:: FACIRC_2 semantic presentation

REAL is set
NAT is non empty V5() V12() V13() V14() V39() cardinal limit_cardinal V54() V55() Element of K23(REAL)
K23(REAL) is non empty set
COMPLEX is set
RAT is set
INT is set
K24(COMPLEX,COMPLEX) is Relation-like set
K23(K24(COMPLEX,COMPLEX)) is non empty set
K24(K24(COMPLEX,COMPLEX),COMPLEX) is Relation-like set
K23(K24(K24(COMPLEX,COMPLEX),COMPLEX)) is non empty set
K24(REAL,REAL) is Relation-like set
K23(K24(REAL,REAL)) is non empty set
K24(K24(REAL,REAL),REAL) is Relation-like set
K23(K24(K24(REAL,REAL),REAL)) is non empty set
K24(RAT,RAT) is Relation-like set
K23(K24(RAT,RAT)) is non empty set
K24(K24(RAT,RAT),RAT) is Relation-like set
K23(K24(K24(RAT,RAT),RAT)) is non empty set
K24(INT,INT) is Relation-like set
K23(K24(INT,INT)) is non empty set
K24(K24(INT,INT),INT) is Relation-like set
K23(K24(K24(INT,INT),INT)) is non empty set
K24(NAT,NAT) is non empty V5() Relation-like V39() set
K24(K24(NAT,NAT),NAT) is non empty V5() Relation-like V39() set
K23(K24(K24(NAT,NAT),NAT)) is non empty V5() V39() set
NAT is non empty V5() V12() V13() V14() V39() cardinal limit_cardinal V54() V55() set
K23(NAT) is non empty V5() V39() set
K23(NAT) is non empty V5() V39() set
BOOLEAN is non empty set
0 is ext-real non positive non negative empty Relation-like non-empty empty-yielding NAT -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of NAT
{} is ext-real non positive non negative empty Relation-like non-empty empty-yielding NAT -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair set
the ext-real non positive non negative empty Relation-like non-empty empty-yielding NAT -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair set is ext-real non positive non negative empty Relation-like non-empty empty-yielding NAT -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair set
1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
{0,1} is non empty V39() V43() V54() non with_pair set
{{},1} is non empty V39() V43() V54() non with_pair set
K353() is set
K23(K353()) is non empty set
K354() is Element of K23(K353())
K394() is non empty V98() L10()
the carrier of K394() is non empty set
K357( the carrier of K394()) is non empty M24( the carrier of K394())
K393(K394()) is Element of K23(K357( the carrier of K394()))
K23(K357( the carrier of K394())) is non empty set
K24(K393(K394()),NAT) is Relation-like set
K23(K24(K393(K394()),NAT)) is non empty set
K24(NAT,K393(K394())) is Relation-like set
K23(K24(NAT,K393(K394()))) is non empty set
2 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
2 -tuples_on BOOLEAN is non empty functional FinSequence-membered FinSequenceSet of BOOLEAN
K24((2 -tuples_on BOOLEAN),BOOLEAN) is non empty Relation-like set
K23(K24((2 -tuples_on BOOLEAN),BOOLEAN)) is non empty set
3 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
3 -tuples_on BOOLEAN is non empty functional FinSequence-membered FinSequenceSet of BOOLEAN
K24((3 -tuples_on BOOLEAN),BOOLEAN) is non empty Relation-like set
K23(K24((3 -tuples_on BOOLEAN),BOOLEAN)) is non empty set
'xor' is Relation-like 2 -tuples_on BOOLEAN -defined BOOLEAN -valued Function-like V30(2 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K23(K24((2 -tuples_on BOOLEAN),BOOLEAN))
Seg 1 is non empty V5() V39() 1 -element V54() Element of K23(NAT)
'&' is Relation-like 2 -tuples_on BOOLEAN -defined BOOLEAN -valued Function-like V30(2 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K23(K24((2 -tuples_on BOOLEAN),BOOLEAN))
or3 is Relation-like 3 -tuples_on BOOLEAN -defined BOOLEAN -valued Function-like V30(3 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K23(K24((3 -tuples_on BOOLEAN),BOOLEAN))
n is set
g is set
f is set
{n,f} is non empty V39() V54() set
{g} is non empty V5() V39() 1 -element V54() set
{n,f} \ {g} is V39() V54() Element of K23({n,f})
K23({n,f}) is non empty V39() V43() V54() set
S0 is set
n is set
f is set
<*n,f*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
g is set
[<*n,f*>,g] is non empty pair set
{<*n,f*>,g} is non empty V39() V54() set
{<*n,f*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*n,f*>,g},{<*n,f*>}} is non empty V39() V43() V54() set
proj2 <*n,f*> is non empty V39() V54() set
{n,f} is non empty V39() V54() set
the_rank_of n is V12() V13() V14() set
the_rank_of [<*n,f*>,g] is V12() V13() V14() set
the_rank_of f is V12() V13() V14() set
n is ManySortedSign
the carrier' of n is set
the ResultSort of n is Relation-like the carrier' of n -defined the carrier of n -valued Function-like V30( the carrier' of n, the carrier of n) Element of K23(K24( the carrier' of n, the carrier of n))
the carrier of n is set
K24( the carrier' of n, the carrier of n) is Relation-like set
K23(K24( the carrier' of n, the carrier of n)) is non empty set
id the carrier' of n is Relation-like the carrier' of n -defined the carrier' of n -valued Function-like one-to-one total Element of K23(K24( the carrier' of n, the carrier' of n))
K24( the carrier' of n, the carrier' of n) is Relation-like set
K23(K24( the carrier' of n, the carrier' of n)) is non empty set
f is set
the Arity of n is Relation-like the carrier' of n -defined the carrier of n * -valued Function-like V30( the carrier' of n, the carrier of n * ) Element of K23(K24( the carrier' of n,( the carrier of n *)))
the carrier of n * is non empty functional FinSequence-membered FinSequenceSet of the carrier of n
K24( the carrier' of n,( the carrier of n *)) is Relation-like set
K23(K24( the carrier' of n,( the carrier of n *))) is non empty set
the Arity of n . f is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
f `2 is set
[( the Arity of n . f),(f `2)] is non empty pair set
{( the Arity of n . f),(f `2)} is non empty V39() V54() set
{( the Arity of n . f)} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{( the Arity of n . f),(f `2)},{( the Arity of n . f)}} is non empty V39() V43() V54() set
f is set
the Arity of n is Relation-like the carrier' of n -defined the carrier of n * -valued Function-like V30( the carrier' of n, the carrier of n * ) Element of K23(K24( the carrier' of n,( the carrier of n *)))
the carrier of n * is non empty functional FinSequence-membered FinSequenceSet of the carrier of n
K24( the carrier' of n,( the carrier of n *)) is Relation-like set
K23(K24( the carrier' of n,( the carrier of n *))) is non empty set
the Arity of n . f is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
f `1 is set
g is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
len g is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
(len g) -tuples_on BOOLEAN is non empty functional FinSequence-membered FinSequenceSet of BOOLEAN
K24(((len g) -tuples_on BOOLEAN),BOOLEAN) is non empty Relation-like set
K23(K24(((len g) -tuples_on BOOLEAN),BOOLEAN)) is non empty set
the void V74() trivial' strict unsplit gate`1=arity gate`2isBoolean ManySortedSign is void V74() trivial' strict unsplit gate`1=arity gate`2isBoolean ManySortedSign
n is set
{n} is non empty V5() V39() 1 -element V54() set
{n} * is non empty functional FinSequence-membered FinSequenceSet of {n}
K24({},({n} *)) is Relation-like set
K23(K24({},({n} *))) is non empty set
the ext-real non positive non negative empty Relation-like non-empty empty-yielding {} -defined {n} * -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( {} ,{n} * ) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24({},({n} *))) is ext-real non positive non negative empty Relation-like non-empty empty-yielding {} -defined {n} * -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( {} ,{n} * ) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24({},({n} *)))
K24({},{n}) is Relation-like V39() V54() set
K23(K24({},{n})) is non empty V39() V43() V54() set
the ext-real non positive non negative empty Relation-like non-empty empty-yielding {} -defined {n} -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( {} ,{n}) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24({},{n})) is ext-real non positive non negative empty Relation-like non-empty empty-yielding {} -defined {n} -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( {} ,{n}) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24({},{n}))
ManySortedSign(# {n},{}, the ext-real non positive non negative empty Relation-like non-empty empty-yielding {} -defined {n} * -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( {} ,{n} * ) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24({},({n} *))), the ext-real non positive non negative empty Relation-like non-empty empty-yielding {} -defined {n} -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( {} ,{n}) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24({},{n})) #) is strict ManySortedSign
S0 is void V74() trivial' strict unsplit gate`1=arity gate`2isBoolean ManySortedSign
the carrier of S0 is set
f is void V74() trivial' strict unsplit gate`1=arity gate`2isBoolean ManySortedSign
the carrier of f is set
g is void V74() trivial' strict unsplit gate`1=arity gate`2isBoolean ManySortedSign
the carrier of g is set
the Arity of f is ext-real non positive non negative empty Relation-like non-empty empty-yielding the carrier' of f -defined the carrier of f * -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( the carrier' of f, the carrier of f * ) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24( the carrier' of f,( the carrier of f *)))
the carrier' of f is ext-real non positive non negative empty V5() Relation-like non-empty empty-yielding NAT -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair set
the carrier of f * is non empty functional FinSequence-membered FinSequenceSet of the carrier of f
K24( the carrier' of f,( the carrier of f *)) is Relation-like set
K23(K24( the carrier' of f,( the carrier of f *))) is non empty set
the Arity of g is ext-real non positive non negative empty Relation-like non-empty empty-yielding the carrier' of g -defined the carrier of g * -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( the carrier' of g, the carrier of g * ) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24( the carrier' of g,( the carrier of g *)))
the carrier' of g is ext-real non positive non negative empty V5() Relation-like non-empty empty-yielding NAT -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair set
the carrier of g * is non empty functional FinSequence-membered FinSequenceSet of the carrier of g
K24( the carrier' of g,( the carrier of g *)) is Relation-like set
K23(K24( the carrier' of g,( the carrier of g *))) is non empty set
n is set
(n) is void V74() trivial' strict unsplit gate`1=arity gate`2isBoolean ManySortedSign
the carrier of (n) is set
{n} is non empty V5() V39() 1 -element V54() set
n is set
(n) is non empty void V74() trivial' strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
g is strict non-empty finitely-generated V110((n)) Boolean MSAlgebra over (n)
S0 is strict non-empty finitely-generated V110((n)) Boolean MSAlgebra over (n)
the Sorts of g is Relation-like non-empty the carrier of (n) -defined Function-like total set
the carrier of (n) is non empty set
the carrier of (n) --> BOOLEAN is Relation-like the carrier of (n) -defined {BOOLEAN} -valued Function-like V30( the carrier of (n),{BOOLEAN}) Element of K23(K24( the carrier of (n),{BOOLEAN}))
{BOOLEAN} is non empty V5() V39() 1 -element V54() set
K24( the carrier of (n),{BOOLEAN}) is non empty Relation-like set
K23(K24( the carrier of (n),{BOOLEAN})) is non empty set
the Charact of g is ext-real non positive non negative empty Relation-like non-empty empty-yielding the carrier' of (n) -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional total non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair ManySortedFunction of the Arity of (n) * ( the Sorts of g #), the ResultSort of (n) * the Sorts of g
the carrier' of (n) is ext-real non positive non negative empty V5() Relation-like non-empty empty-yielding NAT -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair set
the Arity of (n) is ext-real non positive non negative empty Relation-like non-empty empty-yielding the carrier' of (n) -defined the carrier of (n) * -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( the carrier' of (n), the carrier of (n) * ) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24( the carrier' of (n),( the carrier of (n) *)))
the carrier of (n) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (n)
K24( the carrier' of (n),( the carrier of (n) *)) is Relation-like set
K23(K24( the carrier' of (n),( the carrier of (n) *))) is non empty set
the Sorts of g # is Relation-like non-empty the carrier of (n) * -defined Function-like total set
the Arity of (n) * ( the Sorts of g #) is ext-real non positive non negative empty Relation-like non-empty empty-yielding NAT -defined the carrier' of (n) -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair set
the ResultSort of (n) is ext-real non positive non negative empty Relation-like non-empty empty-yielding the carrier' of (n) -defined the carrier of (n) -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( the carrier' of (n), the carrier of (n)) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24( the carrier' of (n), the carrier of (n)))
K24( the carrier' of (n), the carrier of (n)) is Relation-like set
K23(K24( the carrier' of (n), the carrier of (n))) is non empty set
the ResultSort of (n) * the Sorts of g is ext-real non positive non negative empty Relation-like non-empty empty-yielding NAT -defined the carrier' of (n) -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair set
the Charact of S0 is ext-real non positive non negative empty Relation-like non-empty empty-yielding the carrier' of (n) -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional total non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair ManySortedFunction of the Arity of (n) * ( the Sorts of S0 #), the ResultSort of (n) * the Sorts of S0
the Sorts of S0 is Relation-like non-empty the carrier of (n) -defined Function-like total set
the Sorts of S0 # is Relation-like non-empty the carrier of (n) * -defined Function-like total set
the Arity of (n) * ( the Sorts of S0 #) is ext-real non positive non negative empty Relation-like non-empty empty-yielding NAT -defined the carrier' of (n) -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair set
the ResultSort of (n) * the Sorts of S0 is ext-real non positive non negative empty Relation-like non-empty empty-yielding NAT -defined the carrier' of (n) -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair set
n is set
(n) is non empty void V74() trivial' strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f is ManySortedSign
the Arity of (n) is ext-real non positive non negative empty Relation-like non-empty empty-yielding the carrier' of (n) -defined the carrier of (n) * -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( the carrier' of (n), the carrier of (n) * ) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24( the carrier' of (n),( the carrier of (n) *)))
the carrier' of (n) is ext-real non positive non negative empty V5() Relation-like non-empty empty-yielding NAT -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair set
the carrier of (n) is non empty set
the carrier of (n) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (n)
K24( the carrier' of (n),( the carrier of (n) *)) is Relation-like set
K23(K24( the carrier' of (n),( the carrier of (n) *))) is non empty set
the Arity of f is Relation-like the carrier' of f -defined the carrier of f * -valued Function-like V30( the carrier' of f, the carrier of f * ) Element of K23(K24( the carrier' of f,( the carrier of f *)))
the carrier' of f is set
the carrier of f is set
the carrier of f * is non empty functional FinSequence-membered FinSequenceSet of the carrier of f
K24( the carrier' of f,( the carrier of f *)) is Relation-like set
K23(K24( the carrier' of f,( the carrier of f *))) is non empty set
the ResultSort of (n) is ext-real non positive non negative empty Relation-like non-empty empty-yielding the carrier' of (n) -defined the carrier of (n) -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( the carrier' of (n), the carrier of (n)) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24( the carrier' of (n), the carrier of (n)))
K24( the carrier' of (n), the carrier of (n)) is Relation-like set
K23(K24( the carrier' of (n), the carrier of (n))) is non empty set
the ResultSort of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V30( the carrier' of f, the carrier of f) Element of K23(K24( the carrier' of f, the carrier of f))
K24( the carrier' of f, the carrier of f) is Relation-like set
K23(K24( the carrier' of f, the carrier of f)) is non empty set
n is set
(n) is non empty void V74() trivial' strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f is non empty V74() ManySortedSign
the carrier of f is non empty set
(n) +* f is non empty V74() strict ManySortedSign
the carrier' of f is set
the Arity of f is Relation-like the carrier' of f -defined the carrier of f * -valued Function-like V30( the carrier' of f, the carrier of f * ) Element of K23(K24( the carrier' of f,( the carrier of f *)))
the carrier of f * is non empty functional FinSequence-membered FinSequenceSet of the carrier of f
K24( the carrier' of f,( the carrier of f *)) is Relation-like set
K23(K24( the carrier' of f,( the carrier of f *))) is non empty set
the ResultSort of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V30( the carrier' of f, the carrier of f) Element of K23(K24( the carrier' of f, the carrier of f))
K24( the carrier' of f, the carrier of f) is Relation-like set
K23(K24( the carrier' of f, the carrier of f)) is non empty set
ManySortedSign(# the carrier of f, the carrier' of f, the Arity of f, the ResultSort of f #) is strict ManySortedSign
{n} is non empty V5() V39() 1 -element V54() set
{n} \/ the carrier of f is non empty set
{} \/ the carrier' of f is set
the carrier of (n) is non empty set
