),N} is V36() V51() set
h is non empty pair set
A0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
N is non empty V71() ManySortedSign
(A0,n,f) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h is set
g . A0 is set
(A0,n,f) is Element of InnerVertices (A0,n,f)
the carrier of (A0,n,f) is non empty set
InnerVertices (A0,n,f) is non empty Element of K18( the carrier of (A0,n,f))
K18( the carrier of (A0,n,f)) is set
the ResultSort of (A0,n,f) is Relation-like Function-like V27( the carrier' of (A0,n,f), the carrier of (A0,n,f)) Element of K18(K19( the carrier' of (A0,n,f), the carrier of (A0,n,f)))
the carrier' of (A0,n,f) is non empty set
K19( the carrier' of (A0,n,f), the carrier of (A0,n,f)) is Relation-like set
K18(K19( the carrier' of (A0,n,f), the carrier of (A0,n,f))) is set
K547( the carrier of (A0,n,f), the ResultSort of (A0,n,f)) is Element of K18( the carrier of (A0,n,f))
A0 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
g . (A0 + 1) is set
((A0 + 1),n,f) is non empty pair Element of InnerVertices ((A0 + 1),n,f)
((A0 + 1),n,f) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of ((A0 + 1),n,f) is non empty set
InnerVertices ((A0 + 1),n,f) is non empty Element of K18( the carrier of ((A0 + 1),n,f))
K18( the carrier of ((A0 + 1),n,f)) is set
the ResultSort of ((A0 + 1),n,f) is Relation-like Function-like V27( the carrier' of ((A0 + 1),n,f), the carrier of ((A0 + 1),n,f)) Element of K18(K19( the carrier' of ((A0 + 1),n,f), the carrier of ((A0 + 1),n,f)))
the carrier' of ((A0 + 1),n,f) is non empty set
K19( the carrier' of ((A0 + 1),n,f), the carrier of ((A0 + 1),n,f)) is Relation-like set
K18(K19( the carrier' of ((A0 + 1),n,f), the carrier of ((A0 + 1),n,f))) is set
K547( the carrier of ((A0 + 1),n,f), the ResultSort of ((A0 + 1),n,f)) is Element of K18( the carrier of ((A0 + 1),n,f))
n . (A0 + 1) is non pair set
f . (A0 + 1) is non pair set
BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (A0 + 1)),(f . (A0 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V36() V40() V51() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],h*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],h*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],h*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((n . (A0 + 1)),(f . (A0 + 1)),h) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (A0 + 1)),h*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (A0 + 1)),h*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (A0 + 1)),h*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (A0 + 1)),h*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(n . (A0 + 1)),h*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (A0 + 1)),h*>,and2))) +* (1GateCircStr (<*(n . (A0 + 1)),h*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V36() V40() V51() set
[<*(f . (A0 + 1)),h*>,and2] is non empty pair set
{<*(f . (A0 + 1)),h*>,and2} is non empty functional V36() V51() set
{<*(f . (A0 + 1)),h*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (A0 + 1)),h*>,and2},{<*(f . (A0 + 1)),h*>}} is non empty V36() V40() V51() set
[<*(n . (A0 + 1)),h*>,and2a] is non empty pair set
{<*(n . (A0 + 1)),h*>,and2a} is non empty functional V36() V51() set
{<*(n . (A0 + 1)),h*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (A0 + 1)),h*>,and2a},{<*(n . (A0 + 1)),h*>}} is non empty V36() V40() V51() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),h*>,and2],[<*(n . (A0 + 1)),h*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),h*>,and2],[<*(n . (A0 + 1)),h*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) +* (1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),h*>,and2],[<*(n . (A0 + 1)),h*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')) +* (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
N +* H<sub>2</sub>(h,A0) is non empty non void V71() strict ManySortedSign
BorrowOutput ((n . (A0 + 1)),(f . (A0 + 1)),h) is Element of InnerVertices (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))
the carrier of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is non empty set
InnerVertices (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is non empty Element of K18( the carrier of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)))
K18( the carrier of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) is set
the ResultSort of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is Relation-like Function-like V27( the carrier' of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) Element of K18(K19( the carrier' of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))))
the carrier' of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is non empty set
K19( the carrier' of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) is Relation-like set
K18(K19( the carrier' of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)))) is set
K547( the carrier of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the ResultSort of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) is Element of K18( the carrier of (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)))
[<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),h*>,and2],[<*(n . (A0 + 1)),h*>,and2a]*>,or3] is non empty pair set
{<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),h*>,and2],[<*(n . (A0 + 1)),h*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),h*>,and2],[<*(n . (A0 + 1)),h*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),h*>,and2],[<*(n . (A0 + 1)),h*>,and2a]*>,or3},{<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),h*>,and2],[<*(n . (A0 + 1)),h*>,and2a]*>}} is non empty V36() V40() V51() set
InputVertices H<sub>2</sub>(h,A0) is Element of K18( the carrier of H<sub>2</sub>(h,A0))
the carrier of H<sub>2</sub>(h,A0) is non empty set
K18( the carrier of H<sub>2</sub>(h,A0)) is set
the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is non empty set
the ResultSort of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))))
the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)))) is set
K547( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the ResultSort of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)))
K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) is set
the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) \ K547( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the ResultSort of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)))
{(n . (A0 + 1)),(f . (A0 + 1)),h} is V36() V51() set
InnerVertices H<sub>2</sub>(h,A0) is non empty Element of K18( the carrier of H<sub>2</sub>(h,A0))
2GatesCircOutput ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor') is non empty pair Element of InnerVertices (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor'))
the carrier of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')) is non empty set
InnerVertices (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')) is non empty Element of K18( the carrier of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')))
K18( the carrier of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor'))) is set
the ResultSort of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')) is Relation-like Function-like V27( the carrier' of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')), the carrier of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor'))) Element of K18(K19( the carrier' of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')), the carrier of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor'))))
the carrier' of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')) is non empty set
K19( the carrier' of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')), the carrier of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor'))) is Relation-like set
K18(K19( the carrier' of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')), the carrier of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')))) is set
K547( the carrier of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')), the ResultSort of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor'))) is Element of K18( the carrier of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')))
[<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],h*>,'xor'] is non empty pair set
{<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],h*>,'xor'} is non empty functional V36() V51() set
{<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],h*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],h*>,'xor'},{<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],h*>}} is non empty V36() V40() V51() set
{[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],(2GatesCircOutput ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor'))} is non empty Relation-like V36() V51() set
{[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),h*>,and2],[<*(n . (A0 + 1)),h*>,and2a]} is Relation-like V36() V51() set
{[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],(2GatesCircOutput ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor'))} \/ {[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),h*>,and2],[<*(n . (A0 + 1)),h*>,and2a]} is non empty Relation-like V36() V51() set
{(BorrowOutput ((n . (A0 + 1)),(f . (A0 + 1)),h))} is non empty V2() V36() 1 -element V51() set
({[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],(2GatesCircOutput ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor'))} \/ {[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),h*>,and2],[<*(n . (A0 + 1)),h*>,and2a]}) \/ {(BorrowOutput ((n . (A0 + 1)),(f . (A0 + 1)),h))} is non empty V36() V51() set
{H<sub>5</sub>(h,A0)} is non empty V2() V36() 1 -element V51() set
A0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
A0 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
((A0 + 1),n,f) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices ((A0 + 1),n,f) is Element of K18( the carrier of ((A0 + 1),n,f))
the carrier of ((A0 + 1),n,f) is non empty set
K18( the carrier of ((A0 + 1),n,f)) is set
the ResultSort of ((A0 + 1),n,f) is Relation-like Function-like V27( the carrier' of ((A0 + 1),n,f), the carrier of ((A0 + 1),n,f)) Element of K18(K19( the carrier' of ((A0 + 1),n,f), the carrier of ((A0 + 1),n,f)))
the carrier' of ((A0 + 1),n,f) is non empty set
K19( the carrier' of ((A0 + 1),n,f), the carrier of ((A0 + 1),n,f)) is Relation-like set
K18(K19( the carrier' of ((A0 + 1),n,f), the carrier of ((A0 + 1),n,f))) is set
K547( the carrier of ((A0 + 1),n,f), the ResultSort of ((A0 + 1),n,f)) is Element of K18( the carrier of ((A0 + 1),n,f))
the carrier of ((A0 + 1),n,f) \ K547( the carrier of ((A0 + 1),n,f), the ResultSort of ((A0 + 1),n,f)) is Element of K18( the carrier of ((A0 + 1),n,f))
(A0,n,f) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (A0,n,f) is Element of K18( the carrier of (A0,n,f))
the carrier of (A0,n,f) is non empty set
K18( the carrier of (A0,n,f)) is set
the ResultSort of (A0,n,f) is Relation-like Function-like V27( the carrier' of (A0,n,f), the carrier of (A0,n,f)) Element of K18(K19( the carrier' of (A0,n,f), the carrier of (A0,n,f)))
the carrier' of (A0,n,f) is non empty set
K19( the carrier' of (A0,n,f), the carrier of (A0,n,f)) is Relation-like set
K18(K19( the carrier' of (A0,n,f), the carrier of (A0,n,f))) is set
K547( the carrier of (A0,n,f), the ResultSort of (A0,n,f)) is Element of K18( the carrier of (A0,n,f))
the carrier of (A0,n,f) \ K547( the carrier of (A0,n,f), the ResultSort of (A0,n,f)) is Element of K18( the carrier of (A0,n,f))
n . (A0 + 1) is non pair set
f . (A0 + 1) is non pair set
(A0,n,f) is non empty pair Element of InnerVertices (A0,n,f)
InnerVertices (A0,n,f) is non empty Element of K18( the carrier of (A0,n,f))
BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f),'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (A0 + 1)),(f . (A0 + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V36() V40() V51() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],(A0,n,f)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],(A0,n,f)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor')) +* (1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],(A0,n,f)*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (A0 + 1)),(A0,n,f)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (A0 + 1)),(A0,n,f)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (A0 + 1)),(A0,n,f)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . (A0 + 1)),(A0,n,f)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(n . (A0 + 1)),(A0,n,f)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a)) +* (1GateCircStr (<*(f . (A0 + 1)),(A0,n,f)*>,and2))) +* (1GateCircStr (<*(n . (A0 + 1)),(A0,n,f)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V36() V40() V51() set
[<*(f . (A0 + 1)),(A0,n,f)*>,and2] is non empty pair set
{<*(f . (A0 + 1)),(A0,n,f)*>,and2} is non empty functional V36() V51() set
{<*(f . (A0 + 1)),(A0,n,f)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (A0 + 1)),(A0,n,f)*>,and2},{<*(f . (A0 + 1)),(A0,n,f)*>}} is non empty V36() V40() V51() set
[<*(n . (A0 + 1)),(A0,n,f)*>,and2a] is non empty pair set
{<*(n . (A0 + 1)),(A0,n,f)*>,and2a} is non empty functional V36() V51() set
{<*(n . (A0 + 1)),(A0,n,f)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(n . (A0 + 1)),(A0,n,f)*>,and2a},{<*(n . (A0 + 1)),(A0,n,f)*>}} is non empty V36() V40() V51() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),(A0,n,f)*>,and2],[<*(n . (A0 + 1)),(A0,n,f)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),(A0,n,f)*>,and2],[<*(n . (A0 + 1)),(A0,n,f)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) +* (1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,and2a],[<*(f . (A0 + 1)),(A0,n,f)*>,and2],[<*(n . (A0 + 1)),(A0,n,f)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f),'xor')) +* (BorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) is non empty set
InputVertices (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))))
K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))) is set
the ResultSort of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))))
the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))), the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))))) is set
K547( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))), the ResultSort of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))))
the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) \ K547( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))), the ResultSort of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))))
{(A0,n,f)} is non empty V2() Relation-like V36() 1 -element V51() set
(InputVertices (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))) \ {(A0,n,f)} is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))))
(InputVertices (A0,n,f)) \/ ((InputVertices (BitSubtracterWithBorrowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))) \ {(A0,n,f)}) is set
g . A0 is set
n is empty Relation-like non-empty empty-yielding NAT -defined V9() V10() V11() V13() V14() V15() Function-like one-to-one constant functional non pair V30() V31() V36() V37() V40() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered V48() V49() V51() non with_pair nonpair-yielding ext-real non positive non negative set
f is empty Relation-like non-empty empty-yielding NAT -defined V9() V10() V11() V13() V14() V15() Function-like one-to-one constant functional non pair V30() V31() V36() V37() V40() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered V48() V49() V51() non with_pair nonpair-yielding ext-real non positive non negative set
(0,n,f) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (0,n,f) is Element of K18( the carrier of (0,n,f))
the carrier of (0,n,f) is non empty set
K18( the carrier of (0,n,f)) is set
the ResultSort of (0,n,f) is Relation-like Function-like V27( the carrier' of (0,n,f), the carrier of (0,n,f)) Element of K18(K19( the carrier' of (0,n,f), the carrier of (0,n,f)))
the carrier' of (0,n,f) is non empty set
K19( the carrier' of (0,n,f), the carrier of (0,n,f)) is Relation-like set
K18(K19( the carrier' of (0,n,f), the carrier of (0,n,f))) is set
K547( the carrier of (0,n,f), the ResultSort of (0,n,f)) is Element of K18( the carrier of (0,n,f))
the carrier of (0,n,f) \ K547( the carrier of (0,n,f), the ResultSort of (0,n,f)) is Element of K18( the carrier of (0,n,f))
proj2 n is empty V2() Relation-like non-empty empty-yielding NAT -defined V9() V10() V11() V13() V14() V15() Function-like one-to-one constant functional non pair V30() V31() V36() V37() V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V48() V49() V51() non with_pair nonpair-yielding ext-real non positive non negative set
proj2 f is empty V2() Relation-like non-empty empty-yielding NAT -defined V9() V10() V11() V13() V14() V15() Function-like one-to-one constant functional non pair V30() V31() V36() V37() V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V48() V49() V51() non with_pair nonpair-yielding ext-real non positive non negative set
(proj2 n) \/ (proj2 f) is empty Relation-like non-empty empty-yielding NAT -defined V9() V10() V11() V13() V14() V15() Function-like one-to-one constant functional non pair V30() V31() V36() V37() V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V48() V49() V51() non with_pair nonpair-yielding ext-real non positive non negative set
proj2 {} is empty V2() Relation-like non-empty empty-yielding NAT -defined V9() V10() V11() V13() V14() V15() Function-like one-to-one constant functional non pair V30() V31() V36() V37() V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V48() V49() V51() non with_pair nonpair-yielding ext-real non positive non negative set
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
n + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f is Relation-like NAT -defined Function-like V36() n + 1 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
g is Relation-like NAT -defined Function-like V36() n + 1 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
((n + 1),f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices ((n + 1),f,g) is Element of K18( the carrier of ((n + 1),f,g))
the carrier of ((n + 1),f,g) is non empty set
K18( the carrier of ((n + 1),f,g)) is set
the ResultSort of ((n + 1),f,g) is Relation-like Function-like V27( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) Element of K18(K19( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)))
the carrier' of ((n + 1),f,g) is non empty set
K19( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) is Relation-like set
K18(K19( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g))) is set
K547( the carrier of ((n + 1),f,g), the ResultSort of ((n + 1),f,g)) is Element of K18( the carrier of ((n + 1),f,g))
the carrier of ((n + 1),f,g) \ K547( the carrier of ((n + 1),f,g), the ResultSort of ((n + 1),f,g)) is Element of K18( the carrier of ((n + 1),f,g))
proj2 f is V36() V51() non with_pair set
proj2 g is V36() V51() non with_pair set
(proj2 f) \/ (proj2 g) is V36() V51() non with_pair set
S0 is Relation-like NAT -defined Function-like V36() n -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
A0 is non pair set
<*A0*> is non empty V2() Relation-like NAT -defined Function-like constant V36() 1 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
S0 ^ <*A0*> is non empty Relation-like NAT -defined Function-like V36() n + 1 -element FinSequence-like FinSubsequence-like V51() set
n + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
N is Relation-like NAT -defined Function-like V36() n -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
h is non pair set
<*h*> is non empty V2() Relation-like NAT -defined Function-like constant V36() 1 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
N ^ <*h*> is non empty Relation-like NAT -defined Function-like V36() n + 1 -element FinSequence-like FinSubsequence-like V51() set
dom <*A0*> is non empty V2() V36() 1 -element V51() Element of K18(NAT)
len S0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
f . (n + 1) is non pair set
<*A0*> . 1 is non pair set
dom <*h*> is non empty V2() V36() 1 -element V51() Element of K18(NAT)
len N is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
g . (n + 1) is non pair set
<*h*> . 1 is non pair set
(n,f,g) is non empty pair Element of InnerVertices (n,f,g)
(n,f,g) is non empty non void V71() 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 K18( the carrier of (n,f,g))
K18( the carrier of (n,f,g)) is set
the ResultSort of (n,f,g) is Relation-like Function-like V27( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K19( the carrier' of (n,f,g), the carrier of (n,f,g)) is Relation-like set
K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g))) is set
K547( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K18( the carrier of (n,f,g))
{A0,h,(n,f,g)} is V36() V51() set
{(n,f,g),A0,h} is V36() V51() set
proj2 S0 is V36() V51() non with_pair set
proj2 <*A0*> is non empty V2() V36() 1 -element V51() non with_pair set
(proj2 S0) \/ (proj2 <*A0*>) is non empty V36() V51() non with_pair set
{A0} is non empty V2() V36() 1 -element V51() non with_pair set
(proj2 S0) \/ {A0} is non empty V36() V51() non with_pair set
proj2 N is V36() V51() non with_pair set
proj2 <*h*> is non empty V2() V36() 1 -element V51() non with_pair set
(proj2 N) \/ (proj2 <*h*>) is non empty V36() V51() non with_pair set
{h} is non empty V2() V36() 1 -element V51() non with_pair set
(proj2 N) \/ {h} is non empty V36() V51() non with_pair set
<*A0,h*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
[<*A0,h*>,and2a] is non empty pair set
{<*A0,h*>,and2a} is non empty functional V36() V51() set
{<*A0,h*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*A0,h*>,and2a},{<*A0,h*>}} is non empty V36() V40() V51() set
[<*A0,h*>,'xor'] is non empty pair set
{<*A0,h*>,'xor'} is non empty functional V36() V51() set
{{<*A0,h*>,'xor'},{<*A0,h*>}} is non empty V36() V40() V51() set
S0 ^ {} is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
N ^ {} is Relation-like NAT -defined Function-like V36() FinSequence-like FinSubsequence-like V51() set
(n,S0,N) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (n,S0,N) is Element of K18( the carrier of (n,S0,N))
the carrier of (n,S0,N) is non empty set
K18( the carrier of (n,S0,N)) is set
the ResultSort of (n,S0,N) is Relation-like Function-like V27( the carrier' of (n,S0,N), the carrier of (n,S0,N)) Element of K18(K19( the carrier' of (n,S0,N), the carrier of (n,S0,N)))
the carrier' of (n,S0,N) is non empty set
K19( the carrier' of (n,S0,N), the carrier of (n,S0,N)) is Relation-like set
K18(K19( the carrier' of (n,S0,N), the carrier of (n,S0,N))) is set
K547( the carrier of (n,S0,N), the ResultSort of (n,S0,N)) is Element of K18( the carrier of (n,S0,N))
the carrier of (n,S0,N) \ K547( the carrier of (n,S0,N), the ResultSort of (n,S0,N)) is Element of K18( the carrier of (n,S0,N))
BitSubtracterWithBorrowStr (A0,h,(n,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (A0,h,(n,f,g),'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*A0,h*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*A0,h*>,'xor'],(n,f,g)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*A0,h*>,'xor'],(n,f,g)*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*A0,h*>,'xor')) +* (1GateCircStr (<*[<*A0,h*>,'xor'],(n,f,g)*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr (A0,h,(n,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr (A0,h,(n,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*A0,h*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*h,(n,f,g)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*h,(n,f,g)*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*A0,h*>,and2a)) +* (1GateCircStr (<*h,(n,f,g)*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*A0,(n,f,g)*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*A0,(n,f,g)*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*A0,h*>,and2a)) +* (1GateCircStr (<*h,(n,f,g)*>,and2))) +* (1GateCircStr (<*A0,(n,f,g)*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*h,(n,f,g)*>,and2] is non empty pair set
{<*h,(n,f,g)*>,and2} is non empty functional V36() V51() set
{<*h,(n,f,g)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*h,(n,f,g)*>,and2},{<*h,(n,f,g)*>}} is non empty V36() V40() V51() set
[<*A0,(n,f,g)*>,and2a] is non empty pair set
{<*A0,(n,f,g)*>,and2a} is non empty functional V36() V51() set
{<*A0,(n,f,g)*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*A0,(n,f,g)*>,and2a},{<*A0,(n,f,g)*>}} is non empty V36() V40() V51() set
<*[<*A0,h*>,and2a],[<*h,(n,f,g)*>,and2],[<*A0,(n,f,g)*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*A0,h*>,and2a],[<*h,(n,f,g)*>,and2],[<*A0,(n,f,g)*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr (A0,h,(n,f,g))) +* (1GateCircStr (<*[<*A0,h*>,and2a],[<*h,(n,f,g)*>,and2],[<*A0,(n,f,g)*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (A0,h,(n,f,g),'xor')) +* (BorrowStr (A0,h,(n,f,g))) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BitSubtracterWithBorrowStr (A0,h,(n,f,g))) is non empty set
InputVertices (BitSubtracterWithBorrowStr (A0,h,(n,f,g))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr (A0,h,(n,f,g))))
K18( the carrier of (BitSubtracterWithBorrowStr (A0,h,(n,f,g)))) is set
the ResultSort of (BitSubtracterWithBorrowStr (A0,h,(n,f,g))) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr (A0,h,(n,f,g))), the carrier of (BitSubtracterWithBorrowStr (A0,h,(n,f,g)))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr (A0,h,(n,f,g))), the carrier of (BitSubtracterWithBorrowStr (A0,h,(n,f,g)))))
the carrier' of (BitSubtracterWithBorrowStr (A0,h,(n,f,g))) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr (A0,h,(n,f,g))), the carrier of (BitSubtracterWithBorrowStr (A0,h,(n,f,g)))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr (A0,h,(n,f,g))), the carrier of (BitSubtracterWithBorrowStr (A0,h,(n,f,g))))) is set
K547( the carrier of (BitSubtracterWithBorrowStr (A0,h,(n,f,g))), the ResultSort of (BitSubtracterWithBorrowStr (A0,h,(n,f,g)))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr (A0,h,(n,f,g))))
the carrier of (BitSubtracterWithBorrowStr (A0,h,(n,f,g))) \ K547( the carrier of (BitSubtracterWithBorrowStr (A0,h,(n,f,g))), the ResultSort of (BitSubtracterWithBorrowStr (A0,h,(n,f,g)))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr (A0,h,(n,f,g))))
{(n,f,g)} is non empty V2() Relation-like V36() 1 -element V51() set
(InputVertices (BitSubtracterWithBorrowStr (A0,h,(n,f,g)))) \ {(n,f,g)} is Element of K18( the carrier of (BitSubtracterWithBorrowStr (A0,h,(n,f,g))))
(InputVertices (n,S0,N)) \/ ((InputVertices (BitSubtracterWithBorrowStr (A0,h,(n,f,g)))) \ {(n,f,g)}) is set
(proj2 S0) \/ (proj2 N) is V36() V51() non with_pair set
((proj2 S0) \/ (proj2 N)) \/ ((InputVertices (BitSubtracterWithBorrowStr (A0,h,(n,f,g)))) \ {(n,f,g)}) is set
{A0,h,(n,f,g)} \ {(n,f,g)} is V36() V51() Element of K18({A0,h,(n,f,g)})
K18({A0,h,(n,f,g)}) is V36() V40() V51() set
((proj2 S0) \/ (proj2 N)) \/ ({A0,h,(n,f,g)} \ {(n,f,g)}) is V36() V51() set
{A0,h} is non empty V36() V51() non with_pair set
((proj2 S0) \/ (proj2 N)) \/ {A0,h} is non empty V36() V51() non with_pair set
{A0} \/ {h} is non empty V36() V51() non with_pair set
((proj2 S0) \/ (proj2 N)) \/ ({A0} \/ {h}) is non empty V36() V51() non with_pair set
((proj2 S0) \/ (proj2 N)) \/ {A0} is non empty V36() V51() non with_pair set
(((proj2 S0) \/ (proj2 N)) \/ {A0}) \/ {h} is non empty V36() V51() non with_pair set
((proj2 S0) \/ {A0}) \/ (proj2 N) is non empty V36() V51() non with_pair set
(((proj2 S0) \/ {A0}) \/ (proj2 N)) \/ {h} is non empty V36() V51() non with_pair set
n is set
f is set
g is set
BorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,f*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*n,f*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*f,g*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*n,g*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*n,f*>,and2a] is non empty pair set
{<*n,f*>,and2a} is non empty functional V36() V51() set
{<*n,f*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,f*>,and2a},{<*n,f*>}} is non empty V36() V40() V51() set