the ResultSort of (n) is ext-real non positive non negative empty Relation-like non-empty empty-yielding the carrier' of (n) -defined the carrier of (n) -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( the carrier' of (n), the carrier of (n)) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24( the carrier' of (n), the carrier of (n)))
the carrier' of (n) is ext-real non positive non negative empty V5() Relation-like non-empty empty-yielding NAT -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair set
K24( the carrier' of (n), the carrier of (n)) is Relation-like set
K23(K24( the carrier' of (n), the carrier of (n))) is non empty set
the Arity of (n) is ext-real non positive non negative empty Relation-like non-empty empty-yielding the carrier' of (n) -defined the carrier of (n) * -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( the carrier' of (n), the carrier of (n) * ) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24( the carrier' of (n),( the carrier of (n) *)))
the carrier of (n) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (n)
K24( the carrier' of (n),( the carrier of (n) *)) is Relation-like set
K23(K24( the carrier' of (n),( the carrier of (n) *))) is non empty set
{} +* the ResultSort of f is Relation-like Function-like set
{} +* the Arity of f is Relation-like Function-like set
the carrier of ((n) +* f) is non empty set
the carrier' of ((n) +* f) is set
the ResultSort of ((n) +* f) is Relation-like the carrier' of ((n) +* f) -defined the carrier of ((n) +* f) -valued Function-like V30( the carrier' of ((n) +* f), the carrier of ((n) +* f)) Element of K23(K24( the carrier' of ((n) +* f), the carrier of ((n) +* f)))
K24( the carrier' of ((n) +* f), the carrier of ((n) +* f)) is Relation-like set
K23(K24( the carrier' of ((n) +* f), the carrier of ((n) +* f))) is non empty set
n is set
(n) is non empty void V74() trivial' strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n) is strict non-empty finitely-generated V110((n)) Boolean MSAlgebra over (n)
f is non empty V74() strict ManySortedSign
the carrier of f is non empty set
g is non-empty finitely-generated V110(f) Boolean MSAlgebra over f
(n) +* g is strict non-empty MSAlgebra over (n) +* f
(n) +* f is non empty V74() strict ManySortedSign
the Sorts of g is Relation-like non-empty the carrier of f -defined Function-like total set
the Charact of g is Relation-like the carrier' of f -defined Function-like total ManySortedFunction of the Arity of f * ( the Sorts of g #), the ResultSort of f * the Sorts of g
the carrier' of f is set
the Arity of f is Relation-like the carrier' of f -defined the carrier of f * -valued Function-like V30( the carrier' of f, the carrier of f * ) Element of K23(K24( the carrier' of f,( the carrier of f *)))
the carrier of f * is non empty functional FinSequence-membered FinSequenceSet of the carrier of f
K24( the carrier' of f,( the carrier of f *)) is Relation-like set
K23(K24( the carrier' of f,( the carrier of f *))) is non empty set
the Sorts of g # is Relation-like non-empty the carrier of f * -defined Function-like total set
the Arity of f * ( the Sorts of g #) is Relation-like non-empty the carrier' of f -defined Function-like set
the ResultSort of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V30( the carrier' of f, the carrier of f) Element of K23(K24( the carrier' of f, the carrier of f))
K24( the carrier' of f, the carrier of f) is Relation-like set
K23(K24( the carrier' of f, the carrier of f)) is non empty set
the ResultSort of f * the Sorts of g is Relation-like non-empty the carrier' of f -defined Function-like set
MSAlgebra(# the Sorts of g, the Charact of g #) is strict MSAlgebra over f
{n} is non empty V5() V39() 1 -element V54() set
the carrier of (n) is non empty set
the carrier of f --> BOOLEAN is Relation-like the carrier of f -defined {BOOLEAN} -valued Function-like V30( the carrier of f,{BOOLEAN}) Element of K23(K24( the carrier of f,{BOOLEAN}))
{BOOLEAN} is non empty V5() V39() 1 -element V54() set
K24( the carrier of f,{BOOLEAN}) is non empty Relation-like set
K23(K24( the carrier of f,{BOOLEAN})) is non empty set
the Sorts of (n) is Relation-like non-empty the carrier of (n) -defined Function-like total set
the carrier of (n) --> BOOLEAN is Relation-like the carrier of (n) -defined {BOOLEAN} -valued Function-like V30( the carrier of (n),{BOOLEAN}) Element of K23(K24( the carrier of (n),{BOOLEAN}))
K24( the carrier of (n),{BOOLEAN}) is non empty Relation-like set
K23(K24( the carrier of (n),{BOOLEAN})) is non empty set
the Charact of (n) is ext-real non positive non negative empty Relation-like non-empty empty-yielding the carrier' of (n) -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional total non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair ManySortedFunction of the Arity of (n) * ( the Sorts of (n) #), the ResultSort of (n) * the Sorts of (n)
the carrier' of (n) is ext-real non positive non negative empty V5() Relation-like non-empty empty-yielding NAT -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair set
the Arity of (n) is ext-real non positive non negative empty Relation-like non-empty empty-yielding the carrier' of (n) -defined the carrier of (n) * -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( the carrier' of (n), the carrier of (n) * ) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24( the carrier' of (n),( the carrier of (n) *)))
the carrier of (n) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (n)
K24( the carrier' of (n),( the carrier of (n) *)) is Relation-like set
K23(K24( the carrier' of (n),( the carrier of (n) *))) is non empty set
the Sorts of (n) # is Relation-like non-empty the carrier of (n) * -defined Function-like total set
the Arity of (n) * ( the Sorts of (n) #) is ext-real non positive non negative empty Relation-like non-empty empty-yielding NAT -defined the carrier' of (n) -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair set
the ResultSort of (n) is ext-real non positive non negative empty Relation-like non-empty empty-yielding the carrier' of (n) -defined the carrier of (n) -valued V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V30( the carrier' of (n), the carrier of (n)) V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair Element of K23(K24( the carrier' of (n), the carrier of (n)))
K24( the carrier' of (n), the carrier of (n)) is Relation-like set
K23(K24( the carrier' of (n), the carrier of (n))) is non empty set
the ResultSort of (n) * the Sorts of (n) is ext-real non positive non negative empty Relation-like non-empty empty-yielding NAT -defined the carrier' of (n) -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair set
the Charact of (n) +* the Charact of g is Relation-like the carrier' of (n) \/ the carrier' of f -defined Function-like total set
the carrier' of (n) \/ the carrier' of f is set
the Sorts of ((n) +* g) is Relation-like non-empty the carrier of ((n) +* f) -defined Function-like total set
the carrier of ((n) +* f) is non empty set
the Sorts of (n) +* the Sorts of g is Relation-like non-empty the carrier of (n) \/ the carrier of f -defined Function-like total set
the carrier of (n) \/ the carrier of f is non empty set
the Charact of ((n) +* g) is Relation-like the carrier' of ((n) +* f) -defined Function-like total ManySortedFunction of the Arity of ((n) +* f) * ( the Sorts of ((n) +* g) #), the ResultSort of ((n) +* f) * the Sorts of ((n) +* g)
the carrier' of ((n) +* f) is set
the Arity of ((n) +* f) is Relation-like the carrier' of ((n) +* f) -defined the carrier of ((n) +* f) * -valued Function-like V30( the carrier' of ((n) +* f), the carrier of ((n) +* f) * ) Element of K23(K24( the carrier' of ((n) +* f),( the carrier of ((n) +* f) *)))
the carrier of ((n) +* f) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of ((n) +* f)
K24( the carrier' of ((n) +* f),( the carrier of ((n) +* f) *)) is Relation-like set
K23(K24( the carrier' of ((n) +* f),( the carrier of ((n) +* f) *))) is non empty set
the Sorts of ((n) +* g) # is Relation-like non-empty the carrier of ((n) +* f) * -defined Function-like total set
the Arity of ((n) +* f) * ( the Sorts of ((n) +* g) #) is Relation-like non-empty the carrier' of ((n) +* f) -defined Function-like set
the ResultSort of ((n) +* f) is Relation-like the carrier' of ((n) +* f) -defined the carrier of ((n) +* f) -valued Function-like V30( the carrier' of ((n) +* f), the carrier of ((n) +* f)) Element of K23(K24( the carrier' of ((n) +* f), the carrier of ((n) +* f)))
K24( the carrier' of ((n) +* f), the carrier of ((n) +* f)) is Relation-like set
K23(K24( the carrier' of ((n) +* f), the carrier of ((n) +* f))) is non empty set
the ResultSort of ((n) +* f) * the Sorts of ((n) +* g) is Relation-like non-empty the carrier' of ((n) +* f) -defined Function-like set
proj1 the Sorts of (n) is set
proj1 the Sorts of g is set
0 -tuples_on BOOLEAN is non empty functional FinSequence-membered FinSequenceSet of BOOLEAN
FALSE is boolean Element of BOOLEAN
(0 -tuples_on BOOLEAN) --> FALSE is Relation-like 0 -tuples_on BOOLEAN -defined BOOLEAN -valued Function-like V30(0 -tuples_on BOOLEAN, BOOLEAN ) boolean-valued Element of K23(K24((0 -tuples_on BOOLEAN),BOOLEAN))
K24((0 -tuples_on BOOLEAN),BOOLEAN) is non empty Relation-like set
K23(K24((0 -tuples_on BOOLEAN),BOOLEAN)) is non empty set
1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
[{},((0 -tuples_on BOOLEAN) --> FALSE)] is non empty pair set
{{},((0 -tuples_on BOOLEAN) --> FALSE)} is non empty functional V39() V54() set
{{}} is non empty V5() functional V39() V43() 1 -element V52() V54() non with_pair set
{{{},((0 -tuples_on BOOLEAN) --> FALSE)},{{}}} is non empty V39() V43() V54() set
f is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
g is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
S0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
A0 is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h is Relation-like NAT -defined Function-like total set
h . n is set
h . 0 is set
Sn is Relation-like NAT -defined Function-like total set
Sn . 0 is set
N is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
An is Relation-like NAT -defined Function-like total set
An . n is set
An . 0 is set
o0 is Relation-like NAT -defined Function-like total set
o0 . 0 is set
S0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
A0 is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
N is Relation-like NAT -defined Function-like total set
N . S0 is set
N . 0 is set
h is Relation-like NAT -defined Function-like total set
h . 0 is set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
f is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
g is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
(n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE)) is strict non-empty finitely-generated V110( 1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) gate`2=den Boolean MSAlgebra over 1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))
Sn is non empty V74() ManySortedSign
f1 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
f1 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . (f1 + 1) is set
g . (f1 + 1) is set
o0 is set
BitAdderWithOverflowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(f . (f1 + 1)),(g . (f1 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'},{<*(f . (f1 + 1)),(g . (f1 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (f1 + 1)),o0*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*o0,(f . (f1 + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*o0,(f . (f1 + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,'&'))) +* (1GateCircStr (<*o0,(f . (f1 + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'] is non empty pair set
{<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'},{<*(f . (f1 + 1)),(g . (f1 + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (f1 + 1)),o0*>,'&'] is non empty pair set
{<*(g . (f1 + 1)),o0*>,'&'} is non empty functional V39() V54() set
{<*(g . (f1 + 1)),o0*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (f1 + 1)),o0*>,'&'},{<*(g . (f1 + 1)),o0*>}} is non empty V39() V43() V54() set
[<*o0,(f . (f1 + 1))*>,'&'] is non empty pair set
{<*o0,(f . (f1 + 1))*>,'&'} is non empty functional V39() V54() set
{<*o0,(f . (f1 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*o0,(f . (f1 + 1))*>,'&'},{<*o0,(f . (f1 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) +* (MajorityStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
An is non-empty MSAlgebra over Sn
BitAdderWithOverflowCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V110( BitAdderWithOverflowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over BitAdderWithOverflowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
BitAdderCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110((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'))
MajorityCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V110( MajorityStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over MajorityStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
MajorityICirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V110( MajorityIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over MajorityIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')
1GateCircuit (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')
1GateCircuit ((g . (f1 + 1)),o0,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(g . (f1 + 1)),o0*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (f1 + 1)),o0*>,'&')
1GateCircuit (<*(g . (f1 + 1)),o0*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(g . (f1 + 1)),o0*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (f1 + 1)),o0*>,'&')
(1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),'&')) +* (1GateCircuit ((g . (f1 + 1)),o0,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,'&'))
1GateCircuit (o0,(f . (f1 + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*o0,(f . (f1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*o0,(f . (f1 + 1))*>,'&')
1GateCircuit (<*o0,(f . (f1 + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*o0,(f . (f1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*o0,(f . (f1 + 1))*>,'&')
((1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),'&')) +* (1GateCircuit ((g . (f1 + 1)),o0,'&'))) +* (1GateCircuit (o0,(f . (f1 + 1)),'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,'&'))) +* (1GateCircStr (<*o0,(f . (f1 + 1))*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,'&'))) +* (1GateCircStr (<*o0,(f . (f1 + 1))*>,'&'))
1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3)
1GateCircuit (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3)
(MajorityICirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3))
(BitAdderCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (MajorityCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is strict non-empty finitely-generated V110((2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) +* (MajorityStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) +* (MajorityStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))
An +* (BitAdderWithOverflowCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is strict non-empty MSAlgebra over Sn +* (BitAdderWithOverflowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))
Sn +* (BitAdderWithOverflowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is non empty non void V74() strict ManySortedSign
Sn is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
o0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
o0 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . (o0 + 1) is set
g . (o0 + 1) is set
An is set
BitAdderWithOverflowStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(f . (o0 + 1)),(g . (o0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (o0 + 1)),(g . (o0 + 1))*>,'xor'},{<*(f . (o0 + 1)),(g . (o0 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,'xor'],An*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,'xor'],An*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (o0 + 1)),(g . (o0 + 1)),An) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (o0 + 1)),An*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,'&')) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*An,(f . (o0 + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*An,(f . (o0 + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (o0 + 1)),(g . (o0 + 1))*>,'&')) +* (1GateCircStr (<*(g . (o0 + 1)),An*>,'&'))) +* (1GateCircStr (<*An,(f . (o0 + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (o0 + 1)),(g . (o0 + 1))*>,'&'] is non empty pair set
{<*(f . (o0 + 1)),(g . (o0 + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (o0 + 1)),(g . (o0 + 1))*>,'&'},{<*(f . (o0 + 1)),(g . (o0 + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (o0 + 1)),An*>,'&'] is non empty pair set
{<*(g . (o0 + 1)),An*>,'&'} is non empty functional V39() V54() set
{<*(g . (o0 + 1)),An*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (o0 + 1)),An*>,'&'},{<*(g . (o0 + 1)),An*>}} is non empty V39() V43() V54() set
[<*An,(f . (o0 + 1))*>,'&'] is non empty pair set
{<*An,(f . (o0 + 1))*>,'&'} is non empty functional V39() V54() set
{<*An,(f . (o0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*An,(f . (o0 + 1))*>,'&'},{<*An,(f . (o0 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,'&'],[<*(g . (o0 + 1)),An*>,'&'],[<*An,(f . (o0 + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,'&'],[<*(g . (o0 + 1)),An*>,'&'],[<*An,(f . (o0 + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) +* (1GateCircStr (<*[<*(f . (o0 + 1)),(g . (o0 + 1))*>,'&'],[<*(g . (o0 + 1)),An*>,'&'],[<*An,(f . (o0 + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (o0 + 1)),(g . (o0 + 1)),An,'xor')) +* (MajorityStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
Sn +* (BitAdderWithOverflowStr ((f . (o0 + 1)),(g . (o0 + 1)),An)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f1 is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
h1 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
h1 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . (h1 + 1) is set
g . (h1 + 1) is set
g1 is set
BitAdderWithOverflowStr ((f . (h1 + 1)),(g . (h1 + 1)),g1) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (h1 + 1)),(g . (h1 + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(f . (h1 + 1)),(g . (h1 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (h1 + 1)),(g . (h1 + 1))*>,'xor'},{<*(f . (h1 + 1)),(g . (h1 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (h1 + 1)),(g . (h1 + 1))*>,'xor'],g1*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (h1 + 1)),(g . (h1 + 1))*>,'xor'],g1*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (h1 + 1)),(g . (h1 + 1)),g1) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (h1 + 1)),(g . (h1 + 1)),g1) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (h1 + 1)),(g . (h1 + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (h1 + 1)),g1*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (h1 + 1)),(g . (h1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (h1 + 1)),g1*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*g1,(f . (h1 + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*g1,(f . (h1 + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (h1 + 1)),(g . (h1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (h1 + 1)),g1*>,'&'))) +* (1GateCircStr (<*g1,(f . (h1 + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (h1 + 1)),(g . (h1 + 1))*>,'&'] is non empty pair set
{<*(f . (h1 + 1)),(g . (h1 + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (h1 + 1)),(g . (h1 + 1))*>,'&'},{<*(f . (h1 + 1)),(g . (h1 + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (h1 + 1)),g1*>,'&'] is non empty pair set
{<*(g . (h1 + 1)),g1*>,'&'} is non empty functional V39() V54() set
{<*(g . (h1 + 1)),g1*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (h1 + 1)),g1*>,'&'},{<*(g . (h1 + 1)),g1*>}} is non empty V39() V43() V54() set
[<*g1,(f . (h1 + 1))*>,'&'] is non empty pair set
{<*g1,(f . (h1 + 1))*>,'&'} is non empty functional V39() V54() set
{<*g1,(f . (h1 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g1,(f . (h1 + 1))*>,'&'},{<*g1,(f . (h1 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (h1 + 1)),(g . (h1 + 1))*>,'&'],[<*(g . (h1 + 1)),g1*>,'&'],[<*g1,(f . (h1 + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (h1 + 1)),(g . (h1 + 1))*>,'&'],[<*(g . (h1 + 1)),g1*>,'&'],[<*g1,(f . (h1 + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (h1 + 1)),(g . (h1 + 1)),g1)) +* (1GateCircStr (<*[<*(f . (h1 + 1)),(g . (h1 + 1))*>,'&'],[<*(g . (h1 + 1)),g1*>,'&'],[<*g1,(f . (h1 + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (h1 + 1)),(g . (h1 + 1)),g1,'xor')) +* (MajorityStr ((f . (h1 + 1)),(g . (h1 + 1)),g1)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f1 +* (BitAdderWithOverflowStr ((f . (h1 + 1)),(g . (h1 + 1)),g1)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
n is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
xx is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
xx + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . (xx + 1) is set
g . (xx + 1) is set
x is set
BitAdderWithOverflowStr ((f . (xx + 1)),(g . (xx + 1)),x) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (xx + 1)),(g . (xx + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(f . (xx + 1)),(g . (xx + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (xx + 1)),(g . (xx + 1))*>,'xor'},{<*(f . (xx + 1)),(g . (xx + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (xx + 1)),(g . (xx + 1))*>,'xor'],x*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (xx + 1)),(g . (xx + 1))*>,'xor'],x*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (xx + 1)),(g . (xx + 1)),x) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (xx + 1)),(g . (xx + 1)),x) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (xx + 1)),(g . (xx + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (xx + 1)),x*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (xx + 1)),(g . (xx + 1))*>,'&')) +* (1GateCircStr (<*(g . (xx + 1)),x*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*x,(f . (xx + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*x,(f . (xx + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (xx + 1)),(g . (xx + 1))*>,'&')) +* (1GateCircStr (<*(g . (xx + 1)),x*>,'&'))) +* (1GateCircStr (<*x,(f . (xx + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (xx + 1)),(g . (xx + 1))*>,'&'] is non empty pair set
{<*(f . (xx + 1)),(g . (xx + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (xx + 1)),(g . (xx + 1))*>,'&'},{<*(f . (xx + 1)),(g . (xx + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (xx + 1)),x*>,'&'] is non empty pair set
{<*(g . (xx + 1)),x*>,'&'} is non empty functional V39() V54() set
{<*(g . (xx + 1)),x*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (xx + 1)),x*>,'&'},{<*(g . (xx + 1)),x*>}} is non empty V39() V43() V54() set
[<*x,(f . (xx + 1))*>,'&'] is non empty pair set
{<*x,(f . (xx + 1))*>,'&'} is non empty functional V39() V54() set
{<*x,(f . (xx + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*x,(f . (xx + 1))*>,'&'},{<*x,(f . (xx + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (xx + 1)),(g . (xx + 1))*>,'&'],[<*(g . (xx + 1)),x*>,'&'],[<*x,(f . (xx + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (xx + 1)),(g . (xx + 1))*>,'&'],[<*(g . (xx + 1)),x*>,'&'],[<*x,(f . (xx + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (xx + 1)),(g . (xx + 1)),x)) +* (1GateCircStr (<*[<*(f . (xx + 1)),(g . (xx + 1))*>,'&'],[<*(g . (xx + 1)),x*>,'&'],[<*x,(f . (xx + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (xx + 1)),(g . (xx + 1)),x,'xor')) +* (MajorityStr ((f . (xx + 1)),(g . (xx + 1)),x)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
n +* (BitAdderWithOverflowStr ((f . (xx + 1)),(g . (xx + 1)),x)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
xy is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
c₁₉ is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
c₁₉ + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . (c₁₉ + 1) is set
g . (c₁₉ + 1) is set
c₁₈ is set
BitAdderWithOverflowStr ((f . (c₁₉ + 1)),(g . (c₁₉ + 1)),c₁₈) is non empty non void V74() 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') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,'xor') is non empty non void V74() 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))*>,'xor'] is non empty pair set
{<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>,'xor'} is non empty functional V39() V54() set
{<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>,'xor'},{<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>,'xor'],c<sub>18</sub>*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>,'xor'],c<sub>18</sub>*>,'xor') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,'xor')) +* (1GateCircStr (<*[<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,'xor'],c₁₈*>,'xor')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1)),c<sub>18</sub>) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (c₁₉ + 1)),(g . (c₁₉ + 1)),c₁₈) is non empty non void V74() 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))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (c₁₉ + 1)),c₁₈*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (c₁₉ + 1)),c₁₈*>,'&') is non empty non void V74() 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))*>,'&')) +* (1GateCircStr (<*(g . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*c₁₈,(f . (c₁₉ + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*c₁₈,(f . (c₁₉ + 1))*>,'&') is non empty non void V74() 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))*>,'&')) +* (1GateCircStr (<*(g . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,'&'))) +* (1GateCircStr (<*c<sub>18</sub>,(f . (c<sub>19</sub> + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,'&'] is non empty pair set
{<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,'&'},{<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (c₁₉ + 1)),c₁₈*>,'&'] is non empty pair set
{<*(g . (c₁₉ + 1)),c₁₈*>,'&'} is non empty functional V39() V54() set
{<*(g . (c₁₉ + 1)),c₁₈*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (c₁₉ + 1)),c₁₈*>,'&'},{<*(g . (c₁₉ + 1)),c₁₈*>}} is non empty V39() V43() V54() set
[<*c₁₈,(f . (c₁₉ + 1))*>,'&'] is non empty pair set
{<*c₁₈,(f . (c₁₉ + 1))*>,'&'} is non empty functional V39() V54() set
{<*c₁₈,(f . (c₁₉ + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*c₁₈,(f . (c₁₉ + 1))*>,'&'},{<*c₁₈,(f . (c₁₉ + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,'&'],[<*(g . (c₁₉ + 1)),c₁₈*>,'&'],[<*c₁₈,(f . (c₁₉ + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (c₁₉ + 1)),(g . (c₁₉ + 1))*>,'&'],[<*(g . (c₁₉ + 1)),c₁₈*>,'&'],[<*c₁₈,(f . (c₁₉ + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1)),c<sub>18</sub>)) +* (1GateCircStr (<*[<*(f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1))*>,'&'],[<*(g . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,'&'],[<*c<sub>18</sub>,(f . (c<sub>19</sub> + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (c₁₉ + 1)),(g . (c₁₉ + 1)),c₁₈,'xor')) +* (MajorityStr ((f . (c₁₉ + 1)),(g . (c₁₉ + 1)),c₁₈)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
xy +* (BitAdderWithOverflowStr ((f . (c<sub>19</sub> + 1)),(g . (c<sub>19</sub> + 1)),c<sub>18</sub>)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
c₂₀ is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
c<sub>22</sub> is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
c<sub>22</sub> + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . (c<sub>22</sub> + 1) is set
g . (c<sub>22</sub> + 1) is set
c<sub>21</sub> is set
BitAdderWithOverflowStr ((f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1)),c<sub>21</sub>) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((f . (c₂₂ + 1)),(g . (c₂₂ + 1)),c₂₁,'xor') is non empty non void V74() 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))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>,'xor') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,'xor'] is non empty pair set
{<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,'xor'} is non empty functional V39() V54() set
{<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,'xor'},{<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,'xor'],c₂₁*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,'xor'],c₂₁*>,'xor') is non empty non void V74() 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))*>,'xor')) +* (1GateCircStr (<*[<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>,'xor'],c<sub>21</sub>*>,'xor')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (c₂₂ + 1)),(g . (c₂₂ + 1)),c₂₁) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1)),c<sub>21</sub>) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (c<sub>22</sub> + 1)),c<sub>21</sub>*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (c<sub>22</sub> + 1)),c<sub>21</sub>*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,'&')) +* (1GateCircStr (<*(g . (c₂₂ + 1)),c₂₁*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*c<sub>21</sub>,(f . (c<sub>22</sub> + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*c<sub>21</sub>,(f . (c<sub>22</sub> + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,'&')) +* (1GateCircStr (<*(g . (c₂₂ + 1)),c₂₁*>,'&'))) +* (1GateCircStr (<*c₂₁,(f . (c₂₂ + 1))*>,'&')) is non empty non void V74() 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))*>,'&'] is non empty pair set
{<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>,'&'},{<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (c<sub>22</sub> + 1)),c<sub>21</sub>*>,'&'] is non empty pair set
{<*(g . (c<sub>22</sub> + 1)),c<sub>21</sub>*>,'&'} is non empty functional V39() V54() set
{<*(g . (c<sub>22</sub> + 1)),c<sub>21</sub>*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (c<sub>22</sub> + 1)),c<sub>21</sub>*>,'&'},{<*(g . (c<sub>22</sub> + 1)),c<sub>21</sub>*>}} is non empty V39() V43() V54() set
[<*c<sub>21</sub>,(f . (c<sub>22</sub> + 1))*>,'&'] is non empty pair set
{<*c<sub>21</sub>,(f . (c<sub>22</sub> + 1))*>,'&'} is non empty functional V39() V54() set
{<*c<sub>21</sub>,(f . (c<sub>22</sub> + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*c<sub>21</sub>,(f . (c<sub>22</sub> + 1))*>,'&'},{<*c<sub>21</sub>,(f . (c<sub>22</sub> + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>,'&'],[<*(g . (c<sub>22</sub> + 1)),c<sub>21</sub>*>,'&'],[<*c<sub>21</sub>,(f . (c<sub>22</sub> + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1))*>,'&'],[<*(g . (c<sub>22</sub> + 1)),c<sub>21</sub>*>,'&'],[<*c<sub>21</sub>,(f . (c<sub>22</sub> + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (c₂₂ + 1)),(g . (c₂₂ + 1)),c₂₁)) +* (1GateCircStr (<*[<*(f . (c₂₂ + 1)),(g . (c₂₂ + 1))*>,'&'],[<*(g . (c₂₂ + 1)),c₂₁*>,'&'],[<*c₂₁,(f . (c₂₂ + 1))*>,'&']*>,or3)) is non empty non void V74() 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')) +* (MajorityStr ((f . (c<sub>22</sub> + 1)),(g . (c<sub>22</sub> + 1)),c<sub>21</sub>)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
c₂₀ +* (BitAdderWithOverflowStr ((f . (c₂₂ + 1)),(g . (c₂₂ + 1)),c₂₁)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
Sn is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
An is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
g1 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
g1 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . (g1 + 1) is set
g . (g1 + 1) is set
f1 is set
BitAdderWithOverflowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(f . (g1 + 1)),(g . (g1 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'},{<*(f . (g1 + 1)),(g . (g1 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'],f1*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'xor'],f1*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (g1 + 1)),(g . (g1 + 1)),f1) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (g1 + 1)),f1*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f1,(f . (g1 + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*f1,(f . (g1 + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,'&'))) +* (1GateCircStr (<*f1,(f . (g1 + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&'] is non empty pair set
{<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&'},{<*(f . (g1 + 1)),(g . (g1 + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (g1 + 1)),f1*>,'&'] is non empty pair set
{<*(g . (g1 + 1)),f1*>,'&'} is non empty functional V39() V54() set
{<*(g . (g1 + 1)),f1*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (g1 + 1)),f1*>,'&'},{<*(g . (g1 + 1)),f1*>}} is non empty V39() V43() V54() set
[<*f1,(f . (g1 + 1))*>,'&'] is non empty pair set
{<*f1,(f . (g1 + 1))*>,'&'} is non empty functional V39() V54() set
{<*f1,(f . (g1 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*f1,(f . (g1 + 1))*>,'&'},{<*f1,(f . (g1 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&'],[<*(g . (g1 + 1)),f1*>,'&'],[<*f1,(f . (g1 + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&'],[<*(g . (g1 + 1)),f1*>,'&'],[<*f1,(f . (g1 + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&'],[<*(g . (g1 + 1)),f1*>,'&'],[<*f1,(f . (g1 + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (g1 + 1)),(g . (g1 + 1)),f1,'xor')) +* (MajorityStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
Sn +* (BitAdderWithOverflowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
o0 is strict non-empty finitely-generated V110(Sn) gate`2=den Boolean MSAlgebra over Sn
BitAdderWithOverflowCirc ((f . (g1 + 1)),(g . (g1 + 1)),f1) is strict non-empty finitely-generated V110( BitAdderWithOverflowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) gate`2=den Boolean MSAlgebra over BitAdderWithOverflowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)
BitAdderCirc ((f . (g1 + 1)),(g . (g1 + 1)),f1) is strict non-empty finitely-generated V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110((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'))
MajorityCirc ((f . (g1 + 1)),(g . (g1 + 1)),f1) is strict non-empty finitely-generated V110( MajorityStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) gate`2=den Boolean MSAlgebra over MajorityStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)
MajorityICirc ((f . (g1 + 1)),(g . (g1 + 1)),f1) is strict non-empty finitely-generated V110( MajorityIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) gate`2=den Boolean MSAlgebra over MajorityIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)
1GateCircuit ((f . (g1 + 1)),(g . (g1 + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&')
1GateCircuit (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&')
1GateCircuit ((g . (g1 + 1)),f1,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(g . (g1 + 1)),f1*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (g1 + 1)),f1*>,'&')
1GateCircuit (<*(g . (g1 + 1)),f1*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(g . (g1 + 1)),f1*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (g1 + 1)),f1*>,'&')
(1GateCircuit ((f . (g1 + 1)),(g . (g1 + 1)),'&')) +* (1GateCircuit ((g . (g1 + 1)),f1,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,'&'))
1GateCircuit (f1,(f . (g1 + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f1,(f . (g1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f1,(f . (g1 + 1))*>,'&')
1GateCircuit (<*f1,(f . (g1 + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f1,(f . (g1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f1,(f . (g1 + 1))*>,'&')
((1GateCircuit ((f . (g1 + 1)),(g . (g1 + 1)),'&')) +* (1GateCircuit ((g . (g1 + 1)),f1,'&'))) +* (1GateCircuit (f1,(f . (g1 + 1)),'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,'&'))) +* (1GateCircStr (<*f1,(f . (g1 + 1))*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (g1 + 1)),f1*>,'&'))) +* (1GateCircStr (<*f1,(f . (g1 + 1))*>,'&'))