[<*f,g*>,and2] is non empty pair set
{<*f,g*>,and2} is non empty functional V36() V51() set
{<*f,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*f,g*>,and2},{<*f,g*>}} is non empty V36() V40() V51() set
[<*n,g*>,and2a] is non empty pair set
{<*n,g*>,and2a} is non empty functional V36() V51() set
{<*n,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,g*>,and2a},{<*n,g*>}} is non empty V36() V40() V51() set
<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowCirc (n,f,g) is strict non-empty finitely-generated V107( BorrowStr (n,f,g)) gate`2=den Boolean MSAlgebra over BorrowStr (n,f,g)
BorrowICirc (n,f,g) is strict non-empty finitely-generated V107( BorrowIStr (n,f,g)) gate`2=den Boolean MSAlgebra over BorrowIStr (n,f,g)
1GateCircuit (n,f,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2a)
1GateCircuit (<*n,f*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2a)
1GateCircuit (f,g,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
1GateCircuit (<*f,g*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
(1GateCircuit (n,f,and2a)) +* (1GateCircuit (f,g,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))
1GateCircuit (n,g,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,g*>,and2a)
1GateCircuit (<*n,g*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,g*>,and2a)
((1GateCircuit (n,f,and2a)) +* (1GateCircuit (f,g,and2))) +* (1GateCircuit (n,g,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a))
1GateCircuit ([<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)
1GateCircuit (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)
(BorrowICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))
the Sorts of (BorrowCirc (n,f,g)) is Relation-like the carrier of (BorrowStr (n,f,g)) -defined Function-like V23( the carrier of (BorrowStr (n,f,g))) set
the carrier of (BorrowStr (n,f,g)) is non empty set
K230( the Sorts of (BorrowCirc (n,f,g))) is functional V49() V50() set
S0 is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
S0 . n is set
S0 . f is set
S0 . g is set
Following S0 is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
(Following S0) . [<*n,f*>,and2a] is set
(Following S0) . [<*f,g*>,and2] is set
(Following S0) . [<*n,g*>,and2a] is set
A0 is boolean Element of BOOLEAN
N is boolean Element of BOOLEAN
h is boolean Element of BOOLEAN
'not' A0 is boolean Element of BOOLEAN
('not' A0) '&' N is boolean Element of BOOLEAN
N '&' h is boolean Element of BOOLEAN
('not' A0) '&' h is boolean Element of BOOLEAN
InnerVertices (BorrowStr (n,f,g)) is non empty Element of K18( the carrier of (BorrowStr (n,f,g)))
K18( the carrier of (BorrowStr (n,f,g))) is set
the ResultSort of (BorrowStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) Element of K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))))
the carrier' of (BorrowStr (n,f,g)) is non empty set
K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g)))) is set
K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
proj1 S0 is set
<*n,f*> * S0 is Relation-like NAT -defined Function-like V36() V51() set
and2a . (<*n,f*> * S0) is boolean set
<*A0,N*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
and2a . <*A0,N*> is boolean set
<*f,g*> * S0 is Relation-like NAT -defined Function-like V36() V51() set
and2 . (<*f,g*> * S0) is boolean set
<*N,h*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
and2 . <*N,h*> is boolean set
<*n,g*> * S0 is Relation-like NAT -defined Function-like V36() V51() set
and2a . (<*n,g*> * S0) is boolean set
<*A0,h*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
and2a . <*A0,h*> is boolean set
n is set
f is set
g is set
BorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,f*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*n,f*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*f,g*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*n,g*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*n,f*>,and2a] is non empty pair set
{<*n,f*>,and2a} is non empty functional V36() V51() set
{<*n,f*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,f*>,and2a},{<*n,f*>}} is non empty V36() V40() V51() set
[<*f,g*>,and2] is non empty pair set
{<*f,g*>,and2} is non empty functional V36() V51() set
{<*f,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*f,g*>,and2},{<*f,g*>}} is non empty V36() V40() V51() set
[<*n,g*>,and2a] is non empty pair set
{<*n,g*>,and2a} is non empty functional V36() V51() set
{<*n,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,g*>,and2a},{<*n,g*>}} is non empty V36() V40() V51() set
<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowCirc (n,f,g) is strict non-empty finitely-generated V107( BorrowStr (n,f,g)) gate`2=den Boolean MSAlgebra over BorrowStr (n,f,g)
BorrowICirc (n,f,g) is strict non-empty finitely-generated V107( BorrowIStr (n,f,g)) gate`2=den Boolean MSAlgebra over BorrowIStr (n,f,g)
1GateCircuit (n,f,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2a)
1GateCircuit (<*n,f*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2a)
1GateCircuit (f,g,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
1GateCircuit (<*f,g*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
(1GateCircuit (n,f,and2a)) +* (1GateCircuit (f,g,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))
1GateCircuit (n,g,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,g*>,and2a)
1GateCircuit (<*n,g*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,g*>,and2a)
((1GateCircuit (n,f,and2a)) +* (1GateCircuit (f,g,and2))) +* (1GateCircuit (n,g,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a))
1GateCircuit ([<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)
1GateCircuit (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)
(BorrowICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))
the Sorts of (BorrowCirc (n,f,g)) is Relation-like the carrier of (BorrowStr (n,f,g)) -defined Function-like V23( the carrier of (BorrowStr (n,f,g))) set
the carrier of (BorrowStr (n,f,g)) is non empty set
K230( the Sorts of (BorrowCirc (n,f,g))) is functional V49() V50() set
BorrowOutput (n,f,g) is Element of InnerVertices (BorrowStr (n,f,g))
InnerVertices (BorrowStr (n,f,g)) is non empty Element of K18( the carrier of (BorrowStr (n,f,g)))
K18( the carrier of (BorrowStr (n,f,g))) is set
the ResultSort of (BorrowStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) Element of K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))))
the carrier' of (BorrowStr (n,f,g)) is non empty set
K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g)))) is set
K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
[<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3] is non empty pair set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3},{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>}} is non empty V36() V40() V51() set
S0 is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
S0 . [<*n,f*>,and2a] is set
S0 . [<*f,g*>,and2] is set
S0 . [<*n,g*>,and2a] is set
Following S0 is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
(Following S0) . (BorrowOutput (n,f,g)) is boolean Element of BOOLEAN
A0 is boolean Element of BOOLEAN
N is boolean Element of BOOLEAN
h is boolean Element of BOOLEAN
A0 'or' N is boolean Element of BOOLEAN
(A0 'or' N) 'or' h is boolean Element of BOOLEAN
proj1 S0 is set
g1 is Element of InnerVertices (BorrowStr (n,f,g))
h1 is Element of InnerVertices (BorrowStr (n,f,g))
n is Element of InnerVertices (BorrowStr (n,f,g))
<*g1,h1,n*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
<*g1,h1,n*> * S0 is Relation-like NAT -defined Function-like V36() V51() set
or3 . (<*g1,h1,n*> * S0) is boolean set
<*A0,N,h*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
or3 . <*A0,N,h*> is boolean set
n is set
f is set
g is set
<*f,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*f,g*>,and2] is non empty pair set
{<*f,g*>,and2} is non empty functional V36() V51() set
{<*f,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*f,g*>,and2},{<*f,g*>}} is non empty V36() V40() V51() set
<*n,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*n,g*>,and2a] is non empty pair set
{<*n,g*>,and2a} is non empty functional V36() V51() set
{<*n,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,g*>,and2a},{<*n,g*>}} is non empty V36() V40() V51() set
<*n,f*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*n,f*>,and2a] is non empty pair set
{<*n,f*>,and2a} is non empty functional V36() V51() set
{<*n,f*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,f*>,and2a},{<*n,f*>}} is non empty V36() V40() V51() set
BorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*f,g*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,g*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowCirc (n,f,g) is strict non-empty finitely-generated V107( BorrowStr (n,f,g)) gate`2=den Boolean MSAlgebra over BorrowStr (n,f,g)
BorrowICirc (n,f,g) is strict non-empty finitely-generated V107( BorrowIStr (n,f,g)) gate`2=den Boolean MSAlgebra over BorrowIStr (n,f,g)
1GateCircuit (n,f,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2a)
1GateCircuit (<*n,f*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2a)
1GateCircuit (f,g,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
1GateCircuit (<*f,g*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
(1GateCircuit (n,f,and2a)) +* (1GateCircuit (f,g,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))
1GateCircuit (n,g,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,g*>,and2a)
1GateCircuit (<*n,g*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,g*>,and2a)
((1GateCircuit (n,f,and2a)) +* (1GateCircuit (f,g,and2))) +* (1GateCircuit (n,g,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a))
1GateCircuit ([<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)
1GateCircuit (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)
(BorrowICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))
the Sorts of (BorrowCirc (n,f,g)) is Relation-like the carrier of (BorrowStr (n,f,g)) -defined Function-like V23( the carrier of (BorrowStr (n,f,g))) set
the carrier of (BorrowStr (n,f,g)) is non empty set
K230( the Sorts of (BorrowCirc (n,f,g))) is functional V49() V50() set
BorrowOutput (n,f,g) is Element of InnerVertices (BorrowStr (n,f,g))
InnerVertices (BorrowStr (n,f,g)) is non empty Element of K18( the carrier of (BorrowStr (n,f,g)))
K18( the carrier of (BorrowStr (n,f,g))) is set
the ResultSort of (BorrowStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) Element of K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))))
the carrier' of (BorrowStr (n,f,g)) is non empty set
K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g)))) is set
K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
[<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3] is non empty pair set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3},{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>}} is non empty V36() V40() V51() set
S0 is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
S0 . n is set
S0 . f is set
S0 . g is set
Following (S0,2) is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
(Following (S0,2)) . (BorrowOutput (n,f,g)) is boolean Element of BOOLEAN
(Following (S0,2)) . [<*n,f*>,and2a] is set
(Following (S0,2)) . [<*f,g*>,and2] is set
(Following (S0,2)) . [<*n,g*>,and2a] is set
A0 is boolean Element of BOOLEAN
N is boolean Element of BOOLEAN
h is boolean Element of BOOLEAN
'not' A0 is boolean Element of BOOLEAN
('not' A0) '&' N is boolean Element of BOOLEAN
N '&' h is boolean Element of BOOLEAN
(('not' A0) '&' N) 'or' (N '&' h) is boolean Element of BOOLEAN
('not' A0) '&' h is boolean Element of BOOLEAN
((('not' A0) '&' N) 'or' (N '&' h)) 'or' (('not' A0) '&' h) is boolean Element of BOOLEAN
InputVertices (BorrowStr (n,f,g)) is Element of K18( the carrier of (BorrowStr (n,f,g)))
the carrier of (BorrowStr (n,f,g)) \ K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
{n,f,g} is V36() V51() set
Following S0 is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
g1 is Element of the carrier of (BorrowStr (n,f,g))
(Following S0) . g1 is boolean Element of BOOLEAN
h1 is Element of the carrier of (BorrowStr (n,f,g))
(Following S0) . h1 is boolean Element of BOOLEAN
n is Element of the carrier of (BorrowStr (n,f,g))
(Following S0) . n is boolean Element of BOOLEAN
Following (Following S0) is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
(Following S0) . [<*n,f*>,and2a] is set
(Following S0) . [<*f,g*>,and2] is set
(Following S0) . [<*n,g*>,and2a] is set
n is set
f is set
g is set
<*f,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*f,g*>,and2] is non empty pair set
{<*f,g*>,and2} is non empty functional V36() V51() set
{<*f,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*f,g*>,and2},{<*f,g*>}} is non empty V36() V40() V51() set
<*n,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*n,g*>,and2a] is non empty pair set
{<*n,g*>,and2a} is non empty functional V36() V51() set
{<*n,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,g*>,and2a},{<*n,g*>}} is non empty V36() V40() V51() set
<*n,f*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*n,f*>,and2a] is non empty pair set
{<*n,f*>,and2a} is non empty functional V36() V51() set
{<*n,f*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,f*>,and2a},{<*n,f*>}} is non empty V36() V40() V51() set
BorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*f,g*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,g*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowCirc (n,f,g) is strict non-empty finitely-generated V107( BorrowStr (n,f,g)) gate`2=den Boolean MSAlgebra over BorrowStr (n,f,g)
BorrowICirc (n,f,g) is strict non-empty finitely-generated V107( BorrowIStr (n,f,g)) gate`2=den Boolean MSAlgebra over BorrowIStr (n,f,g)
1GateCircuit (n,f,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2a)
1GateCircuit (<*n,f*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2a)
1GateCircuit (f,g,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
1GateCircuit (<*f,g*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
(1GateCircuit (n,f,and2a)) +* (1GateCircuit (f,g,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))
1GateCircuit (n,g,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,g*>,and2a)
1GateCircuit (<*n,g*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,g*>,and2a)
((1GateCircuit (n,f,and2a)) +* (1GateCircuit (f,g,and2))) +* (1GateCircuit (n,g,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a))
1GateCircuit ([<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)
1GateCircuit (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)
(BorrowICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))
the Sorts of (BorrowCirc (n,f,g)) is Relation-like the carrier of (BorrowStr (n,f,g)) -defined Function-like V23( the carrier of (BorrowStr (n,f,g))) set
the carrier of (BorrowStr (n,f,g)) is non empty set
K230( the Sorts of (BorrowCirc (n,f,g))) is functional V49() V50() set
A0 is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
Following (A0,2) is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
Following (Following (A0,2)) is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
proj1 (Following (Following (A0,2))) is set
proj1 (Following (A0,2)) is set
N is Element of the carrier of (BorrowStr (n,f,g))
A0 . N is boolean Element of BOOLEAN
h is Element of the carrier of (BorrowStr (n,f,g))
A0 . h is boolean Element of BOOLEAN
Sn is Element of the carrier of (BorrowStr (n,f,g))
A0 . Sn is boolean Element of BOOLEAN
A0 . n is set
A0 . f is set
A0 . g is set
BorrowOutput (n,f,g) is Element of InnerVertices (BorrowStr (n,f,g))
InnerVertices (BorrowStr (n,f,g)) is non empty Element of K18( the carrier of (BorrowStr (n,f,g)))
K18( the carrier of (BorrowStr (n,f,g))) is set
the ResultSort of (BorrowStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) Element of K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))))
the carrier' of (BorrowStr (n,f,g)) is non empty set
K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g)))) is set
K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
[<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3] is non empty pair set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3},{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>}} is non empty V36() V40() V51() set
(Following (A0,2)) . (BorrowOutput (n,f,g)) is boolean Element of BOOLEAN
'not' (A0 . N) is boolean Element of BOOLEAN
('not' (A0 . N)) '&' (A0 . h) is boolean Element of BOOLEAN
(A0 . h) '&' (A0 . Sn) is boolean Element of BOOLEAN
(('not' (A0 . N)) '&' (A0 . h)) 'or' ((A0 . h) '&' (A0 . Sn)) is boolean Element of BOOLEAN
('not' (A0 . N)) '&' (A0 . Sn) is boolean Element of BOOLEAN
((('not' (A0 . N)) '&' (A0 . h)) 'or' ((A0 . h) '&' (A0 . Sn))) 'or' (('not' (A0 . N)) '&' (A0 . Sn)) is boolean Element of BOOLEAN
(Following (A0,2)) . [<*n,f*>,and2a] is set
(Following (A0,2)) . [<*f,g*>,and2] is set
(Following (A0,2)) . [<*n,g*>,and2a] is set
Following A0 is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
Following (Following A0) is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
InputVertices (BorrowStr (n,f,g)) is Element of K18( the carrier of (BorrowStr (n,f,g)))
the carrier of (BorrowStr (n,f,g)) \ K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
{n,f,g} is V36() V51() set
(Following A0) . n is set
(Following A0) . f is set
(Following A0) . g is set
(Following (A0,2)) . n is set
(Following (A0,2)) . f is set
(Following (A0,2)) . g is set
n is set
x is Element of the carrier of (BorrowStr (n,f,g))
(InputVertices (BorrowStr (n,f,g))) \/ (InnerVertices (BorrowStr (n,f,g))) is non empty Element of K18( the carrier of (BorrowStr (n,f,g)))
(Following (A0,2)) . n is set
(Following (Following (A0,2))) . n is set
{[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]} is Relation-like V36() V51() set
{(BorrowOutput (n,f,g))} is non empty V2() V36() 1 -element V51() set
{[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]} \/ {(BorrowOutput (n,f,g))} is non empty V36() V51() set
n is set
f is set
g is set
<*f,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*f,g*>,and2] is non empty pair set
{<*f,g*>,and2} is non empty functional V36() V51() set
{<*f,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*f,g*>,and2},{<*f,g*>}} is non empty V36() V40() V51() set
<*n,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*n,g*>,and2a] is non empty pair set
{<*n,g*>,and2a} is non empty functional V36() V51() set
{<*n,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,g*>,and2a},{<*n,g*>}} is non empty V36() V40() V51() set
<*n,f*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*n,f*>,and2a] is non empty pair set
{<*n,f*>,and2a} is non empty functional V36() V51() set
{<*n,f*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,f*>,and2a},{<*n,f*>}} is non empty V36() V40() V51() set
[<*n,f*>,'xor'] is non empty pair set
{<*n,f*>,'xor'} is non empty functional V36() V51() set
{{<*n,f*>,'xor'},{<*n,f*>}} is non empty V36() V40() V51() set
BitSubtracterWithBorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (n,f,g,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*n,f*>,'xor'],g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'xor')) +* (1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*f,g*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,g*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitSubtracterWithBorrowCirc (n,f,g) is strict non-empty finitely-generated V107( BitSubtracterWithBorrowStr (n,f,g)) gate`2=den Boolean MSAlgebra over BitSubtracterWithBorrowStr (n,f,g)
BitSubtracterCirc (n,f,g) is strict non-empty finitely-generated V107( 2GatesCircStr (n,f,g,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr (n,f,g,'xor')
2GatesCircuit (n,f,g,'xor') is strict non-empty finitely-generated V107( 2GatesCircStr (n,f,g,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr (n,f,g,'xor')
1GateCircuit (n,f,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'xor')
1GateCircuit (<*n,f*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'xor')
1GateCircuit ([<*n,f*>,'xor'],g,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')
1GateCircuit (<*[<*n,f*>,'xor'],g*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')
(1GateCircuit (n,f,'xor')) +* (1GateCircuit ([<*n,f*>,'xor'],g,'xor')) is strict non-empty finitely-generated V107((1GateCircStr (<*n,f*>,'xor')) +* (1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,'xor')) +* (1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor'))
BorrowCirc (n,f,g) is strict non-empty finitely-generated V107( BorrowStr (n,f,g)) gate`2=den Boolean MSAlgebra over BorrowStr (n,f,g)
BorrowICirc (n,f,g) is strict non-empty finitely-generated V107( BorrowIStr (n,f,g)) gate`2=den Boolean MSAlgebra over BorrowIStr (n,f,g)
1GateCircuit (n,f,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2a)
1GateCircuit (<*n,f*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2a)
1GateCircuit (f,g,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
1GateCircuit (<*f,g*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
(1GateCircuit (n,f,and2a)) +* (1GateCircuit (f,g,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))
1GateCircuit (n,g,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,g*>,and2a)
1GateCircuit (<*n,g*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,g*>,and2a)
((1GateCircuit (n,f,and2a)) +* (1GateCircuit (f,g,and2))) +* (1GateCircuit (n,g,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a))
1GateCircuit ([<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)
1GateCircuit (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)
(BorrowICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))
(BitSubtracterCirc (n,f,g)) +* (BorrowCirc (n,f,g)) is strict non-empty finitely-generated V107((2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g))) gate`2=den Boolean MSAlgebra over (2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g))
the Sorts of (BitSubtracterWithBorrowCirc (n,f,g)) is Relation-like the carrier of (BitSubtracterWithBorrowStr (n,f,g)) -defined Function-like V23( the carrier of (BitSubtracterWithBorrowStr (n,f,g))) set
the carrier of (BitSubtracterWithBorrowStr (n,f,g)) is non empty set
K230( the Sorts of (BitSubtracterWithBorrowCirc (n,f,g))) is functional V49() V50() set
BitSubtracterOutput (n,f,g) is Element of InnerVertices (2GatesCircStr (n,f,g,'xor'))
the carrier of (2GatesCircStr (n,f,g,'xor')) is non empty set
InnerVertices (2GatesCircStr (n,f,g,'xor')) is non empty Element of K18( the carrier of (2GatesCircStr (n,f,g,'xor')))
K18( the carrier of (2GatesCircStr (n,f,g,'xor'))) is set
the ResultSort of (2GatesCircStr (n,f,g,'xor')) is Relation-like Function-like V27( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) Element of K18(K19( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))))
the carrier' of (2GatesCircStr (n,f,g,'xor')) is non empty set
K19( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) is Relation-like set
K18(K19( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor')))) is set
K547( the carrier of (2GatesCircStr (n,f,g,'xor')), the ResultSort of (2GatesCircStr (n,f,g,'xor'))) is Element of K18( the carrier of (2GatesCircStr (n,f,g,'xor')))
2GatesCircOutput (n,f,g,'xor') is non empty pair Element of InnerVertices (2GatesCircStr (n,f,g,'xor'))
[<*[<*n,f*>,'xor'],g*>,'xor'] is non empty pair set
{<*[<*n,f*>,'xor'],g*>,'xor'} is non empty functional V36() V51() set
{<*[<*n,f*>,'xor'],g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*n,f*>,'xor'],g*>,'xor'},{<*[<*n,f*>,'xor'],g*>}} is non empty V36() V40() V51() set
BorrowOutput (n,f,g) is Element of InnerVertices (BorrowStr (n,f,g))
the carrier of (BorrowStr (n,f,g)) is non empty set
InnerVertices (BorrowStr (n,f,g)) is non empty Element of K18( the carrier of (BorrowStr (n,f,g)))
K18( the carrier of (BorrowStr (n,f,g))) is set
the ResultSort of (BorrowStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) Element of K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))))
the carrier' of (BorrowStr (n,f,g)) is non empty set
K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g)))) is set
K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
[<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3] is non empty pair set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3},{<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>}} is non empty V36() V40() V51() set
o0 is Relation-like Function-like Element of K230( the Sorts of (BitSubtracterWithBorrowCirc (n,f,g)))
o0 . n is set
o0 . f is set
o0 . g is set
Following (o0,2) is Relation-like Function-like Element of K230( the Sorts of (BitSubtracterWithBorrowCirc (n,f,g)))
(Following (o0,2)) . (BitSubtracterOutput (n,f,g)) is set
(Following (o0,2)) . (BorrowOutput (n,f,g)) is set
f1 is boolean Element of BOOLEAN
g1 is boolean Element of BOOLEAN
h1 is boolean Element of BOOLEAN
f1 'xor' g1 is boolean Element of BOOLEAN
(f1 'xor' g1) 'xor' h1 is boolean Element of BOOLEAN
'not' f1 is boolean Element of BOOLEAN
('not' f1) '&' g1 is boolean Element of BOOLEAN
g1 '&' h1 is boolean Element of BOOLEAN
(('not' f1) '&' g1) 'or' (g1 '&' h1) is boolean Element of BOOLEAN
('not' f1) '&' h1 is boolean Element of BOOLEAN
((('not' f1) '&' g1) 'or' (g1 '&' h1)) 'or' (('not' f1) '&' h1) is boolean Element of BOOLEAN
the Sorts of (BitSubtracterCirc (n,f,g)) is Relation-like the carrier of (2GatesCircStr (n,f,g,'xor')) -defined Function-like V23( the carrier of (2GatesCircStr (n,f,g,'xor'))) set
K230( the Sorts of (BitSubtracterCirc (n,f,g))) is functional V49() V50() set
o0 | the carrier of (2GatesCircStr (n,f,g,'xor')) is Relation-like Function-like set
the Sorts of (BorrowCirc (n,f,g)) is Relation-like the carrier of (BorrowStr (n,f,g)) -defined Function-like V23( the carrier of (BorrowStr (n,f,g))) set
K230( the Sorts of (BorrowCirc (n,f,g))) is functional V49() V50() set
o0 | the carrier of (BorrowStr (n,f,g)) is Relation-like Function-like set
the Sorts of ((BitSubtracterCirc (n,f,g)) +* (BorrowCirc (n,f,g))) is Relation-like the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g))) -defined Function-like V23( the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g)))) set
the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g))) is non empty set
K230( the Sorts of ((BitSubtracterCirc (n,f,g)) +* (BorrowCirc (n,f,g)))) is functional V49() V50() set
InputVertices (BorrowStr (n,f,g)) is Element of K18( the carrier of (BorrowStr (n,f,g)))
the carrier of (BorrowStr (n,f,g)) \ K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
{n,f,g} is V36() V51() set
InputVertices (2GatesCircStr (n,f,g,'xor')) is Element of K18( the carrier of (2GatesCircStr (n,f,g,'xor')))
the carrier of (2GatesCircStr (n,f,g,'xor')) \ K547( the carrier of (2GatesCircStr (n,f,g,'xor')), the ResultSort of (2GatesCircStr (n,f,g,'xor'))) is Element of K18( the carrier of (2GatesCircStr (n,f,g,'xor')))
n is Relation-like Function-like Element of K230( the Sorts of (BitSubtracterCirc (n,f,g)))
proj1 n is set
n . n is set
n . f is set
n . g is set
xx is Relation-like Function-like Element of K230( the Sorts of ((BitSubtracterCirc (n,f,g)) +* (BorrowCirc (n,f,g))))
Following (xx,2) is Relation-like Function-like Element of K230( the Sorts of ((BitSubtracterCirc (n,f,g)) +* (BorrowCirc (n,f,g))))
(Following (xx,2)) . (2GatesCircOutput (n,f,g,'xor')) is set
Following (n,2) is Relation-like Function-like Element of K230( the Sorts of (BitSubtracterCirc (n,f,g)))
(Following (n,2)) . (2GatesCircOutput (n,f,g,'xor')) is boolean Element of BOOLEAN
x is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
proj1 x is set
x . n is set
x . f is set
x . g is set
(Following (xx,2)) . (BorrowOutput (n,f,g)) is set
Following (x,2) is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
(Following (x,2)) . (BorrowOutput (n,f,g)) is boolean Element of BOOLEAN
n is set
f is set
g is set
<*f,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*f,g*>,and2] is non empty pair set
{<*f,g*>,and2} is non empty functional V36() V51() set