1GateCircuit ([<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&'],[<*(g . (g1 + 1)),f1*>,'&'],[<*f1,(f . (g1 + 1))*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&'],[<*(g . (g1 + 1)),f1*>,'&'],[<*f1,(f . (g1 + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&'],[<*(g . (g1 + 1)),f1*>,'&'],[<*f1,(f . (g1 + 1))*>,'&']*>,or3)
1GateCircuit (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&'],[<*(g . (g1 + 1)),f1*>,'&'],[<*f1,(f . (g1 + 1))*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&'],[<*(g . (g1 + 1)),f1*>,'&'],[<*f1,(f . (g1 + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&'],[<*(g . (g1 + 1)),f1*>,'&'],[<*f1,(f . (g1 + 1))*>,'&']*>,or3)
(MajorityICirc ((f . (g1 + 1)),(g . (g1 + 1)),f1)) +* (1GateCircuit ([<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&'],[<*(g . (g1 + 1)),f1*>,'&'],[<*f1,(f . (g1 + 1))*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&'],[<*(g . (g1 + 1)),f1*>,'&'],[<*f1,(f . (g1 + 1))*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr ((f . (g1 + 1)),(g . (g1 + 1)),f1)) +* (1GateCircStr (<*[<*(f . (g1 + 1)),(g . (g1 + 1))*>,'&'],[<*(g . (g1 + 1)),f1*>,'&'],[<*f1,(f . (g1 + 1))*>,'&']*>,or3))
(BitAdderCirc ((f . (g1 + 1)),(g . (g1 + 1)),f1)) +* (MajorityCirc ((f . (g1 + 1)),(g . (g1 + 1)),f1)) is strict non-empty finitely-generated V110((2GatesCircStr ((f . (g1 + 1)),(g . (g1 + 1)),f1,'xor')) +* (MajorityStr ((f . (g1 + 1)),(g . (g1 + 1)),f1))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((f . (g1 + 1)),(g . (g1 + 1)),f1,'xor')) +* (MajorityStr ((f . (g1 + 1)),(g . (g1 + 1)),f1))
o0 +* (BitAdderWithOverflowCirc ((f . (g1 + 1)),(g . (g1 + 1)),f1)) is strict non-empty finitely-generated V110(Sn +* (BitAdderWithOverflowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1))) gate`2=den Boolean MSAlgebra over Sn +* (BitAdderWithOverflowStr ((f . (g1 + 1)),(g . (g1 + 1)),f1))
Sn is non empty V74() ManySortedSign
f1 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
f1 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . (f1 + 1) is set
g . (f1 + 1) is set
o0 is set
BitAdderWithOverflowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(f . (f1 + 1)),(g . (f1 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'},{<*(f . (f1 + 1)),(g . (f1 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'xor'],o0*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (f1 + 1)),o0*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*o0,(f . (f1 + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*o0,(f . (f1 + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,'&'))) +* (1GateCircStr (<*o0,(f . (f1 + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'] is non empty pair set
{<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'},{<*(f . (f1 + 1)),(g . (f1 + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (f1 + 1)),o0*>,'&'] is non empty pair set
{<*(g . (f1 + 1)),o0*>,'&'} is non empty functional V39() V54() set
{<*(g . (f1 + 1)),o0*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (f1 + 1)),o0*>,'&'},{<*(g . (f1 + 1)),o0*>}} is non empty V39() V43() V54() set
[<*o0,(f . (f1 + 1))*>,'&'] is non empty pair set
{<*o0,(f . (f1 + 1))*>,'&'} is non empty functional V39() V54() set
{<*o0,(f . (f1 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*o0,(f . (f1 + 1))*>,'&'},{<*o0,(f . (f1 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) +* (MajorityStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
An is non-empty MSAlgebra over Sn
BitAdderWithOverflowCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V110( BitAdderWithOverflowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over BitAdderWithOverflowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
BitAdderCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110((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'))
MajorityCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V110( MajorityStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over MajorityStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
MajorityICirc ((f . (f1 + 1)),(g . (f1 + 1)),o0) is strict non-empty finitely-generated V110( MajorityIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) gate`2=den Boolean MSAlgebra over MajorityIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)
1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')
1GateCircuit (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')
1GateCircuit ((g . (f1 + 1)),o0,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(g . (f1 + 1)),o0*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (f1 + 1)),o0*>,'&')
1GateCircuit (<*(g . (f1 + 1)),o0*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(g . (f1 + 1)),o0*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (f1 + 1)),o0*>,'&')
(1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),'&')) +* (1GateCircuit ((g . (f1 + 1)),o0,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,'&'))
1GateCircuit (o0,(f . (f1 + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*o0,(f . (f1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*o0,(f . (f1 + 1))*>,'&')
1GateCircuit (<*o0,(f . (f1 + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*o0,(f . (f1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*o0,(f . (f1 + 1))*>,'&')
((1GateCircuit ((f . (f1 + 1)),(g . (f1 + 1)),'&')) +* (1GateCircuit ((g . (f1 + 1)),o0,'&'))) +* (1GateCircuit (o0,(f . (f1 + 1)),'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,'&'))) +* (1GateCircStr (<*o0,(f . (f1 + 1))*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&')) +* (1GateCircStr (<*(g . (f1 + 1)),o0*>,'&'))) +* (1GateCircStr (<*o0,(f . (f1 + 1))*>,'&'))
1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3)
1GateCircuit (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3)
(MajorityICirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircuit ([<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (1GateCircStr (<*[<*(f . (f1 + 1)),(g . (f1 + 1))*>,'&'],[<*(g . (f1 + 1)),o0*>,'&'],[<*o0,(f . (f1 + 1))*>,'&']*>,or3))
(BitAdderCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) +* (MajorityCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is strict non-empty finitely-generated V110((2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) +* (MajorityStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((f . (f1 + 1)),(g . (f1 + 1)),o0,'xor')) +* (MajorityStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))
An +* (BitAdderWithOverflowCirc ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is strict non-empty MSAlgebra over Sn +* (BitAdderWithOverflowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0))
Sn +* (BitAdderWithOverflowStr ((f . (f1 + 1)),(g . (f1 + 1)),o0)) is non empty non void V74() strict ManySortedSign
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
f is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
g is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
(n,f,g) is non empty non void V74() 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 K23( the carrier of (n,f,g))
K23( the carrier of (n,f,g)) is non empty set
the ResultSort of (n,f,g) is Relation-like the carrier' of (n,f,g) -defined the carrier of (n,f,g) -valued Function-like V30( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K24( the carrier' of (n,f,g), the carrier of (n,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g))) is non empty set
K497( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K23( 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 total set
h . n is set
h . 0 is set
Sn is Relation-like NAT -defined Function-like total set
Sn . n is set
Sn . 0 is set
proj1 h is set
An is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
An + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
h . (An + 1) is set
f . (An + 1) is set
g . (An + 1) is set
h . An is set
MajorityOutput ((f . (An + 1)),(g . (An + 1)),(h . An)) is Element of InnerVertices (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An)))
MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (An + 1)),(g . (An + 1)),(h . An)) is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (An + 1)),(h . An)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,'&')) +* (1GateCircStr (<*(g . (An + 1)),(h . An)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(h . An),(f . (An + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(h . An),(f . (An + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,'&')) +* (1GateCircStr (<*(g . (An + 1)),(h . An)*>,'&'))) +* (1GateCircStr (<*(h . An),(f . (An + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (An + 1)),(g . (An + 1))*>,'&'] is non empty pair set
{<*(f . (An + 1)),(g . (An + 1))*>,'&'} is non empty functional V39() V54() set
{<*(f . (An + 1)),(g . (An + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (An + 1)),(g . (An + 1))*>,'&'},{<*(f . (An + 1)),(g . (An + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (An + 1)),(h . An)*>,'&'] is non empty pair set
{<*(g . (An + 1)),(h . An)*>,'&'} is non empty functional V39() V54() set
{<*(g . (An + 1)),(h . An)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (An + 1)),(h . An)*>,'&'},{<*(g . (An + 1)),(h . An)*>}} is non empty V39() V43() V54() set
[<*(h . An),(f . (An + 1))*>,'&'] is non empty pair set
{<*(h . An),(f . (An + 1))*>,'&'} is non empty functional V39() V54() set
{<*(h . An),(f . (An + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(h . An),(f . (An + 1))*>,'&'},{<*(h . An),(f . (An + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(h . An)*>,'&'],[<*(h . An),(f . (An + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(h . An)*>,'&'],[<*(h . An),(f . (An + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (An + 1)),(g . (An + 1)),(h . An))) +* (1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(h . An)*>,'&'],[<*(h . An),(f . (An + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An))) is non empty set
InnerVertices (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An))) is non empty Element of K23( the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An))))
K23( the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An)))) is non empty set
the ResultSort of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An))) is Relation-like the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An))) -defined the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An))) -valued Function-like V30( the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An))), the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An)))) Element of K23(K24( the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An))), the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An)))))
the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An))) is non empty set
K24( the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An))), the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An)))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An))), the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An))))) is non empty set
K497( the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An))), the ResultSort of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An)))) is Element of K23( the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(h . An))))
[<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(h . An)*>,'&'],[<*(h . An),(f . (An + 1))*>,'&']*>,or3] is non empty pair set
{<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(h . An)*>,'&'],[<*(h . An),(f . (An + 1))*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(h . An)*>,'&'],[<*(h . An),(f . (An + 1))*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(h . An)*>,'&'],[<*(h . An),(f . (An + 1))*>,'&']*>,or3},{<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(h . An)*>,'&'],[<*(h . An),(f . (An + 1))*>,'&']*>}} is non empty V39() V43() V54() set
proj1 Sn is set
An is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
An + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
Sn . (An + 1) is set
f . (An + 1) is set
g . (An + 1) is set
Sn . An is set
MajorityOutput ((f . (An + 1)),(g . (An + 1)),(Sn . An)) is Element of InnerVertices (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)))
MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)) is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (An + 1)),(Sn . An)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,'&')) +* (1GateCircStr (<*(g . (An + 1)),(Sn . An)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(Sn . An),(f . (An + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(Sn . An),(f . (An + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,'&')) +* (1GateCircStr (<*(g . (An + 1)),(Sn . An)*>,'&'))) +* (1GateCircStr (<*(Sn . An),(f . (An + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (An + 1)),(g . (An + 1))*>,'&'] is non empty pair set
{<*(f . (An + 1)),(g . (An + 1))*>,'&'} is non empty functional V39() V54() set
{<*(f . (An + 1)),(g . (An + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (An + 1)),(g . (An + 1))*>,'&'},{<*(f . (An + 1)),(g . (An + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (An + 1)),(Sn . An)*>,'&'] is non empty pair set
{<*(g . (An + 1)),(Sn . An)*>,'&'} is non empty functional V39() V54() set
{<*(g . (An + 1)),(Sn . An)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (An + 1)),(Sn . An)*>,'&'},{<*(g . (An + 1)),(Sn . An)*>}} is non empty V39() V43() V54() set
[<*(Sn . An),(f . (An + 1))*>,'&'] is non empty pair set
{<*(Sn . An),(f . (An + 1))*>,'&'} is non empty functional V39() V54() set
{<*(Sn . An),(f . (An + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(Sn . An),(f . (An + 1))*>,'&'},{<*(Sn . An),(f . (An + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(Sn . An)*>,'&'],[<*(Sn . An),(f . (An + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(Sn . An)*>,'&'],[<*(Sn . An),(f . (An + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))) +* (1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(Sn . An)*>,'&'],[<*(Sn . An),(f . (An + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))) is non empty set
InnerVertices (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))) is non empty Element of K23( the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))))
K23( the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)))) is non empty set
the ResultSort of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))) is Relation-like the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))) -defined the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))) -valued Function-like V30( the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))), the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)))) Element of K23(K24( the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))), the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)))))
the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))) is non empty set
K24( the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))), the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))), the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))))) is non empty set
K497( the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))), the ResultSort of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An)))) is Element of K23( the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),(Sn . An))))
[<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(Sn . An)*>,'&'],[<*(Sn . An),(f . (An + 1))*>,'&']*>,or3] is non empty pair set
{<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(Sn . An)*>,'&'],[<*(Sn . An),(f . (An + 1))*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(Sn . An)*>,'&'],[<*(Sn . An),(f . (An + 1))*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(Sn . An)*>,'&'],[<*(Sn . An),(f . (An + 1))*>,'&']*>,or3},{<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),(Sn . An)*>,'&'],[<*(Sn . An),(f . (An + 1))*>,'&']*>}} is non empty V39() V43() V54() set
A0 is Relation-like NAT -defined Function-like total set
A0 . n is set
A0 . 0 is set
N is Relation-like NAT -defined Function-like total set
N . 0 is set
InnerVertices (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) is non empty Element of K23( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))))
the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) is non empty set
K23( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)))) is non empty set
the ResultSort of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) is Relation-like the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) -defined the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) -valued Function-like V30( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)))) Element of K23(K24( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)))))
the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) is non empty set
K24( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)))) is non empty Relation-like set
K23(K24( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))))) is non empty set
K497( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))), the ResultSort of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)))) is Element of K23( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))))
{[{},((0 -tuples_on BOOLEAN) --> FALSE)]} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
h is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
A0 . h is set
N . h is set
h + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
A0 . (h + 1) is set
N . (h + 1) is set
Sn is non empty V74() ManySortedSign
InnerVertices Sn is Element of K23( the carrier of Sn)
the carrier of Sn is non empty set
K23( the carrier of Sn) is non empty set
the ResultSort of Sn is Relation-like the carrier' of Sn -defined the carrier of Sn -valued Function-like V30( the carrier' of Sn, the carrier of Sn) Element of K23(K24( the carrier' of Sn, the carrier of Sn))
the carrier' of Sn is set
K24( the carrier' of Sn, the carrier of Sn) is Relation-like set
K23(K24( the carrier' of Sn, the carrier of Sn)) is non empty set
K497( the carrier of Sn, the ResultSort of Sn) is Element of K23( the carrier of Sn)