{<*f,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*f,g*>,and2},{<*f,g*>}} is non empty V36() V40() V51() set
<*n,g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*n,g*>,and2a] is non empty pair set
{<*n,g*>,and2a} is non empty functional V36() V51() set
{<*n,g*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,g*>,and2a},{<*n,g*>}} is non empty V36() V40() V51() set
<*n,f*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
[<*n,f*>,and2a] is non empty pair set
{<*n,f*>,and2a} is non empty functional V36() V51() set
{<*n,f*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*n,f*>,and2a},{<*n,f*>}} is non empty V36() V40() V51() set
[<*n,f*>,'xor'] is non empty pair set
{<*n,f*>,'xor'} is non empty functional V36() V51() set
{{<*n,f*>,'xor'},{<*n,f*>}} is non empty V36() V40() V51() set
BitSubtracterWithBorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (n,f,g,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*n,f*>,'xor'],g*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'xor')) +* (1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr (n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*f,g*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,g*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitSubtracterWithBorrowCirc (n,f,g) is strict non-empty finitely-generated V107( BitSubtracterWithBorrowStr (n,f,g)) gate`2=den Boolean MSAlgebra over BitSubtracterWithBorrowStr (n,f,g)
BitSubtracterCirc (n,f,g) is strict non-empty finitely-generated V107( 2GatesCircStr (n,f,g,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr (n,f,g,'xor')
2GatesCircuit (n,f,g,'xor') is strict non-empty finitely-generated V107( 2GatesCircStr (n,f,g,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr (n,f,g,'xor')
1GateCircuit (n,f,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'xor')
1GateCircuit (<*n,f*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'xor')
1GateCircuit ([<*n,f*>,'xor'],g,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')
1GateCircuit (<*[<*n,f*>,'xor'],g*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor')
(1GateCircuit (n,f,'xor')) +* (1GateCircuit ([<*n,f*>,'xor'],g,'xor')) is strict non-empty finitely-generated V107((1GateCircStr (<*n,f*>,'xor')) +* (1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,'xor')) +* (1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor'))
BorrowCirc (n,f,g) is strict non-empty finitely-generated V107( BorrowStr (n,f,g)) gate`2=den Boolean MSAlgebra over BorrowStr (n,f,g)
BorrowICirc (n,f,g) is strict non-empty finitely-generated V107( BorrowIStr (n,f,g)) gate`2=den Boolean MSAlgebra over BorrowIStr (n,f,g)
1GateCircuit (n,f,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2a)
1GateCircuit (<*n,f*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,f*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,and2a)
1GateCircuit (f,g,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
1GateCircuit (<*f,g*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*f,g*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,and2)
(1GateCircuit (n,f,and2a)) +* (1GateCircuit (f,g,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))
1GateCircuit (n,g,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,g*>,and2a)
1GateCircuit (<*n,g*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*n,g*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,g*>,and2a)
((1GateCircuit (n,f,and2a)) +* (1GateCircuit (f,g,and2))) +* (1GateCircuit (n,g,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,and2a)) +* (1GateCircStr (<*f,g*>,and2))) +* (1GateCircStr (<*n,g*>,and2a))
1GateCircuit ([<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)
1GateCircuit (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3)
(BorrowICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,and2a],[<*f,g*>,and2],[<*n,g*>,and2a]*>,or3))
(BitSubtracterCirc (n,f,g)) +* (BorrowCirc (n,f,g)) is strict non-empty finitely-generated V107((2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g))) gate`2=den Boolean MSAlgebra over (2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g))
the Sorts of (BitSubtracterWithBorrowCirc (n,f,g)) is Relation-like the carrier of (BitSubtracterWithBorrowStr (n,f,g)) -defined Function-like V23( the carrier of (BitSubtracterWithBorrowStr (n,f,g))) set
the carrier of (BitSubtracterWithBorrowStr (n,f,g)) is non empty set
K230( the Sorts of (BitSubtracterWithBorrowCirc (n,f,g))) is functional V49() V50() set
o0 is Relation-like Function-like Element of K230( the Sorts of (BitSubtracterWithBorrowCirc (n,f,g)))
Following (o0,2) is Relation-like Function-like Element of K230( the Sorts of (BitSubtracterWithBorrowCirc (n,f,g)))
the Sorts of (BitSubtracterCirc (n,f,g)) is Relation-like the carrier of (2GatesCircStr (n,f,g,'xor')) -defined Function-like V23( the carrier of (2GatesCircStr (n,f,g,'xor'))) set
the carrier of (2GatesCircStr (n,f,g,'xor')) is non empty set
K230( the Sorts of (BitSubtracterCirc (n,f,g))) is functional V49() V50() set
o0 | the carrier of (2GatesCircStr (n,f,g,'xor')) is Relation-like Function-like set
the Sorts of (BorrowCirc (n,f,g)) is Relation-like the carrier of (BorrowStr (n,f,g)) -defined Function-like V23( the carrier of (BorrowStr (n,f,g))) set
the carrier of (BorrowStr (n,f,g)) is non empty set
K230( the Sorts of (BorrowCirc (n,f,g))) is functional V49() V50() set
o0 | the carrier of (BorrowStr (n,f,g)) is Relation-like Function-like set
the Sorts of ((BitSubtracterCirc (n,f,g)) +* (BorrowCirc (n,f,g))) is Relation-like the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g))) -defined Function-like V23( the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g)))) set
the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (BorrowStr (n,f,g))) is non empty set
K230( the Sorts of ((BitSubtracterCirc (n,f,g)) +* (BorrowCirc (n,f,g)))) is functional V49() V50() set
InputVertices (BorrowStr (n,f,g)) is Element of K18( the carrier of (BorrowStr (n,f,g)))
K18( the carrier of (BorrowStr (n,f,g))) is set
the ResultSort of (BorrowStr (n,f,g)) is Relation-like Function-like V27( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) Element of K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))))
the carrier' of (BorrowStr (n,f,g)) is non empty set
K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g))) is Relation-like set
K18(K19( the carrier' of (BorrowStr (n,f,g)), the carrier of (BorrowStr (n,f,g)))) is set
K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
the carrier of (BorrowStr (n,f,g)) \ K547( the carrier of (BorrowStr (n,f,g)), the ResultSort of (BorrowStr (n,f,g))) is Element of K18( the carrier of (BorrowStr (n,f,g)))
{n,f,g} is V36() V51() set
InnerVertices (2GatesCircStr (n,f,g,'xor')) is non empty Element of K18( the carrier of (2GatesCircStr (n,f,g,'xor')))
K18( the carrier of (2GatesCircStr (n,f,g,'xor'))) is set
the ResultSort of (2GatesCircStr (n,f,g,'xor')) is Relation-like Function-like V27( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) Element of K18(K19( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))))
the carrier' of (2GatesCircStr (n,f,g,'xor')) is non empty set
K19( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) is Relation-like set
K18(K19( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor')))) is set
K547( the carrier of (2GatesCircStr (n,f,g,'xor')), the ResultSort of (2GatesCircStr (n,f,g,'xor'))) is Element of K18( the carrier of (2GatesCircStr (n,f,g,'xor')))
InputVertices (2GatesCircStr (n,f,g,'xor')) is Element of K18( the carrier of (2GatesCircStr (n,f,g,'xor')))
the carrier of (2GatesCircStr (n,f,g,'xor')) \ K547( the carrier of (2GatesCircStr (n,f,g,'xor')), the ResultSort of (2GatesCircStr (n,f,g,'xor'))) is Element of K18( the carrier of (2GatesCircStr (n,f,g,'xor')))
InnerVertices (BorrowStr (n,f,g)) is non empty Element of K18( the carrier of (BorrowStr (n,f,g)))
f1 is Relation-like Function-like Element of K230( the Sorts of (BitSubtracterCirc (n,f,g)))
Following (f1,2) is Relation-like Function-like Element of K230( the Sorts of (BitSubtracterCirc (n,f,g)))
h1 is Relation-like Function-like Element of K230( the Sorts of ((BitSubtracterCirc (n,f,g)) +* (BorrowCirc (n,f,g))))
Following (h1,2) is Relation-like Function-like Element of K230( the Sorts of ((BitSubtracterCirc (n,f,g)) +* (BorrowCirc (n,f,g))))
(Following (h1,2)) | the carrier of (2GatesCircStr (n,f,g,'xor')) is Relation-like Function-like set
Following (f1,3) is Relation-like Function-like Element of K230( the Sorts of (BitSubtracterCirc (n,f,g)))
Following (h1,3) is Relation-like Function-like Element of K230( the Sorts of ((BitSubtracterCirc (n,f,g)) +* (BorrowCirc (n,f,g))))
(Following (h1,3)) | the carrier of (2GatesCircStr (n,f,g,'xor')) is Relation-like Function-like set
g1 is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
Following (g1,2) is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
(Following (h1,2)) | the carrier of (BorrowStr (n,f,g)) is Relation-like Function-like set
Following (g1,3) is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
(Following (h1,3)) | the carrier of (BorrowStr (n,f,g)) is Relation-like Function-like set
Following (Following (f1,2)) is Relation-like Function-like Element of K230( the Sorts of (BitSubtracterCirc (n,f,g)))
2 + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
Following (f1,(2 + 1)) is Relation-like Function-like Element of K230( the Sorts of (BitSubtracterCirc (n,f,g)))
Following (Following (g1,2)) is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
Following (g1,(2 + 1)) is Relation-like Function-like Element of K230( the Sorts of (BorrowCirc (n,f,g)))
Following (o0,(2 + 1)) is Relation-like Function-like Element of K230( the Sorts of (BitSubtracterWithBorrowCirc (n,f,g)))
Following (Following (o0,2)) is Relation-like Function-like Element of K230( the Sorts of (BitSubtracterWithBorrowCirc (n,f,g)))
proj1 (Following (o0,2)) is set
Following (o0,3) is Relation-like Function-like Element of K230( the Sorts of (BitSubtracterWithBorrowCirc (n,f,g)))
proj1 (Following (o0,3)) is set
proj1 (Following (f1,2)) is set
proj1 (Following (g1,2)) is set
the carrier of (2GatesCircStr (n,f,g,'xor')) \/ the carrier of (BorrowStr (n,f,g)) is non empty set
n is set
(Following (o0,2)) . n is set
(Following (f1,2)) . n is set
(Following (o0,3)) . n is set
(Following (f1,3)) . n is set
(Following (g1,2)) . n is set
(Following (g1,3)) . n is set
(Following (Following (o0,2))) . n is set
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
2 * n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
1 + (2 * n) is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f is Relation-like NAT -defined Function-like V36() n -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
g is Relation-like NAT -defined Function-like V36() n -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
(n,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,f,g) is strict non-empty finitely-generated V107((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 V23( the carrier of (n,f,g)) set
the carrier of (n,f,g) is non empty set
K230( the Sorts of (n,f,g)) is functional V49() V50() set
N is Relation-like Function-like V27( NAT , NAT ) Element of K18(K19(NAT,NAT))
N . 0 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
N . 1 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
N . 2 is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
Sn is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
Sn + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f . (Sn + 1) is non pair set
g . (Sn + 1) is non pair set
h is set
BitSubtracterWithBorrowCirc ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V107( BitSubtracterWithBorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) gate`2=den Boolean MSAlgebra over BitSubtracterWithBorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),h)
BitSubtracterWithBorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),h) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (Sn + 1)),(g . (Sn + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'] is non empty pair set
{<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (Sn + 1)),(g . (Sn + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'},{<*(f . (Sn + 1)),(g . (Sn + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],h*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],h*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],h*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),h) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (Sn + 1)),(g . (Sn + 1)),h) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (Sn + 1)),h*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (Sn + 1)),h*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (Sn + 1)),h*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (Sn + 1)),h*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2))) +* (1GateCircStr (<*(f . (Sn + 1)),h*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a] is non empty pair set
{<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a},{<*(f . (Sn + 1)),(g . (Sn + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (Sn + 1)),h*>,and2] is non empty pair set
{<*(g . (Sn + 1)),h*>,and2} is non empty functional V36() V51() set
{<*(g . (Sn + 1)),h*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (Sn + 1)),h*>,and2},{<*(g . (Sn + 1)),h*>}} is non empty V36() V40() V51() set
[<*(f . (Sn + 1)),h*>,and2a] is non empty pair set
{<*(f . (Sn + 1)),h*>,and2a} is non empty functional V36() V51() set
{<*(f . (Sn + 1)),h*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (Sn + 1)),h*>,and2a},{<*(f . (Sn + 1)),h*>}} is non empty V36() V40() V51() set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),h*>,and2],[<*(f . (Sn + 1)),h*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),h*>,and2],[<*(f . (Sn + 1)),h*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),h*>,and2],[<*(f . (Sn + 1)),h*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,'xor')) +* (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitSubtracterCirc ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V107( 2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,'xor')