Sn is non empty V74() ManySortedSign
InnerVertices Sn is Element of K23( the carrier of Sn)
the carrier of Sn is non empty set
K23( the carrier of Sn) is non empty set
the ResultSort of Sn is Relation-like the carrier' of Sn -defined the carrier of Sn -valued Function-like V30( the carrier' of Sn, the carrier of Sn) Element of K23(K24( the carrier' of Sn, the carrier of Sn))
the carrier' of Sn is set
K24( the carrier' of Sn, the carrier of Sn) is Relation-like set
K23(K24( the carrier' of Sn, the carrier of Sn)) is non empty set
K497( the carrier of Sn, the ResultSort of Sn) is Element of K23( the carrier of Sn)
f . (h + 1) is set
g . (h + 1) is set
MajorityOutput ((f . (h + 1)),(g . (h + 1)),(N . h)) is Element of InnerVertices (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h)))
MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (h + 1)),(g . (h + 1)),(N . h)) is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (h + 1)),(g . (h + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (h + 1)),(N . h)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (h + 1)),(g . (h + 1))*>,'&')) +* (1GateCircStr (<*(g . (h + 1)),(N . h)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(N . h),(f . (h + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(N . h),(f . (h + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (h + 1)),(g . (h + 1))*>,'&')) +* (1GateCircStr (<*(g . (h + 1)),(N . h)*>,'&'))) +* (1GateCircStr (<*(N . h),(f . (h + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (h + 1)),(g . (h + 1))*>,'&'] is non empty pair set
{<*(f . (h + 1)),(g . (h + 1))*>,'&'} is non empty functional V39() V54() set
{<*(f . (h + 1)),(g . (h + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (h + 1)),(g . (h + 1))*>,'&'},{<*(f . (h + 1)),(g . (h + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (h + 1)),(N . h)*>,'&'] is non empty pair set
{<*(g . (h + 1)),(N . h)*>,'&'} is non empty functional V39() V54() set
{<*(g . (h + 1)),(N . h)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (h + 1)),(N . h)*>,'&'},{<*(g . (h + 1)),(N . h)*>}} is non empty V39() V43() V54() set
[<*(N . h),(f . (h + 1))*>,'&'] is non empty pair set
{<*(N . h),(f . (h + 1))*>,'&'} is non empty functional V39() V54() set
{<*(N . h),(f . (h + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(N . h),(f . (h + 1))*>,'&'},{<*(N . h),(f . (h + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (h + 1)),(g . (h + 1))*>,'&'],[<*(g . (h + 1)),(N . h)*>,'&'],[<*(N . h),(f . (h + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (h + 1)),(g . (h + 1))*>,'&'],[<*(g . (h + 1)),(N . h)*>,'&'],[<*(N . h),(f . (h + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (h + 1)),(g . (h + 1)),(N . h))) +* (1GateCircStr (<*[<*(f . (h + 1)),(g . (h + 1))*>,'&'],[<*(g . (h + 1)),(N . h)*>,'&'],[<*(N . h),(f . (h + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty set
InnerVertices (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty Element of K23( the carrier of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h))))
K23( the carrier of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is non empty set
the ResultSort of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is Relation-like the carrier' of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h))) -defined the carrier of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h))) -valued Function-like V30( the carrier' of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) Element of K23(K24( the carrier' of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h)))))
the carrier' of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty set
K24( the carrier' of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h))))) is non empty set
K497( the carrier of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the ResultSort of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is Element of K23( the carrier of (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h))))
[<*[<*(f . (h + 1)),(g . (h + 1))*>,'&'],[<*(g . (h + 1)),(N . h)*>,'&'],[<*(N . h),(f . (h + 1))*>,'&']*>,or3] is non empty pair set
{<*[<*(f . (h + 1)),(g . (h + 1))*>,'&'],[<*(g . (h + 1)),(N . h)*>,'&'],[<*(N . h),(f . (h + 1))*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*(f . (h + 1)),(g . (h + 1))*>,'&'],[<*(g . (h + 1)),(N . h)*>,'&'],[<*(N . h),(f . (h + 1))*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(f . (h + 1)),(g . (h + 1))*>,'&'],[<*(g . (h + 1)),(N . h)*>,'&'],[<*(N . h),(f . (h + 1))*>,'&']*>,or3},{<*[<*(f . (h + 1)),(g . (h + 1))*>,'&'],[<*(g . (h + 1)),(N . h)*>,'&'],[<*(N . h),(f . (h + 1))*>,'&']*>}} is non empty V39() V43() V54() set
BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)) is non empty non void V74() 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 V74() 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 V74() 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 V39() V54() set
{{<*(f . (h + 1)),(g . (h + 1))*>,'xor'},{<*(f . (h + 1)),(g . (h + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (h + 1)),(g . (h + 1))*>,'xor'],(N . h)*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (h + 1)),(g . (h + 1))*>,'xor'],(N . h)*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (h + 1)),(g . (h + 1)),(N . h),'xor')) +* (MajorityStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty Element of K23( the carrier of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))
the carrier of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty set
K23( the carrier of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is non empty set
the ResultSort of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is Relation-like the carrier' of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) -defined the carrier of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))))
the carrier' of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the carrier of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))), the ResultSort of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))
Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))) is non empty non void V74() strict ManySortedSign
InnerVertices (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is non empty Element of K23( the carrier of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))))
the carrier of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is non empty set
K23( the carrier of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))) is non empty set
the ResultSort of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is Relation-like the carrier' of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) -defined the carrier of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) -valued Function-like V30( the carrier' of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))), the carrier of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))) Element of K23(K24( the carrier' of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))), the carrier of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))))
the carrier' of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))) is non empty set
K24( the carrier' of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))), the carrier of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))) is non empty Relation-like set
K23(K24( the carrier' of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))), the carrier of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))))) is non empty set
K497( the carrier of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))), the ResultSort of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h))))) is Element of K23( the carrier of (Sn +* (BitAdderWithOverflowStr ((f . (h + 1)),(g . (h + 1)),(N . h)))))
h is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
A0 . h is set
N . n is set
N . h is set
An is non empty V74() ManySortedSign
InnerVertices An is Element of K23( the carrier of An)
the carrier of An is non empty set
K23( the carrier of An) is non empty set
the ResultSort of An is Relation-like the carrier' of An -defined the carrier of An -valued Function-like V30( the carrier' of An, the carrier of An) Element of K23(K24( the carrier' of An, the carrier of An))
the carrier' of An is set
K24( the carrier' of An, the carrier of An) is Relation-like set
K23(K24( the carrier' of An, the carrier of An)) is non empty set
K497( the carrier of An, the ResultSort of An) is Element of K23( the carrier of An)
Sn is Element of InnerVertices (n,f,g)
An is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
N . An is set
An + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
N . (An + 1) is set
f . (An + 1) is set
g . (An + 1) is set
f1 is non empty V74() ManySortedSign
o0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
A0 . o0 is set
g1 is set
N . o0 is set
A0 . An is set
o0 is set
MajorityOutput ((f . (An + 1)),(g . (An + 1)),o0) is Element of InnerVertices (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0))
MajorityStr ((f . (An + 1)),(g . (An + 1)),o0) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (An + 1)),(g . (An + 1)),o0) is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (An + 1)),o0*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (An + 1)),o0*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,'&')) +* (1GateCircStr (<*(g . (An + 1)),o0*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*o0,(f . (An + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*o0,(f . (An + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (An + 1)),(g . (An + 1))*>,'&')) +* (1GateCircStr (<*(g . (An + 1)),o0*>,'&'))) +* (1GateCircStr (<*o0,(f . (An + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (An + 1)),(g . (An + 1))*>,'&'] is non empty pair set
{<*(f . (An + 1)),(g . (An + 1))*>,'&'} is non empty functional V39() V54() set
{<*(f . (An + 1)),(g . (An + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (An + 1)),(g . (An + 1))*>,'&'},{<*(f . (An + 1)),(g . (An + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (An + 1)),o0*>,'&'] is non empty pair set
{<*(g . (An + 1)),o0*>,'&'} is non empty functional V39() V54() set
{<*(g . (An + 1)),o0*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (An + 1)),o0*>,'&'},{<*(g . (An + 1)),o0*>}} is non empty V39() V43() V54() set
[<*o0,(f . (An + 1))*>,'&'] is non empty pair set
{<*o0,(f . (An + 1))*>,'&'} is non empty functional V39() V54() set
{<*o0,(f . (An + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*o0,(f . (An + 1))*>,'&'},{<*o0,(f . (An + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),o0*>,'&'],[<*o0,(f . (An + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),o0*>,'&'],[<*o0,(f . (An + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (An + 1)),(g . (An + 1)),o0)) +* (1GateCircStr (<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),o0*>,'&'],[<*o0,(f . (An + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0)) is non empty set
InnerVertices (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0)) is non empty Element of K23( the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0)))
K23( the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0))) is non empty set
the ResultSort of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0)) is Relation-like the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0)) -defined the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0)) -valued Function-like V30( the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0)), the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0))) Element of K23(K24( the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0)), the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0))))
the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0)) is non empty set
K24( the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0)), the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0)), the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0)))) is non empty set
K497( the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0)), the ResultSort of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0))) is Element of K23( the carrier of (MajorityStr ((f . (An + 1)),(g . (An + 1)),o0)))
[<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),o0*>,'&'],[<*o0,(f . (An + 1))*>,'&']*>,or3] is non empty pair set
{<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),o0*>,'&'],[<*o0,(f . (An + 1))*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),o0*>,'&'],[<*o0,(f . (An + 1))*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),o0*>,'&'],[<*o0,(f . (An + 1))*>,'&']*>,or3},{<*[<*(f . (An + 1)),(g . (An + 1))*>,'&'],[<*(g . (An + 1)),o0*>,'&'],[<*o0,(f . (An + 1))*>,'&']*>}} is non empty V39() V43() V54() set
f1 is non empty V74() ManySortedSign
n is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
f is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
g is Relation-like NAT -defined Function-like total set
g . 0 is set
S0 is Relation-like NAT -defined Function-like total set
S0 . 0 is set
A0 is Relation-like NAT -defined Function-like total set
A0 . 0 is set
N is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
(N,n,f) is non empty non void V74() 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 V110((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 K23( the carrier of (N,n,f))
K23( the carrier of (N,n,f)) is non empty set
the ResultSort of (N,n,f) is Relation-like the carrier' of (N,n,f) -defined the carrier of (N,n,f) -valued Function-like V30( the carrier' of (N,n,f), the carrier of (N,n,f)) Element of K23(K24( the carrier' of (N,n,f), the carrier of (N,n,f)))
the carrier' of (N,n,f) is non empty set
K24( the carrier' of (N,n,f), the carrier of (N,n,f)) is non empty Relation-like set
K23(K24( the carrier' of (N,n,f), the carrier of (N,n,f))) is non empty set
K497( the carrier of (N,n,f), the ResultSort of (N,n,f)) is Element of K23( the carrier of (N,n,f))
A0 . N is set
h is Relation-like NAT -defined Function-like total set
h . N is set
Sn is Relation-like NAT -defined Function-like total set
Sn . N is set
h . 0 is set
Sn . 0 is set
An is Relation-like NAT -defined Function-like total set
An . 0 is set
o0 is non empty V74() ManySortedSign
h1 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
h1 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n . (h1 + 1) is set
f . (h1 + 1) is set
g1 is set
BitAdderWithOverflowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(n . (h1 + 1)),(f . (h1 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'},{<*(n . (h1 + 1)),(f . (h1 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'],g1*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'xor'],g1*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((n . (h1 + 1)),(f . (h1 + 1)),g1) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((n . (h1 + 1)),(f . (h1 + 1)),g1) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (h1 + 1)),g1*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&')) +* (1GateCircStr (<*(f . (h1 + 1)),g1*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*g1,(n . (h1 + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*g1,(n . (h1 + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&')) +* (1GateCircStr (<*(f . (h1 + 1)),g1*>,'&'))) +* (1GateCircStr (<*g1,(n . (h1 + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&'] is non empty pair set
{<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&'},{<*(n . (h1 + 1)),(f . (h1 + 1))*>}} is non empty V39() V43() V54() set
[<*(f . (h1 + 1)),g1*>,'&'] is non empty pair set
{<*(f . (h1 + 1)),g1*>,'&'} is non empty functional V39() V54() set
{<*(f . (h1 + 1)),g1*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (h1 + 1)),g1*>,'&'},{<*(f . (h1 + 1)),g1*>}} is non empty V39() V43() V54() set
[<*g1,(n . (h1 + 1))*>,'&'] is non empty pair set
{<*g1,(n . (h1 + 1))*>,'&'} is non empty functional V39() V54() set
{<*g1,(n . (h1 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g1,(n . (h1 + 1))*>,'&'},{<*g1,(n . (h1 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&'],[<*(f . (h1 + 1)),g1*>,'&'],[<*g1,(n . (h1 + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&'],[<*(f . (h1 + 1)),g1*>,'&'],[<*g1,(n . (h1 + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) +* (1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&'],[<*(f . (h1 + 1)),g1*>,'&'],[<*g1,(n . (h1 + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((n . (h1 + 1)),(f . (h1 + 1)),g1,'xor')) +* (MajorityStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
f1 is non-empty MSAlgebra over o0
BitAdderWithOverflowCirc ((n . (h1 + 1)),(f . (h1 + 1)),g1) is strict non-empty finitely-generated V110( BitAdderWithOverflowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) gate`2=den Boolean MSAlgebra over BitAdderWithOverflowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)
BitAdderCirc ((n . (h1 + 1)),(f . (h1 + 1)),g1) is strict non-empty finitely-generated V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110((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'))
MajorityCirc ((n . (h1 + 1)),(f . (h1 + 1)),g1) is strict non-empty finitely-generated V110( MajorityStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) gate`2=den Boolean MSAlgebra over MajorityStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)
MajorityICirc ((n . (h1 + 1)),(f . (h1 + 1)),g1) is strict non-empty finitely-generated V110( MajorityIStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) gate`2=den Boolean MSAlgebra over MajorityIStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)
1GateCircuit ((n . (h1 + 1)),(f . (h1 + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&')
1GateCircuit (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&')
1GateCircuit ((f . (h1 + 1)),g1,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (h1 + 1)),g1*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (h1 + 1)),g1*>,'&')
1GateCircuit (<*(f . (h1 + 1)),g1*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (h1 + 1)),g1*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (h1 + 1)),g1*>,'&')
(1GateCircuit ((n . (h1 + 1)),(f . (h1 + 1)),'&')) +* (1GateCircuit ((f . (h1 + 1)),g1,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&')) +* (1GateCircStr (<*(f . (h1 + 1)),g1*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&')) +* (1GateCircStr (<*(f . (h1 + 1)),g1*>,'&'))
1GateCircuit (g1,(n . (h1 + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g1,(n . (h1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g1,(n . (h1 + 1))*>,'&')
1GateCircuit (<*g1,(n . (h1 + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g1,(n . (h1 + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g1,(n . (h1 + 1))*>,'&')
((1GateCircuit ((n . (h1 + 1)),(f . (h1 + 1)),'&')) +* (1GateCircuit ((f . (h1 + 1)),g1,'&'))) +* (1GateCircuit (g1,(n . (h1 + 1)),'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&')) +* (1GateCircStr (<*(f . (h1 + 1)),g1*>,'&'))) +* (1GateCircStr (<*g1,(n . (h1 + 1))*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&')) +* (1GateCircStr (<*(f . (h1 + 1)),g1*>,'&'))) +* (1GateCircStr (<*g1,(n . (h1 + 1))*>,'&'))
1GateCircuit ([<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&'],[<*(f . (h1 + 1)),g1*>,'&'],[<*g1,(n . (h1 + 1))*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&'],[<*(f . (h1 + 1)),g1*>,'&'],[<*g1,(n . (h1 + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&'],[<*(f . (h1 + 1)),g1*>,'&'],[<*g1,(n . (h1 + 1))*>,'&']*>,or3)
1GateCircuit (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&'],[<*(f . (h1 + 1)),g1*>,'&'],[<*g1,(n . (h1 + 1))*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&'],[<*(f . (h1 + 1)),g1*>,'&'],[<*g1,(n . (h1 + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&'],[<*(f . (h1 + 1)),g1*>,'&'],[<*g1,(n . (h1 + 1))*>,'&']*>,or3)
(MajorityICirc ((n . (h1 + 1)),(f . (h1 + 1)),g1)) +* (1GateCircuit ([<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&'],[<*(f . (h1 + 1)),g1*>,'&'],[<*g1,(n . (h1 + 1))*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) +* (1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&'],[<*(f . (h1 + 1)),g1*>,'&'],[<*g1,(n . (h1 + 1))*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) +* (1GateCircStr (<*[<*(n . (h1 + 1)),(f . (h1 + 1))*>,'&'],[<*(f . (h1 + 1)),g1*>,'&'],[<*g1,(n . (h1 + 1))*>,'&']*>,or3))
(BitAdderCirc ((n . (h1 + 1)),(f . (h1 + 1)),g1)) +* (MajorityCirc ((n . (h1 + 1)),(f . (h1 + 1)),g1)) is strict non-empty finitely-generated V110((2GatesCircStr ((n . (h1 + 1)),(f . (h1 + 1)),g1,'xor')) +* (MajorityStr ((n . (h1 + 1)),(f . (h1 + 1)),g1))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((n . (h1 + 1)),(f . (h1 + 1)),g1,'xor')) +* (MajorityStr ((n . (h1 + 1)),(f . (h1 + 1)),g1))
f1 +* (BitAdderWithOverflowCirc ((n . (h1 + 1)),(f . (h1 + 1)),g1)) is strict non-empty MSAlgebra over o0 +* (BitAdderWithOverflowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1))
o0 +* (BitAdderWithOverflowStr ((n . (h1 + 1)),(f . (h1 + 1)),g1)) is non empty non void V74() strict ManySortedSign
proj1 A0 is set
o0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
o0 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
A0 . (o0 + 1) is set
n . (o0 + 1) is set
f . (o0 + 1) is set
A0 . o0 is set
MajorityOutput ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)) is Element of InnerVertices (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)))
MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)) is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(n . (o0 + 1)),(f . (o0 + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (o0 + 1)),(A0 . o0)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (o0 + 1)),(f . (o0 + 1))*>,'&')) +* (1GateCircStr (<*(f . (o0 + 1)),(A0 . o0)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0 . o0),(n . (o0 + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(A0 . o0),(n . (o0 + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (o0 + 1)),(f . (o0 + 1))*>,'&')) +* (1GateCircStr (<*(f . (o0 + 1)),(A0 . o0)*>,'&'))) +* (1GateCircStr (<*(A0 . o0),(n . (o0 + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (o0 + 1)),(f . (o0 + 1))*>,'&'] is non empty pair set
{<*(n . (o0 + 1)),(f . (o0 + 1))*>,'&'} is non empty functional V39() V54() set
{<*(n . (o0 + 1)),(f . (o0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(n . (o0 + 1)),(f . (o0 + 1))*>,'&'},{<*(n . (o0 + 1)),(f . (o0 + 1))*>}} is non empty V39() V43() V54() set
[<*(f . (o0 + 1)),(A0 . o0)*>,'&'] is non empty pair set
{<*(f . (o0 + 1)),(A0 . o0)*>,'&'} is non empty functional V39() V54() set
{<*(f . (o0 + 1)),(A0 . o0)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (o0 + 1)),(A0 . o0)*>,'&'},{<*(f . (o0 + 1)),(A0 . o0)*>}} is non empty V39() V43() V54() set
[<*(A0 . o0),(n . (o0 + 1))*>,'&'] is non empty pair set
{<*(A0 . o0),(n . (o0 + 1))*>,'&'} is non empty functional V39() V54() set
{<*(A0 . o0),(n . (o0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(A0 . o0),(n . (o0 + 1))*>,'&'},{<*(A0 . o0),(n . (o0 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,'&'],[<*(f . (o0 + 1)),(A0 . o0)*>,'&'],[<*(A0 . o0),(n . (o0 + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,'&'],[<*(f . (o0 + 1)),(A0 . o0)*>,'&'],[<*(A0 . o0),(n . (o0 + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))) +* (1GateCircStr (<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,'&'],[<*(f . (o0 + 1)),(A0 . o0)*>,'&'],[<*(A0 . o0),(n . (o0 + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))) is non empty set
InnerVertices (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))) is non empty Element of K23( the carrier of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))))
K23( the carrier of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)))) is non empty set
the ResultSort of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))) is Relation-like the carrier' of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))) -defined the carrier of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))) -valued Function-like V30( the carrier' of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))), the carrier of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)))) Element of K23(K24( the carrier' of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))), the carrier of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)))))
the carrier' of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))) is non empty set
K24( the carrier' of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))), the carrier of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))), the carrier of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))))) is non empty set
K497( the carrier of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))), the ResultSort of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0)))) is Element of K23( the carrier of (MajorityStr ((n . (o0 + 1)),(f . (o0 + 1)),(A0 . o0))))
[<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,'&'],[<*(f . (o0 + 1)),(A0 . o0)*>,'&'],[<*(A0 . o0),(n . (o0 + 1))*>,'&']*>,or3] is non empty pair set
{<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,'&'],[<*(f . (o0 + 1)),(A0 . o0)*>,'&'],[<*(A0 . o0),(n . (o0 + 1))*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,'&'],[<*(f . (o0 + 1)),(A0 . o0)*>,'&'],[<*(A0 . o0),(n . (o0 + 1))*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,'&'],[<*(f . (o0 + 1)),(A0 . o0)*>,'&'],[<*(A0 . o0),(n . (o0 + 1))*>,'&']*>,or3},{<*[<*(n . (o0 + 1)),(f . (o0 + 1))*>,'&'],[<*(f . (o0 + 1)),(A0 . o0)*>,'&'],[<*(A0 . o0),(n . (o0 + 1))*>,'&']*>}} is non empty V39() V43() V54() set
o0 is Relation-like NAT -defined Function-like total set
o0 . N is set
o0 . 0 is set
proj1 o0 is set
f1 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
f1 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
o0 . (f1 + 1) is set
n . (f1 + 1) is set
f . (f1 + 1) is set
o0 . f1 is set
MajorityOutput ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)) is Element of InnerVertices (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)))
MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)) is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(n . (f1 + 1)),(f . (f1 + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (f1 + 1)),(o0 . f1)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (f1 + 1)),(f . (f1 + 1))*>,'&')) +* (1GateCircStr (<*(f . (f1 + 1)),(o0 . f1)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(o0 . f1),(n . (f1 + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(o0 . f1),(n . (f1 + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (f1 + 1)),(f . (f1 + 1))*>,'&')) +* (1GateCircStr (<*(f . (f1 + 1)),(o0 . f1)*>,'&'))) +* (1GateCircStr (<*(o0 . f1),(n . (f1 + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (f1 + 1)),(f . (f1 + 1))*>,'&'] is non empty pair set
{<*(n . (f1 + 1)),(f . (f1 + 1))*>,'&'} is non empty functional V39() V54() set
{<*(n . (f1 + 1)),(f . (f1 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(n . (f1 + 1)),(f . (f1 + 1))*>,'&'},{<*(n . (f1 + 1)),(f . (f1 + 1))*>}} is non empty V39() V43() V54() set
[<*(f . (f1 + 1)),(o0 . f1)*>,'&'] is non empty pair set
{<*(f . (f1 + 1)),(o0 . f1)*>,'&'} is non empty functional V39() V54() set
{<*(f . (f1 + 1)),(o0 . f1)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (f1 + 1)),(o0 . f1)*>,'&'},{<*(f . (f1 + 1)),(o0 . f1)*>}} is non empty V39() V43() V54() set
[<*(o0 . f1),(n . (f1 + 1))*>,'&'] is non empty pair set
{<*(o0 . f1),(n . (f1 + 1))*>,'&'} is non empty functional V39() V54() set
{<*(o0 . f1),(n . (f1 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(o0 . f1),(n . (f1 + 1))*>,'&'},{<*(o0 . f1),(n . (f1 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,'&'],[<*(f . (f1 + 1)),(o0 . f1)*>,'&'],[<*(o0 . f1),(n . (f1 + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,'&'],[<*(f . (f1 + 1)),(o0 . f1)*>,'&'],[<*(o0 . f1),(n . (f1 + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))) +* (1GateCircStr (<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,'&'],[<*(f . (f1 + 1)),(o0 . f1)*>,'&'],[<*(o0 . f1),(n . (f1 + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))) is non empty set
InnerVertices (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))) is non empty Element of K23( the carrier of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))))
K23( the carrier of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)))) is non empty set
the ResultSort of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))) is Relation-like the carrier' of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))) -defined the carrier of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))) -valued Function-like V30( the carrier' of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))), the carrier of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)))) Element of K23(K24( the carrier' of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))), the carrier of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)))))
the carrier' of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))) is non empty set
K24( the carrier' of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))), the carrier of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))), the carrier of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))))) is non empty set
K497( the carrier of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))), the ResultSort of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1)))) is Element of K23( the carrier of (MajorityStr ((n . (f1 + 1)),(f . (f1 + 1)),(o0 . f1))))
[<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,'&'],[<*(f . (f1 + 1)),(o0 . f1)*>,'&'],[<*(o0 . f1),(n . (f1 + 1))*>,'&']*>,or3] is non empty pair set
{<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,'&'],[<*(f . (f1 + 1)),(o0 . f1)*>,'&'],[<*(o0 . f1),(n . (f1 + 1))*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,'&'],[<*(f . (f1 + 1)),(o0 . f1)*>,'&'],[<*(o0 . f1),(n . (f1 + 1))*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,'&'],[<*(f . (f1 + 1)),(o0 . f1)*>,'&'],[<*(o0 . f1),(n . (f1 + 1))*>,'&']*>,or3},{<*[<*(n . (f1 + 1)),(f . (f1 + 1))*>,'&'],[<*(f . (f1 + 1)),(o0 . f1)*>,'&'],[<*(o0 . f1),(n . (f1 + 1))*>,'&']*>}} is non empty V39() V43() V54() set
n is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
f is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
(0,n,f) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(0,n,f) is strict non-empty finitely-generated V110((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 K23( the carrier of (0,n,f))
K23( the carrier of (0,n,f)) is non empty set
the ResultSort of (0,n,f) is Relation-like the carrier' of (0,n,f) -defined the carrier of (0,n,f) -valued Function-like V30( the carrier' of (0,n,f), the carrier of (0,n,f)) Element of K23(K24( the carrier' of (0,n,f), the carrier of (0,n,f)))
the carrier' of (0,n,f) is non empty set
K24( the carrier' of (0,n,f), the carrier of (0,n,f)) is non empty Relation-like set
K23(K24( the carrier' of (0,n,f), the carrier of (0,n,f))) is non empty set
K497( the carrier of (0,n,f), the ResultSort of (0,n,f)) is Element of K23( the carrier of (0,n,f))
g is Relation-like NAT -defined Function-like total set
g . 0 is set
S0 is Relation-like NAT -defined Function-like total set
S0 . 0 is set
A0 is Relation-like NAT -defined Function-like total set
A0 . 0 is set
g is Relation-like NAT -defined Function-like total set
g . 0 is set
S0 is Relation-like NAT -defined Function-like total set
S0 . 0 is set
A0 is Relation-like NAT -defined Function-like total set
A0 . 0 is set
{[{},((0 -tuples_on BOOLEAN) --> FALSE)]} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
g is Relation-like NAT -defined Function-like total set
g . 0 is set
S0 is Relation-like NAT -defined Function-like total set
S0 . 0 is set
A0 is Relation-like NAT -defined Function-like total set
A0 . 0 is set
n is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
f is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
(1,n,f) is non empty non void V74() 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 V110((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 K23( the carrier of (1,n,f))
K23( the carrier of (1,n,f)) is non empty set
the ResultSort of (1,n,f) is Relation-like the carrier' of (1,n,f) -defined the carrier of (1,n,f) -valued Function-like V30( the carrier' of (1,n,f), the carrier of (1,n,f)) Element of K23(K24( the carrier' of (1,n,f), the carrier of (1,n,f)))
the carrier' of (1,n,f) is non empty set
K24( the carrier' of (1,n,f), the carrier of (1,n,f)) is non empty Relation-like set
K23(K24( the carrier' of (1,n,f), the carrier of (1,n,f))) is non empty set
K497( the carrier of (1,n,f), the ResultSort of (1,n,f)) is Element of K23( the carrier of (1,n,f))
g is set
BitAdderWithOverflowStr ((n . 1),(f . 1),g) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(n . 1),(f . 1)*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(n . 1),(f . 1)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(n . 1),(f . 1)*>,'xor'},{<*(n . 1),(f . 1)*>}} is non empty V39() V43() V54() set
<*[<*(n . 1),(f . 1)*>,'xor'],g*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . 1),(f . 1)*>,'xor'],g*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((n . 1),(f . 1),g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((n . 1),(f . 1),g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . 1),(f . 1)*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . 1),g*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . 1),(f . 1)*>,'&')) +* (1GateCircStr (<*(f . 1),g*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*g,(n . 1)*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*g,(n . 1)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . 1),(f . 1)*>,'&')) +* (1GateCircStr (<*(f . 1),g*>,'&'))) +* (1GateCircStr (<*g,(n . 1)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . 1),(f . 1)*>,'&'] is non empty pair set
{<*(n . 1),(f . 1)*>,'&'} is non empty functional V39() V54() set
{{<*(n . 1),(f . 1)*>,'&'},{<*(n . 1),(f . 1)*>}} is non empty V39() V43() V54() set
[<*(f . 1),g*>,'&'] is non empty pair set
{<*(f . 1),g*>,'&'} is non empty functional V39() V54() set
{<*(f . 1),g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . 1),g*>,'&'},{<*(f . 1),g*>}} is non empty V39() V43() V54() set
[<*g,(n . 1)*>,'&'] is non empty pair set
{<*g,(n . 1)*>,'&'} is non empty functional V39() V54() set
{<*g,(n . 1)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g,(n . 1)*>,'&'},{<*g,(n . 1)*>}} is non empty V39() V43() V54() set
<*[<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((n . 1),(f . 1),g)) +* (1GateCircStr (<*[<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((n . 1),(f . 1),g,'xor')) +* (MajorityStr ((n . 1),(f . 1),g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitAdderWithOverflowStr ((n . 1),(f . 1),g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitAdderWithOverflowCirc ((n . 1),(f . 1),g) is strict non-empty finitely-generated V110( BitAdderWithOverflowStr ((n . 1),(f . 1),g)) gate`2=den Boolean MSAlgebra over BitAdderWithOverflowStr ((n . 1),(f . 1),g)
BitAdderCirc ((n . 1),(f . 1),g) is strict non-empty finitely-generated V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110((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'))
MajorityCirc ((n . 1),(f . 1),g) is strict non-empty finitely-generated V110( MajorityStr ((n . 1),(f . 1),g)) gate`2=den Boolean MSAlgebra over MajorityStr ((n . 1),(f . 1),g)
MajorityICirc ((n . 1),(f . 1),g) is strict non-empty finitely-generated V110( MajorityIStr ((n . 1),(f . 1),g)) gate`2=den Boolean MSAlgebra over MajorityIStr ((n . 1),(f . 1),g)
1GateCircuit ((n . 1),(f . 1),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(n . 1),(f . 1)*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . 1),(f . 1)*>,'&')