2GatesCircuit ((f . (Sn + 1)),(g . (Sn + 1)),h,'xor') is strict non-empty finitely-generated V107( 2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,'xor')
1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor')
1GateCircuit (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor')
1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],h,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],h*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],h*>,'xor')
1GateCircuit (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],h*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],h*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],h*>,'xor')
(1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),'xor')) +* (1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],h,'xor')) is strict non-empty finitely-generated V107((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],h*>,'xor'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],h*>,'xor'))
BorrowCirc ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V107( BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) gate`2=den Boolean MSAlgebra over BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),h)
BorrowICirc ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V107( BorrowIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) gate`2=den Boolean MSAlgebra over BorrowIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)
1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)
1GateCircuit (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)
1GateCircuit ((g . (Sn + 1)),h,and2) is strict non-empty finitely-generated V107( 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 V107( 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)),and2a)) +* (1GateCircuit ((g . (Sn + 1)),h,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2))
1GateCircuit ((f . (Sn + 1)),h,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (Sn + 1)),h*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),h*>,and2a)
1GateCircuit (<*(f . (Sn + 1)),h*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (Sn + 1)),h*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),h*>,and2a)
((1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),and2a)) +* (1GateCircuit ((g . (Sn + 1)),h,and2))) +* (1GateCircuit ((f . (Sn + 1)),h,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2))) +* (1GateCircStr (<*(f . (Sn + 1)),h*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,and2))) +* (1GateCircStr (<*(f . (Sn + 1)),h*>,and2a))
1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),h*>,and2],[<*(f . (Sn + 1)),h*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),h*>,and2],[<*(f . (Sn + 1)),h*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),h*>,and2],[<*(f . (Sn + 1)),h*>,and2a]*>,or3)
1GateCircuit (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),h*>,and2],[<*(f . (Sn + 1)),h*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),h*>,and2],[<*(f . (Sn + 1)),h*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),h*>,and2],[<*(f . (Sn + 1)),h*>,and2a]*>,or3)
(BorrowICirc ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),h*>,and2],[<*(f . (Sn + 1)),h*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),h*>,and2],[<*(f . (Sn + 1)),h*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),h*>,and2],[<*(f . (Sn + 1)),h*>,and2a]*>,or3))
(BitSubtracterCirc ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (BorrowCirc ((f . (Sn + 1)),(g . (Sn + 1)),h)) is strict non-empty finitely-generated V107((2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,'xor')) +* (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),h))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,'xor')) +* (BorrowStr ((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 V23( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)))) set
the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) is non empty set
K230( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE)))) is functional V49() V50() set
h is Relation-like Function-like Element of K230( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE))))
Following (h,1) is Relation-like Function-like Element of K230( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE))))
Following h is Relation-like Function-like Element of K230( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE))))
Following (h,H₄( 0 )) is Relation-like Function-like Element of K230( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> TRUE))))
h is Relation-like NAT -defined Function-like V23( NAT ) set
Sn is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
Sn + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f . (Sn + 1) is non pair set
g . (Sn + 1) is non pair set
h . Sn is set
An is set
BitSubtracterWithBorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),An) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),An,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (Sn + 1)),(g . (Sn + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'] is non empty pair set
{<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (Sn + 1)),(g . (Sn + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'},{<*(f . (Sn + 1)),(g . (Sn + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],An*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],An*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],An*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),An) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (Sn + 1)),(g . (Sn + 1)),An) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (Sn + 1)),An*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (Sn + 1)),An*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) +* (1GateCircStr (<*(g . (Sn + 1)),An*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (Sn + 1)),An*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (Sn + 1)),An*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) +* (1GateCircStr (<*(g . (Sn + 1)),An*>,and2))) +* (1GateCircStr (<*(f . (Sn + 1)),An*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a] is non empty pair set
{<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a},{<*(f . (Sn + 1)),(g . (Sn + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (Sn + 1)),An*>,and2] is non empty pair set
{<*(g . (Sn + 1)),An*>,and2} is non empty functional V36() V51() set
{<*(g . (Sn + 1)),An*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (Sn + 1)),An*>,and2},{<*(g . (Sn + 1)),An*>}} is non empty V36() V40() V51() set
[<*(f . (Sn + 1)),An*>,and2a] is non empty pair set
{<*(f . (Sn + 1)),An*>,and2a} is non empty functional V36() V51() set
{<*(f . (Sn + 1)),An*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (Sn + 1)),An*>,and2a},{<*(f . (Sn + 1)),An*>}} is non empty V36() V40() V51() set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),An*>,and2],[<*(f . (Sn + 1)),An*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),An*>,and2],[<*(f . (Sn + 1)),An*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),An*>,and2],[<*(f . (Sn + 1)),An*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),An,'xor')) +* (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitSubtracterWithBorrowCirc ((f . (Sn + 1)),(g . (Sn + 1)),An) is strict non-empty finitely-generated V107( BitSubtracterWithBorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) gate`2=den Boolean MSAlgebra over BitSubtracterWithBorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),An)
BitSubtracterCirc ((f . (Sn + 1)),(g . (Sn + 1)),An) is strict non-empty finitely-generated V107( 2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),An,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),An,'xor')
2GatesCircuit ((f . (Sn + 1)),(g . (Sn + 1)),An,'xor') is strict non-empty finitely-generated V107( 2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),An,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),An,'xor')
1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor')
1GateCircuit (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor')
1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],An,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],An*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],An*>,'xor')
1GateCircuit (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],An*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],An*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],An*>,'xor')
(1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),'xor')) +* (1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],An,'xor')) is strict non-empty finitely-generated V107((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],An*>,'xor'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],An*>,'xor'))
BorrowCirc ((f . (Sn + 1)),(g . (Sn + 1)),An) is strict non-empty finitely-generated V107( BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) gate`2=den Boolean MSAlgebra over BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),An)
BorrowICirc ((f . (Sn + 1)),(g . (Sn + 1)),An) is strict non-empty finitely-generated V107( BorrowIStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) gate`2=den Boolean MSAlgebra over BorrowIStr ((f . (Sn + 1)),(g . (Sn + 1)),An)
1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)
1GateCircuit (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)
1GateCircuit ((g . (Sn + 1)),An,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*(g . (Sn + 1)),An*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (Sn + 1)),An*>,and2)
1GateCircuit (<*(g . (Sn + 1)),An*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*(g . (Sn + 1)),An*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (Sn + 1)),An*>,and2)
(1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),and2a)) +* (1GateCircuit ((g . (Sn + 1)),An,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) +* (1GateCircStr (<*(g . (Sn + 1)),An*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) +* (1GateCircStr (<*(g . (Sn + 1)),An*>,and2))
1GateCircuit ((f . (Sn + 1)),An,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (Sn + 1)),An*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),An*>,and2a)
1GateCircuit (<*(f . (Sn + 1)),An*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (Sn + 1)),An*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),An*>,and2a)
((1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),and2a)) +* (1GateCircuit ((g . (Sn + 1)),An,and2))) +* (1GateCircuit ((f . (Sn + 1)),An,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) +* (1GateCircStr (<*(g . (Sn + 1)),An*>,and2))) +* (1GateCircStr (<*(f . (Sn + 1)),An*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a)) +* (1GateCircStr (<*(g . (Sn + 1)),An*>,and2))) +* (1GateCircStr (<*(f . (Sn + 1)),An*>,and2a))
1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),An*>,and2],[<*(f . (Sn + 1)),An*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),An*>,and2],[<*(f . (Sn + 1)),An*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),An*>,and2],[<*(f . (Sn + 1)),An*>,and2a]*>,or3)
1GateCircuit (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),An*>,and2],[<*(f . (Sn + 1)),An*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),An*>,and2],[<*(f . (Sn + 1)),An*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),An*>,and2],[<*(f . (Sn + 1)),An*>,and2a]*>,or3)
(BorrowICirc ((f . (Sn + 1)),(g . (Sn + 1)),An)) +* (1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),An*>,and2],[<*(f . (Sn + 1)),An*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),An*>,and2],[<*(f . (Sn + 1)),An*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,and2a],[<*(g . (Sn + 1)),An*>,and2],[<*(f . (Sn + 1)),An*>,and2a]*>,or3))
(BitSubtracterCirc ((f . (Sn + 1)),(g . (Sn + 1)),An)) +* (BorrowCirc ((f . (Sn + 1)),(g . (Sn + 1)),An)) is strict non-empty finitely-generated V107((2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),An,'xor')) +* (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),An))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),An,'xor')) +* (BorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),An))
o0 is non-empty finitely-generated V107(H<sub>1</sub>(An,Sn)) MSAlgebra over H<sub>1</sub>(An,Sn)
the Sorts of o0 is Relation-like the carrier of H<sub>1</sub>(An,Sn) -defined Function-like V23( the carrier of H<sub>1</sub>(An,Sn)) set
the carrier of H<sub>1</sub>(An,Sn) is non empty set
K230( the Sorts of o0) is functional V49() V50() set
(Sn,f,g) is Element of InnerVertices (Sn,f,g)
(Sn,f,g) is non empty non void V71() 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 K18( the carrier of (Sn,f,g))
K18( the carrier of (Sn,f,g)) is set
the ResultSort of (Sn,f,g) is Relation-like Function-like V27( the carrier' of (Sn,f,g), the carrier of (Sn,f,g)) Element of K18(K19( the carrier' of (Sn,f,g), the carrier of (Sn,f,g)))
the carrier' of (Sn,f,g) is non empty set
K19( the carrier' of (Sn,f,g), the carrier of (Sn,f,g)) is Relation-like set
K18(K19( the carrier' of (Sn,f,g), the carrier of (Sn,f,g))) is set
K547( the carrier of (Sn,f,g), the ResultSort of (Sn,f,g)) is Element of K18( the carrier of (Sn,f,g))
f1 is Relation-like Function-like Element of K230( the Sorts of o0)
Following (f1,(N . 1)) is Relation-like Function-like Element of K230( the Sorts of o0)
the Sorts of o0 is Relation-like the carrier of (BitSubtracterWithBorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) -defined Function-like V23( the carrier of (BitSubtracterWithBorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),An))) set
the carrier of (BitSubtracterWithBorrowStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) is non empty set
K230( the Sorts of o0) is functional V49() V50() set
(0,f,g) is non empty pair Element of InnerVertices (0,f,g)
(0,f,g) is non empty non void V71() 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 K18( the carrier of (0,f,g))
K18( the carrier of (0,f,g)) is set
the ResultSort of (0,f,g) is Relation-like Function-like V27( the carrier' of (0,f,g), the carrier of (0,f,g)) Element of K18(K19( the carrier' of (0,f,g), the carrier of (0,f,g)))