1GateCircuit (<*(n . 1),(f . 1)*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(n . 1),(f . 1)*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . 1),(f . 1)*>,'&')
1GateCircuit ((f . 1),g,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . 1),g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . 1),g*>,'&')
1GateCircuit (<*(f . 1),g*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . 1),g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . 1),g*>,'&')
(1GateCircuit ((n . 1),(f . 1),'&')) +* (1GateCircuit ((f . 1),g,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*(n . 1),(f . 1)*>,'&')) +* (1GateCircStr (<*(f . 1),g*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(n . 1),(f . 1)*>,'&')) +* (1GateCircStr (<*(f . 1),g*>,'&'))
1GateCircuit (g,(n . 1),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,(n . 1)*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,(n . 1)*>,'&')
1GateCircuit (<*g,(n . 1)*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,(n . 1)*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,(n . 1)*>,'&')
((1GateCircuit ((n . 1),(f . 1),'&')) +* (1GateCircuit ((f . 1),g,'&'))) +* (1GateCircuit (g,(n . 1),'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*(n . 1),(f . 1)*>,'&')) +* (1GateCircStr (<*(f . 1),g*>,'&'))) +* (1GateCircStr (<*g,(n . 1)*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(n . 1),(f . 1)*>,'&')) +* (1GateCircStr (<*(f . 1),g*>,'&'))) +* (1GateCircStr (<*g,(n . 1)*>,'&'))
1GateCircuit ([<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&']*>,or3)
1GateCircuit (<*[<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&']*>,or3)
(MajorityICirc ((n . 1),(f . 1),g)) +* (1GateCircuit ([<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr ((n . 1),(f . 1),g)) +* (1GateCircStr (<*[<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr ((n . 1),(f . 1),g)) +* (1GateCircStr (<*[<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&']*>,or3))
(BitAdderCirc ((n . 1),(f . 1),g)) +* (MajorityCirc ((n . 1),(f . 1),g)) is strict non-empty finitely-generated V110((2GatesCircStr ((n . 1),(f . 1),g,'xor')) +* (MajorityStr ((n . 1),(f . 1),g))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((n . 1),(f . 1),g,'xor')) +* (MajorityStr ((n . 1),(f . 1),g))
(1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitAdderWithOverflowCirc ((n . 1),(f . 1),g)) is strict non-empty finitely-generated V110((1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitAdderWithOverflowStr ((n . 1),(f . 1),g))) gate`2=den Boolean MSAlgebra over (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitAdderWithOverflowStr ((n . 1),(f . 1),g))
MajorityOutput ((n . 1),(f . 1),g) is Element of InnerVertices (MajorityStr ((n . 1),(f . 1),g))
the carrier of (MajorityStr ((n . 1),(f . 1),g)) is non empty set
InnerVertices (MajorityStr ((n . 1),(f . 1),g)) is non empty Element of K23( the carrier of (MajorityStr ((n . 1),(f . 1),g)))
K23( the carrier of (MajorityStr ((n . 1),(f . 1),g))) is non empty set
the ResultSort of (MajorityStr ((n . 1),(f . 1),g)) is Relation-like the carrier' of (MajorityStr ((n . 1),(f . 1),g)) -defined the carrier of (MajorityStr ((n . 1),(f . 1),g)) -valued Function-like V30( the carrier' of (MajorityStr ((n . 1),(f . 1),g)), the carrier of (MajorityStr ((n . 1),(f . 1),g))) Element of K23(K24( the carrier' of (MajorityStr ((n . 1),(f . 1),g)), the carrier of (MajorityStr ((n . 1),(f . 1),g))))
the carrier' of (MajorityStr ((n . 1),(f . 1),g)) is non empty set
K24( the carrier' of (MajorityStr ((n . 1),(f . 1),g)), the carrier of (MajorityStr ((n . 1),(f . 1),g))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr ((n . 1),(f . 1),g)), the carrier of (MajorityStr ((n . 1),(f . 1),g)))) is non empty set
K497( the carrier of (MajorityStr ((n . 1),(f . 1),g)), the ResultSort of (MajorityStr ((n . 1),(f . 1),g))) is Element of K23( the carrier of (MajorityStr ((n . 1),(f . 1),g)))
[<*[<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&']*>,or3] is non empty pair set
{<*[<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&']*>,or3},{<*[<*(n . 1),(f . 1)*>,'&'],[<*(f . 1),g*>,'&'],[<*g,(n . 1)*>,'&']*>}} is non empty V39() V43() V54() set
S0 is Relation-like NAT -defined Function-like total set
S0 . 1 is set
A0 is Relation-like NAT -defined Function-like total set
A0 . 1 is set
S0 . 0 is set
A0 . 0 is set
N is Relation-like NAT -defined Function-like total set
N . 0 is set
0 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
N . (0 + 1) is set
n is set
<*n*> is non empty V5() Relation-like NAT -defined Function-like constant V39() 1 -element FinSequence-like FinSubsequence-like V54() set
f is set
<*f*> is non empty V5() Relation-like NAT -defined Function-like constant V39() 1 -element FinSequence-like FinSubsequence-like V54() set
(1,<*n*>,<*f*>) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1,<*n*>,<*f*>) is strict non-empty finitely-generated V110((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 K23( the carrier of (1,<*n*>,<*f*>))
K23( the carrier of (1,<*n*>,<*f*>)) is non empty set
the ResultSort of (1,<*n*>,<*f*>) is Relation-like the carrier' of (1,<*n*>,<*f*>) -defined the carrier of (1,<*n*>,<*f*>) -valued Function-like V30( the carrier' of (1,<*n*>,<*f*>), the carrier of (1,<*n*>,<*f*>)) Element of K23(K24( the carrier' of (1,<*n*>,<*f*>), the carrier of (1,<*n*>,<*f*>)))
the carrier' of (1,<*n*>,<*f*>) is non empty set
K24( the carrier' of (1,<*n*>,<*f*>), the carrier of (1,<*n*>,<*f*>)) is non empty Relation-like set
K23(K24( the carrier' of (1,<*n*>,<*f*>), the carrier of (1,<*n*>,<*f*>))) is non empty set
K497( the carrier of (1,<*n*>,<*f*>), the ResultSort of (1,<*n*>,<*f*>)) is Element of K23( the carrier of (1,<*n*>,<*f*>))
<*n*> . 1 is set
<*f*> . 1 is set
g is set
BitAdderWithOverflowStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (n,f,g,'xor') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,f*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*n,f*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*n,f*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*n,f*>,'xor'},{<*n,f*>}} is non empty V39() V43() V54() set
<*[<*n,f*>,'xor'],g*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f,g*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*f,g*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*g,n*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*g,n*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*n,f*>,'&'] is non empty pair set
{<*n,f*>,'&'} is non empty functional V39() V54() set
{{<*n,f*>,'&'},{<*n,f*>}} is non empty V39() V43() V54() set
[<*f,g*>,'&'] is non empty pair set
{<*f,g*>,'&'} is non empty functional V39() V54() set
{<*f,g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*f,g*>,'&'},{<*f,g*>}} is non empty V39() V43() V54() set
[<*g,n*>,'&'] is non empty pair set
{<*g,n*>,'&'} is non empty functional V39() V54() set
{<*g,n*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g,n*>,'&'},{<*g,n*>}} is non empty V39() V43() V54() set
<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitAdderWithOverflowStr (n,f,g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitAdderWithOverflowCirc (n,f,g) is strict non-empty finitely-generated V110( BitAdderWithOverflowStr (n,f,g)) gate`2=den Boolean MSAlgebra over BitAdderWithOverflowStr (n,f,g)
BitAdderCirc (n,f,g) is strict non-empty finitely-generated V110( 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 V110( 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 V110( 1GateCircStr (<*n,f*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'xor')
1GateCircuit (<*n,f*>,'xor') is strict non-empty finitely-generated V110( 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 V110( 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 V110( 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 V110((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'))
MajorityCirc (n,f,g) is strict non-empty finitely-generated V110( MajorityStr (n,f,g)) gate`2=den Boolean MSAlgebra over MajorityStr (n,f,g)
MajorityICirc (n,f,g) is strict non-empty finitely-generated V110( MajorityIStr (n,f,g)) gate`2=den Boolean MSAlgebra over MajorityIStr (n,f,g)
1GateCircuit (n,f,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*n,f*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'&')
1GateCircuit (<*n,f*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*n,f*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'&')
1GateCircuit (f,g,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f,g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,'&')
1GateCircuit (<*f,g*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f,g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,'&')
(1GateCircuit (n,f,'&')) +* (1GateCircuit (f,g,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))
1GateCircuit (g,n,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,n*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,'&')
1GateCircuit (<*g,n*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,n*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,'&')
((1GateCircuit (n,f,'&')) +* (1GateCircuit (f,g,'&'))) +* (1GateCircuit (g,n,'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&'))
1GateCircuit ([<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)
1GateCircuit (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)
(MajorityICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))
(BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g)) is strict non-empty finitely-generated V110((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) gate`2=den Boolean MSAlgebra over (2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))
(1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitAdderWithOverflowCirc (n,f,g)) is strict non-empty finitely-generated V110((1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitAdderWithOverflowStr (n,f,g))) gate`2=den Boolean MSAlgebra over (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitAdderWithOverflowStr (n,f,g))
MajorityOutput (n,f,g) is Element of InnerVertices (MajorityStr (n,f,g))
the carrier of (MajorityStr (n,f,g)) is non empty set
InnerVertices (MajorityStr (n,f,g)) is non empty Element of K23( the carrier of (MajorityStr (n,f,g)))
K23( the carrier of (MajorityStr (n,f,g))) is non empty set
the ResultSort of (MajorityStr (n,f,g)) is Relation-like the carrier' of (MajorityStr (n,f,g)) -defined the carrier of (MajorityStr (n,f,g)) -valued Function-like V30( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) Element of K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))))
the carrier' of (MajorityStr (n,f,g)) is non empty set
K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g)))) is non empty set
K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
[<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3] is non empty pair set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3},{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>}} is non empty V39() V43() V54() set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
g is Relation-like NAT -defined Function-like V39() n -element FinSequence-like FinSubsequence-like V54() set
S0 is Relation-like NAT -defined Function-like V39() n -element FinSequence-like FinSubsequence-like V54() set
A0 is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
g ^ A0 is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
h is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
S0 ^ h is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
(n,(g ^ A0),(S0 ^ h)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
N is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
g ^ N is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
Sn is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
S0 ^ Sn is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
(n,(g ^ N),(S0 ^ Sn)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,(g ^ A0),(S0 ^ h)) is strict non-empty finitely-generated V110((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 V110((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 K23( the carrier of (n,(g ^ A0),(S0 ^ h)))
K23( the carrier of (n,(g ^ A0),(S0 ^ h))) is non empty set
the ResultSort of (n,(g ^ A0),(S0 ^ h)) is Relation-like the carrier' of (n,(g ^ A0),(S0 ^ h)) -defined the carrier of (n,(g ^ A0),(S0 ^ h)) -valued Function-like V30( the carrier' of (n,(g ^ A0),(S0 ^ h)), the carrier of (n,(g ^ A0),(S0 ^ h))) Element of K23(K24( 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
K24( the carrier' of (n,(g ^ A0),(S0 ^ h)), the carrier of (n,(g ^ A0),(S0 ^ h))) is non empty Relation-like set
K23(K24( the carrier' of (n,(g ^ A0),(S0 ^ h)), the carrier of (n,(g ^ A0),(S0 ^ h)))) is non empty set
K497( the carrier of (n,(g ^ A0),(S0 ^ h)), the ResultSort of (n,(g ^ A0),(S0 ^ h))) is Element of K23( 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 K23( the carrier of (n,(g ^ N),(S0 ^ Sn)))
K23( the carrier of (n,(g ^ N),(S0 ^ Sn))) is non empty set
the ResultSort of (n,(g ^ N),(S0 ^ Sn)) is Relation-like the carrier' of (n,(g ^ N),(S0 ^ Sn)) -defined the carrier of (n,(g ^ N),(S0 ^ Sn)) -valued Function-like V30( the carrier' of (n,(g ^ N),(S0 ^ Sn)), the carrier of (n,(g ^ N),(S0 ^ Sn))) Element of K23(K24( 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
K24( the carrier' of (n,(g ^ N),(S0 ^ Sn)), the carrier of (n,(g ^ N),(S0 ^ Sn))) is non empty Relation-like set
K23(K24( the carrier' of (n,(g ^ N),(S0 ^ Sn)), the carrier of (n,(g ^ N),(S0 ^ Sn)))) is non empty set
K497( the carrier of (n,(g ^ N),(S0 ^ Sn)), the ResultSort of (n,(g ^ N),(S0 ^ Sn))) is Element of K23( the carrier of (n,(g ^ N),(S0 ^ Sn)))
An is Relation-like NAT -defined Function-like total set
An . n is set
o0 is Relation-like NAT -defined Function-like total set
o0 . n is set
An . 0 is set
o0 . 0 is set
f1 is Relation-like NAT -defined Function-like total set
f1 . 0 is set
g1 is Relation-like NAT -defined Function-like total set
g1 . n is set
h1 is Relation-like NAT -defined Function-like total set
h1 . n is set
g1 . 0 is set
h1 . 0 is set
n is Relation-like NAT -defined Function-like total set
n . 0 is set
x is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() 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 ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() 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 ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
len S0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
dom g is V39() n -element V54() Element of K23(NAT)
Seg n is V39() n -element V54() Element of K23(NAT)
dom S0 is V39() n -element V54() Element of K23(NAT)
0 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() 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 V74() ManySortedSign
xx is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
An . xx is set
c₁₈ is non-empty MSAlgebra over xy
o0 . xx is set
c₁₉ is set
f1 . xx is set
xx is non empty V74() ManySortedSign
c₁₉ is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
c₁₉ + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
(g ^ A0) . (c₁₉ + 1) is set
(S0 ^ h) . (c₁₉ + 1) is set
c₁₈ is set
BitAdderWithOverflowStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈) is non empty non void V74() 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') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor') is non empty non void V74() 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))*>,'xor'] is non empty pair set
{<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'xor'} is non empty functional V39() V54() set
{<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'xor'},{<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>}} is non empty V39() V43() V54() set
<*[<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'xor'],c<sub>18</sub>*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor')) +* (1GateCircStr (<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor'],c₁₈*>,'xor')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈) is non empty non void V74() 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))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,'&') is non empty non void V74() 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))*>,'&')) +* (1GateCircStr (<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*c₁₈,((g ^ A0) . (c₁₉ + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*c₁₈,((g ^ A0) . (c₁₉ + 1))*>,'&') is non empty non void V74() 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))*>,'&')) +* (1GateCircStr (<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,'&'))) +* (1GateCircStr (<*c<sub>18</sub>,((g ^ A0) . (c<sub>19</sub> + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'&'] is non empty pair set
{<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'&'} is non empty functional V39() V54() set
{{<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'&'},{<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>}} is non empty V39() V43() V54() set
[<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,'&'] is non empty pair set
{<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,'&'} is non empty functional V39() V54() set
{<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,'&'},{<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>}} is non empty V39() V43() V54() set
[<*c₁₈,((g ^ A0) . (c₁₉ + 1))*>,'&'] is non empty pair set
{<*c₁₈,((g ^ A0) . (c₁₉ + 1))*>,'&'} is non empty functional V39() V54() set
{<*c₁₈,((g ^ A0) . (c₁₉ + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*c₁₈,((g ^ A0) . (c₁₉ + 1))*>,'&'},{<*c₁₈,((g ^ A0) . (c₁₉ + 1))*>}} is non empty V39() V43() V54() set
<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'&'],[<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,'&'],[<*c₁₈,((g ^ A0) . (c₁₉ + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'&'],[<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,'&'],[<*c₁₈,((g ^ A0) . (c₁₉ + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr (((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))*>,'&'],[<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,'&'],[<*c<sub>18</sub>,((g ^ A0) . (c<sub>19</sub> + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈,'xor')) +* (MajorityStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