the carrier' of (0,f,g) is non empty set
K19( the carrier' of (0,f,g), the carrier of (0,f,g)) is Relation-like set
K18(K19( the carrier' of (0,f,g), the carrier of (0,f,g))) is set
K547( the carrier of (0,f,g), the ResultSort of (0,f,g)) is Element of K18( the carrier of (0,f,g))
f1 is Relation-like NAT -defined Function-like V23( NAT ) set
f1 . n is set
g1 is Relation-like NAT -defined Function-like V23( NAT ) set
g1 . n is set
f1 . 0 is set
g1 . 0 is set
h1 is Relation-like NAT -defined Function-like V23( NAT ) set
h1 . 0 is set
n is set
h1 . n is set
x is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
(x,f,g) is non empty pair Element of InnerVertices (x,f,g)
(x,f,g) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (x,f,g) is non empty set
InnerVertices (x,f,g) is non empty Element of K18( the carrier of (x,f,g))
K18( the carrier of (x,f,g)) is set
the ResultSort of (x,f,g) is Relation-like Function-like V27( the carrier' of (x,f,g), the carrier of (x,f,g)) Element of K18(K19( the carrier' of (x,f,g), the carrier of (x,f,g)))
the carrier' of (x,f,g) is non empty set
K19( the carrier' of (x,f,g), the carrier of (x,f,g)) is Relation-like set
K18(K19( the carrier' of (x,f,g), the carrier of (x,f,g))) is set
K547( the carrier of (x,f,g), the ResultSort of (x,f,g)) is Element of K18( the carrier of (x,f,g))
h . n is set
h . 0 is set
f1 . H₄(2) is set
g1 . H₄(2) is set
x is non empty V71() ManySortedSign
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
n + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f . (n + 1) is non pair set
g . (n + 1) is non pair set
xy is set
BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),xy) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (n + 1)),(g . (n + 1)),xy,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),(g . (n + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,'xor'] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (n + 1)),(g . (n + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'xor'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],xy*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],xy*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],xy*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (n + 1)),(g . (n + 1)),xy) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (n + 1)),(g . (n + 1)),xy) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (n + 1)),xy*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (n + 1)),xy*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),xy*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),xy*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (n + 1)),xy*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),xy*>,and2))) +* (1GateCircStr (<*(f . (n + 1)),xy*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,and2a] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (n + 1)),(g . (n + 1))*>,and2a},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (n + 1)),xy*>,and2] is non empty pair set
{<*(g . (n + 1)),xy*>,and2} is non empty functional V36() V51() set
{<*(g . (n + 1)),xy*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (n + 1)),xy*>,and2},{<*(g . (n + 1)),xy*>}} is non empty V36() V40() V51() set
[<*(f . (n + 1)),xy*>,and2a] is non empty pair set
{<*(f . (n + 1)),xy*>,and2a} is non empty functional V36() V51() set
{<*(f . (n + 1)),xy*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (n + 1)),xy*>,and2a},{<*(f . (n + 1)),xy*>}} is non empty V36() V40() V51() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (n + 1)),(g . (n + 1)),xy)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (n + 1)),(g . (n + 1)),xy,'xor')) +* (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f1 . n is set
xx is non-empty MSAlgebra over x
g1 . n is set
h . n is set
c<sub>18</sub> is non-empty MSAlgebra over BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),xy)
BitSubtracterWithBorrowCirc ((f . (n + 1)),(g . (n + 1)),xy) is strict non-empty finitely-generated V107( BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),xy)) gate`2=den Boolean MSAlgebra over BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),xy)
BitSubtracterCirc ((f . (n + 1)),(g . (n + 1)),xy) is strict non-empty finitely-generated V107( 2GatesCircStr ((f . (n + 1)),(g . (n + 1)),xy,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (n + 1)),(g . (n + 1)),xy,'xor')
2GatesCircuit ((f . (n + 1)),(g . (n + 1)),xy,'xor') is strict non-empty finitely-generated V107( 2GatesCircStr ((f . (n + 1)),(g . (n + 1)),xy,'xor')) gate`2=den Boolean MSAlgebra over 2GatesCircStr ((f . (n + 1)),(g . (n + 1)),xy,'xor')
1GateCircuit ((f . (n + 1)),(g . (n + 1)),'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')
1GateCircuit (<*(f . (n + 1)),(g . (n + 1))*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')
1GateCircuit ([<*(f . (n + 1)),(g . (n + 1))*>,'xor'],xy,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],xy*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],xy*>,'xor')
1GateCircuit (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],xy*>,'xor') is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],xy*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],xy*>,'xor')
(1GateCircuit ((f . (n + 1)),(g . (n + 1)),'xor')) +* (1GateCircuit ([<*(f . (n + 1)),(g . (n + 1))*>,'xor'],xy,'xor')) is strict non-empty finitely-generated V107((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],xy*>,'xor'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],xy*>,'xor'))
BorrowCirc ((f . (n + 1)),(g . (n + 1)),xy) is strict non-empty finitely-generated V107( BorrowStr ((f . (n + 1)),(g . (n + 1)),xy)) gate`2=den Boolean MSAlgebra over BorrowStr ((f . (n + 1)),(g . (n + 1)),xy)
BorrowICirc ((f . (n + 1)),(g . (n + 1)),xy) is strict non-empty finitely-generated V107( BorrowIStr ((f . (n + 1)),(g . (n + 1)),xy)) gate`2=den Boolean MSAlgebra over BorrowIStr ((f . (n + 1)),(g . (n + 1)),xy)
1GateCircuit ((f . (n + 1)),(g . (n + 1)),and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)
1GateCircuit (<*(f . (n + 1)),(g . (n + 1))*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)
1GateCircuit ((g . (n + 1)),xy,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*(g . (n + 1)),xy*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (n + 1)),xy*>,and2)
1GateCircuit (<*(g . (n + 1)),xy*>,and2) is strict non-empty finitely-generated V107( 1GateCircStr (<*(g . (n + 1)),xy*>,and2)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (n + 1)),xy*>,and2)
(1GateCircuit ((f . (n + 1)),(g . (n + 1)),and2a)) +* (1GateCircuit ((g . (n + 1)),xy,and2)) is strict non-empty finitely-generated V107((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),xy*>,and2))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),xy*>,and2))
1GateCircuit ((f . (n + 1)),xy,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (n + 1)),xy*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),xy*>,and2a)
1GateCircuit (<*(f . (n + 1)),xy*>,and2a) is strict non-empty finitely-generated V107( 1GateCircStr (<*(f . (n + 1)),xy*>,and2a)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),xy*>,and2a)
((1GateCircuit ((f . (n + 1)),(g . (n + 1)),and2a)) +* (1GateCircuit ((g . (n + 1)),xy,and2))) +* (1GateCircuit ((f . (n + 1)),xy,and2a)) is strict non-empty finitely-generated V107(((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),xy*>,and2))) +* (1GateCircStr (<*(f . (n + 1)),xy*>,and2a))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),xy*>,and2))) +* (1GateCircStr (<*(f . (n + 1)),xy*>,and2a))
1GateCircuit ([<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a],or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a]*>,or3)
1GateCircuit (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a]*>,or3) is strict non-empty finitely-generated V107( 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a]*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a]*>,or3)
(BorrowICirc ((f . (n + 1)),(g . (n + 1)),xy)) +* (1GateCircuit ([<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a],or3)) is strict non-empty finitely-generated V107((BorrowIStr ((f . (n + 1)),(g . (n + 1)),xy)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a]*>,or3))) gate`2=den Boolean MSAlgebra over (BorrowIStr ((f . (n + 1)),(g . (n + 1)),xy)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a]*>,or3))
(BitSubtracterCirc ((f . (n + 1)),(g . (n + 1)),xy)) +* (BorrowCirc ((f . (n + 1)),(g . (n + 1)),xy)) is strict non-empty finitely-generated V107((2GatesCircStr ((f . (n + 1)),(g . (n + 1)),xy,'xor')) +* (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),xy,'xor')) +* (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy))
f1 . (n + 1) is set
x +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),xy)) is non empty non void V71() strict ManySortedSign
g1 . (n + 1) is set
xx +* c<sub>18</sub> is strict non-empty MSAlgebra over x +* (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),xy))
h . (n + 1) is set
BorrowOutput ((f . (n + 1)),(g . (n + 1)),xy) is Element of InnerVertices (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy))
the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy)) is non empty set
InnerVertices (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy)) is non empty Element of K18( the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy)))
K18( the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy))) is set
the ResultSort of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy)) is Relation-like Function-like V27( the carrier' of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy)), the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy))) Element of K18(K19( the carrier' of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy)), the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy))))
the carrier' of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy)) is non empty set
K19( the carrier' of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy)), the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy))) is Relation-like set
K18(K19( the carrier' of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy)), the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy)))) is set
K547( the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy)), the ResultSort of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy))) is Element of K18( the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),xy)))
[<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a]*>,or3] is non empty pair set
{<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a]*>,or3},{<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),xy*>,and2],[<*(f . (n + 1)),xy*>,and2a]*>}} is non empty V36() V40() V51() set
InnerVertices (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) is non empty Element of K18( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))))
K18( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)))) is set
the ResultSort of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) is Relation-like Function-like V27( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)))) Element of K18(K19( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)))))
the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) is non empty set
K19( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)))) is Relation-like set
K18(K19( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))))) is set
K547( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))), the ResultSort of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)))) is Element of K18( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))))
InputVertices (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) is Element of K18( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))))
the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))) \ K547( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))), the ResultSort of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE)))) is Element of K18( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> TRUE))))
{[{},((0 -tuples_on BOOLEAN) --> TRUE)]} is non empty V2() Relation-like Function-like constant V36() 1 -element V51() set
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
n + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f . (n + 1) is non pair set
g . (n + 1) is non pair set
x is set
BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),(g . (n + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,'xor'] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (n + 1)),(g . (n + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'xor'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (n + 1)),x*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (n + 1)),x*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),x*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),x*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (n + 1)),x*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),x*>,and2))) +* (1GateCircStr (<*(f . (n + 1)),x*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,and2a] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (n + 1)),(g . (n + 1))*>,and2a},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (n + 1)),x*>,and2] is non empty pair set
{<*(g . (n + 1)),x*>,and2} is non empty functional V36() V51() set
{<*(g . (n + 1)),x*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (n + 1)),x*>,and2},{<*(g . (n + 1)),x*>}} is non empty V36() V40() V51() set
[<*(f . (n + 1)),x*>,and2a] is non empty pair set
{<*(f . (n + 1)),x*>,and2a} is non empty functional V36() V51() set
{<*(f . (n + 1)),x*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (n + 1)),x*>,and2a},{<*(f . (n + 1)),x*>}} is non empty V36() V40() V51() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (n + 1)),(g . (n + 1)),x)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')) +* (BorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty Element of K18( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)))
the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
K18( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))) is set
the ResultSort of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))))
the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)))) is set
K547( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the ResultSort of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)))
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
h . n is set
n + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative Element of NAT
f . (n + 1) is non pair set
g . (n + 1) is non pair set
x is set
BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),(g . (n + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,'xor'] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,'xor'} is non empty functional V36() V51() set
{<*(f . (n + 1)),(g . (n + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'xor'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (n + 1)),x*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (n + 1)),x*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),x*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),x*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (n + 1)),x*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),x*>,and2))) +* (1GateCircStr (<*(f . (n + 1)),x*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,and2a] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,and2a} is non empty functional V36() V51() set
{{<*(f . (n + 1)),(g . (n + 1))*>,and2a},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (n + 1)),x*>,and2] is non empty pair set
{<*(g . (n + 1)),x*>,and2} is non empty functional V36() V51() set
{<*(g . (n + 1)),x*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (n + 1)),x*>,and2},{<*(g . (n + 1)),x*>}} is non empty V36() V40() V51() set
[<*(f . (n + 1)),x*>,and2a] is non empty pair set
{<*(f . (n + 1)),x*>,and2a} is non empty functional V36() V51() set
{<*(f . (n + 1)),x*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (n + 1)),x*>,and2a},{<*(f . (n + 1)),x*>}} is non empty V36() V40() V51() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (n + 1)),(g . (n + 1)),x)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')) +* (BorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of H<sub>1</sub>(x,n) is non empty set
InputVertices H<sub>1</sub>(x,n) is Element of K18( the carrier of H<sub>1</sub>(x,n))
K18( the carrier of H<sub>1</sub>(x,n)) is set
the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
the ResultSort of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))))
the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)))) is set
K547( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the ResultSort of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)))
K18( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))) is set
the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)) \ K547( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the ResultSort of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)))
{x} is non empty V2() V36() 1 -element V51() set
(InputVertices H<sub>1</sub>(x,n)) \ {x} is Element of K18( the carrier of H<sub>1</sub>(x,n))
(n,f,g) is Element of InnerVertices (n,f,g)
(n,f,g) is non empty non void V71() 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 K18( the carrier of (n,f,g))
K18( the carrier of (n,f,g)) is set
the ResultSort of (n,f,g) is Relation-like Function-like V27( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K19( the carrier' of (n,f,g), the carrier of (n,f,g)) is Relation-like set
K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g))) is set
K547( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K18( the carrier of (n,f,g))
{(f . (n + 1)),(g . (n + 1)),x} is V36() V51() set
xx is non empty pair set
n is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative set
h . n is set
n + 1 is non empty V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real positive non negative 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
BorrowOutput ((f . (n + 1)),(g . (n + 1)),x) is Element of InnerVertices (BorrowStr ((f . (n + 1)),(g . (n + 1)),x))
BorrowStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BorrowIStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),(g . (n + 1))*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() nonpair-yielding set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (n + 1)),x*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(g . (n + 1)),x*>,and2) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),x*>,and2)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (n + 1)),x*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*(f . (n + 1)),x*>,and2a) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,and2a)) +* (1GateCircStr (<*(g . (n + 1)),x*>,and2))) +* (1GateCircStr (<*(f . (n + 1)),x*>,and2a)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,and2a] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,and2a} is non empty functional V36() V51() set
{<*(f . (n + 1)),(g . (n + 1))*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (n + 1)),(g . (n + 1))*>,and2a},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V36() V40() V51() set
[<*(g . (n + 1)),x*>,and2] is non empty pair set
{<*(g . (n + 1)),x*>,and2} is non empty functional V36() V51() set
{<*(g . (n + 1)),x*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(g . (n + 1)),x*>,and2},{<*(g . (n + 1)),x*>}} is non empty V36() V40() V51() set
[<*(f . (n + 1)),x*>,and2a] is non empty pair set
{<*(f . (n + 1)),x*>,and2a} is non empty functional V36() V51() set
{<*(f . (n + 1)),x*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*(f . (n + 1)),x*>,and2a},{<*(f . (n + 1)),x*>}} is non empty V36() V40() V51() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]*> is non empty Relation-like NAT -defined Function-like V36() 3 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]*>,or3) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(BorrowIStr ((f . (n + 1)),(g . (n + 1)),x)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]*>,or3)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
InnerVertices (BorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty Element of K18( the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x)))
K18( the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x))) is set
the ResultSort of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is Relation-like Function-like V27( the carrier' of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x))) Element of K18(K19( the carrier' of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x))))
the carrier' of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
K19( the carrier' of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x))) is Relation-like set
K18(K19( the carrier' of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x)))) is set
K547( the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the ResultSort of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x))) is Element of K18( the carrier of (BorrowStr ((f . (n + 1)),(g . (n + 1)),x)))
[<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]*>,or3] is non empty pair set
{<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]*>,or3} is non empty functional V36() V51() set
{<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]*>,or3},{<*[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]*>}} is non empty V36() V40() V51() set
BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,'xor'] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,'xor'} is non empty functional V36() V51() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'xor'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V36() V40() V51() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*> is non empty Relation-like NAT -defined Function-like V36() 2 -element FinSequence-like FinSubsequence-like V51() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>,'xor') is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>,'xor')) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')) +* (BorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty non void V71() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices H<sub>1</sub>(x,n) is Element of K18( the carrier of H<sub>1</sub>(x,n))
the carrier of H<sub>1</sub>(x,n) is non empty set
K18( the carrier of H<sub>1</sub>(x,n)) is set
the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
the ResultSort of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is Relation-like Function-like V27( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))) Element of K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))))
the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))) is Relation-like set
K18(K19( the carrier' of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)))) is set
K547( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the ResultSort of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)))
K18( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))) is set
the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)) \ K547( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)), the ResultSort of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x))) is Element of K18( the carrier of (BitSubtracterWithBorrowStr ((f . (n + 1)),(g . (n + 1)),x)))
InnerVertices H<sub>1</sub>(x,n) is non empty Element of K18( the carrier of H<sub>1</sub>(x,n))
(n,f,g) is Element of InnerVertices (n,f,g)
(n,f,g) is non empty non void V71() 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 K18( the carrier of (n,f,g))
K18( the carrier of (n,f,g)) is set
the ResultSort of (n,f,g) is Relation-like Function-like V27( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K19( the carrier' of (n,f,g), the carrier of (n,f,g)) is Relation-like set
K18(K19( the carrier' of (n,f,g), the carrier of (n,f,g))) is set
K547( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K18( the carrier of (n,f,g))
((n + 1),f,g) is non empty pair Element of InnerVertices ((n + 1),f,g)
((n + 1),f,g) is non empty non void V71() 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 K18( the carrier of ((n + 1),f,g))
K18( the carrier of ((n + 1),f,g)) is set
the ResultSort of ((n + 1),f,g) is Relation-like Function-like V27( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) Element of K18(K19( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)))
the carrier' of ((n + 1),f,g) is non empty set
K19( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) is Relation-like set
K18(K19( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g))) is set
K547( the carrier of ((n + 1),f,g), the ResultSort of ((n + 1),f,g)) is Element of K18( the carrier of ((n + 1),f,g))
{(f . (n + 1)),(g . (n + 1)),x} is V36() V51() set
{H₃(x,n)} is non empty V2() V36() 1 -element V51() set
2GatesCircOutput ((f . (n + 1)),(g . (n + 1)),x,'xor') is non empty pair Element of InnerVertices (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor'))
the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')) is non empty set
InnerVertices (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')) is non empty Element of K18( the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')))
K18( the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor'))) is set
the ResultSort of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')) is Relation-like Function-like V27( the carrier' of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')), the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor'))) Element of K18(K19( the carrier' of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')), the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor'))))
the carrier' of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')) is non empty set
K19( the carrier' of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')), the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor'))) is Relation-like set
K18(K19( the carrier' of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')), the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')))) is set
K547( the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')), the ResultSort of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor'))) is Element of K18( the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')))
[<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>,'xor'] is non empty pair set
{<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>,'xor'} is non empty functional V36() V51() set
{<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>} is non empty V2() functional V36() V40() 1 -element V49() V51() set
{{<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>,'xor'},{<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>}} is non empty V36() V40() V51() set
{[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(2GatesCircOutput ((f . (n + 1)),(g . (n + 1)),x,'xor'))} is non empty Relation-like V36() V51() set
{[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]} is Relation-like V36() V51() set
{[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(2GatesCircOutput ((f . (n + 1)),(g . (n + 1)),x,'xor'))} \/ {[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]} is non empty Relation-like V36() V51() set
{(BorrowOutput ((f . (n + 1)),(g . (n + 1)),x))} is non empty V2() V36() 1 -element V51() set
({[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(2GatesCircOutput ((f . (n + 1)),(g . (n + 1)),x,'xor'))} \/ {[<*(f . (n + 1)),(g . (n + 1))*>,and2a],[<*(g . (n + 1)),x*>,and2],[<*(f . (n + 1)),x*>,and2a]}) \/ {(BorrowOutput ((f . (n + 1)),(g . (n + 1)),x))} is non empty V36() V51() set
H₄(2) * H₄(1) is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
H₄( 0 ) + (H₄(2) * H₄(1)) is V9() V10() V11() V15() non pair V30() V31() V36() cardinal V51() ext-real non negative Element of NAT
n is Relation-like Function-like Element of K230( the Sorts of (n,f,g))
Following (n,(1 + (2 * n))) is Relation-like Function-like Element of K230( the Sorts of (n,f,g))