xy is non-empty MSAlgebra over xx
BitAdderWithOverflowCirc (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>) is strict non-empty finitely-generated V110( BitAdderWithOverflowStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>)) gate`2=den Boolean MSAlgebra over BitAdderWithOverflowStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈)
BitAdderCirc (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈) is strict non-empty finitely-generated V110( 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')
2GatesCircuit (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>,'xor') is strict non-empty finitely-generated V110( 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')
1GateCircuit (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),'xor') is strict non-empty finitely-generated V110( 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') is strict non-empty finitely-generated V110( 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'],c₁₈,'xor') is strict non-empty finitely-generated V110( 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'],c<sub>18</sub>*>,'xor') is strict non-empty finitely-generated V110( 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')) +* (1GateCircuit ([<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor'],c₁₈,'xor')) is strict non-empty finitely-generated V110((1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'xor')) +* (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')) +* (1GateCircStr (<*[<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'xor'],c<sub>18</sub>*>,'xor'))
MajorityCirc (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>) is strict non-empty finitely-generated V110( MajorityStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>)) gate`2=den Boolean MSAlgebra over MajorityStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈)
MajorityICirc (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈) is strict non-empty finitely-generated V110( MajorityIStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈)) gate`2=den Boolean MSAlgebra over MajorityIStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>)
1GateCircuit (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'&')
1GateCircuit (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'&')
1GateCircuit (((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,'&')
1GateCircuit (<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,'&')
(1GateCircuit (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),'&')) +* (1GateCircuit (((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'&')) +* (1GateCircStr (<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'&')) +* (1GateCircStr (<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,'&'))
1GateCircuit (c₁₈,((g ^ A0) . (c₁₉ + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*c₁₈,((g ^ A0) . (c₁₉ + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*c<sub>18</sub>,((g ^ A0) . (c<sub>19</sub> + 1))*>,'&')
1GateCircuit (<*c<sub>18</sub>,((g ^ A0) . (c<sub>19</sub> + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*c<sub>18</sub>,((g ^ A0) . (c<sub>19</sub> + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*c₁₈,((g ^ A0) . (c₁₉ + 1))*>,'&')
((1GateCircuit (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),'&')) +* (1GateCircuit (((S0 ^ h) . (c₁₉ + 1)),c₁₈,'&'))) +* (1GateCircuit (c₁₈,((g ^ A0) . (c₁₉ + 1)),'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'&')) +* (1GateCircStr (<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,'&'))) +* (1GateCircStr (<*c₁₈,((g ^ A0) . (c₁₉ + 1))*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'&')) +* (1GateCircStr (<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,'&'))) +* (1GateCircStr (<*c<sub>18</sub>,((g ^ A0) . (c<sub>19</sub> + 1))*>,'&'))
1GateCircuit ([<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'&'],[<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,'&'],[<*c<sub>18</sub>,((g ^ A0) . (c<sub>19</sub> + 1))*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'&'],[<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,'&'],[<*c<sub>18</sub>,((g ^ A0) . (c<sub>19</sub> + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'&'],[<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,'&'],[<*c₁₈,((g ^ A0) . (c₁₉ + 1))*>,'&']*>,or3)
1GateCircuit (<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'&'],[<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,'&'],[<*c₁₈,((g ^ A0) . (c₁₉ + 1))*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'&'],[<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,'&'],[<*c₁₈,((g ^ A0) . (c₁₉ + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'&'],[<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,'&'],[<*c<sub>18</sub>,((g ^ A0) . (c<sub>19</sub> + 1))*>,'&']*>,or3)
(MajorityICirc (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>)) +* (1GateCircuit ([<*((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1))*>,'&'],[<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,'&'],[<*c<sub>18</sub>,((g ^ A0) . (c<sub>19</sub> + 1))*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr (((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))*>,'&'],[<*((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>*>,'&'],[<*c<sub>18</sub>,((g ^ A0) . (c<sub>19</sub> + 1))*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈)) +* (1GateCircStr (<*[<*((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1))*>,'&'],[<*((S0 ^ h) . (c₁₉ + 1)),c₁₈*>,'&'],[<*c₁₈,((g ^ A0) . (c₁₉ + 1))*>,'&']*>,or3))
(BitAdderCirc (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈)) +* (MajorityCirc (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈)) is strict non-empty finitely-generated V110((2GatesCircStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈,'xor')) +* (MajorityStr (((g ^ A0) . (c₁₉ + 1)),((S0 ^ h) . (c₁₉ + 1)),c₁₈))) 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')) +* (MajorityStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>))
xy +* (BitAdderWithOverflowCirc (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>)) is strict non-empty MSAlgebra over xx +* (BitAdderWithOverflowStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>))
xx +* (BitAdderWithOverflowStr (((g ^ A0) . (c<sub>19</sub> + 1)),((S0 ^ h) . (c<sub>19</sub> + 1)),c<sub>18</sub>)) is non empty non void V74() strict ManySortedSign
xx is non empty V74() ManySortedSign
xy is non-empty MSAlgebra over xx
MajorityOutput (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is Element of InnerVertices (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))
MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&')) +* (1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n . x),((g ^ N) . (x + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(n . x),((g ^ N) . (x + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&')) +* (1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'))) +* (1GateCircStr (<*(n . x),((g ^ N) . (x + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'] is non empty pair set
{<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'} is non empty functional V39() V54() set
{<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'},{<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>}} is non empty V39() V43() V54() set
[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'] is non empty pair set
{<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'} is non empty functional V39() V54() set
{<*((S0 ^ Sn) . (x + 1)),(n . x)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'},{<*((S0 ^ Sn) . (x + 1)),(n . x)*>}} is non empty V39() V43() V54() set
[<*(n . x),((g ^ N) . (x + 1))*>,'&'] is non empty pair set
{<*(n . x),((g ^ N) . (x + 1))*>,'&'} is non empty functional V39() V54() set
{<*(n . x),((g ^ N) . (x + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(n . x),((g ^ N) . (x + 1))*>,'&'},{<*(n . x),((g ^ N) . (x + 1))*>}} is non empty V39() V43() V54() set
<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) +* (1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is non empty set
InnerVertices (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is non empty Element of K23( the carrier of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))))
K23( the carrier of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))) is non empty set
the ResultSort of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is Relation-like the carrier' of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) -defined the carrier of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) -valued Function-like V30( the carrier' of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))), the carrier of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))) Element of K23(K24( the carrier' of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))), the carrier of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))))
the carrier' of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is non empty set
K24( the carrier' of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))), the carrier of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))), the carrier of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))))) is non empty set
K497( the carrier of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))), the ResultSort of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))) is Element of K23( the carrier of (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))))
[<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&']*>,or3] is non empty pair set
{<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&']*>,or3},{<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&']*>}} is non empty V39() V43() V54() set
BitAdderWithOverflowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is non empty non void V74() 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 V74() 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 V74() 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 V39() V54() set
{{<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'},{<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>}} is non empty V39() V43() V54() set
<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'],(n . x)*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'xor'],(n . x)*>,'xor') is non empty non void V74() 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 V74() 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')) +* (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
xx +* (BitAdderWithOverflowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is non empty non void V74() strict ManySortedSign
BitAdderWithOverflowCirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is strict non-empty finitely-generated V110( BitAdderWithOverflowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) gate`2=den Boolean MSAlgebra over BitAdderWithOverflowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))
BitAdderCirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is strict non-empty finitely-generated V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110((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'))
MajorityCirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is strict non-empty finitely-generated V110( MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) gate`2=den Boolean MSAlgebra over MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))
MajorityICirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)) is strict non-empty finitely-generated V110( MajorityIStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) gate`2=den Boolean MSAlgebra over MajorityIStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))
1GateCircuit (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&')
1GateCircuit (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&')
1GateCircuit (((S0 ^ Sn) . (x + 1)),(n . x),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&')
1GateCircuit (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&')
(1GateCircuit (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),'&')) +* (1GateCircuit (((S0 ^ Sn) . (x + 1)),(n . x),'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&')) +* (1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&')) +* (1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'))
1GateCircuit ((n . x),((g ^ N) . (x + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(n . x),((g ^ N) . (x + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . x),((g ^ N) . (x + 1))*>,'&')
1GateCircuit (<*(n . x),((g ^ N) . (x + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(n . x),((g ^ N) . (x + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n . x),((g ^ N) . (x + 1))*>,'&')
((1GateCircuit (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),'&')) +* (1GateCircuit (((S0 ^ Sn) . (x + 1)),(n . x),'&'))) +* (1GateCircuit ((n . x),((g ^ N) . (x + 1)),'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&')) +* (1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'))) +* (1GateCircStr (<*(n . x),((g ^ N) . (x + 1))*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&')) +* (1GateCircStr (<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'))) +* (1GateCircStr (<*(n . x),((g ^ N) . (x + 1))*>,'&'))
1GateCircuit ([<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&']*>,or3)
1GateCircuit (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&']*>,or3)
(MajorityICirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) +* (1GateCircuit ([<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) +* (1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) +* (1GateCircStr (<*[<*((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1))*>,'&'],[<*((S0 ^ Sn) . (x + 1)),(n . x)*>,'&'],[<*(n . x),((g ^ N) . (x + 1))*>,'&']*>,or3))
(BitAdderCirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) +* (MajorityCirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is strict non-empty finitely-generated V110((2GatesCircStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x),'xor')) +* (MajorityStr (((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')) +* (MajorityStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))
xy +* (BitAdderWithOverflowCirc (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x))) is strict non-empty MSAlgebra over xx +* (BitAdderWithOverflowStr (((g ^ N) . (x + 1)),((S0 ^ Sn) . (x + 1)),(n . x)))
f1 . n is set
n . n is set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
g is Relation-like NAT -defined Function-like V39() n -element FinSequence-like FinSubsequence-like V54() set
S0 is Relation-like NAT -defined Function-like V39() n -element FinSequence-like FinSubsequence-like V54() set
(n,g,S0) is non empty non void V74() 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 K23( the carrier of (n,g,S0))
K23( the carrier of (n,g,S0)) is non empty set
the ResultSort of (n,g,S0) is Relation-like the carrier' of (n,g,S0) -defined the carrier of (n,g,S0) -valued Function-like V30( the carrier' of (n,g,S0), the carrier of (n,g,S0)) Element of K23(K24( the carrier' of (n,g,S0), the carrier of (n,g,S0)))
the carrier' of (n,g,S0) is non empty set
K24( the carrier' of (n,g,S0), the carrier of (n,g,S0)) is non empty Relation-like set
K23(K24( the carrier' of (n,g,S0), the carrier of (n,g,S0))) is non empty set
K497( the carrier of (n,g,S0), the ResultSort of (n,g,S0)) is Element of K23( the carrier of (n,g,S0))
(n,g,S0) is strict non-empty finitely-generated V110((n,g,S0)) gate`2=den Boolean MSAlgebra over (n,g,S0)
A0 is set
<*A0*> is non empty V5() Relation-like NAT -defined Function-like constant V39() 1 -element FinSequence-like FinSubsequence-like V54() set
g ^ <*A0*> is non empty Relation-like NAT -defined Function-like V39() n + 1 -element FinSequence-like FinSubsequence-like V54() set
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
N is set
<*N*> is non empty V5() Relation-like NAT -defined Function-like constant V39() 1 -element FinSequence-like FinSubsequence-like V54() set
S0 ^ <*N*> is non empty Relation-like NAT -defined Function-like V39() n + 1 -element FinSequence-like FinSubsequence-like V54() set
((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitAdderWithOverflowStr (A0,N,(n,g,S0)) is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*A0,N*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*A0,N*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*A0,N*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*A0,N*>,'xor'},{<*A0,N*>}} is non empty V39() V43() V54() set
<*[<*A0,N*>,'xor'],(n,g,S0)*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*A0,N*>,'xor'],(n,g,S0)*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr (A0,N,(n,g,S0)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr (A0,N,(n,g,S0)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*A0,N*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*N,(n,g,S0)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*A0,N*>,'&')) +* (1GateCircStr (<*N,(n,g,S0)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n,g,S0),A0*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(n,g,S0),A0*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*A0,N*>,'&')) +* (1GateCircStr (<*N,(n,g,S0)*>,'&'))) +* (1GateCircStr (<*(n,g,S0),A0*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*A0,N*>,'&'] is non empty pair set
{<*A0,N*>,'&'} is non empty functional V39() V54() set
{{<*A0,N*>,'&'},{<*A0,N*>}} is non empty V39() V43() V54() set
[<*N,(n,g,S0)*>,'&'] is non empty pair set
{<*N,(n,g,S0)*>,'&'} is non empty functional V39() V54() set
{<*N,(n,g,S0)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*N,(n,g,S0)*>,'&'},{<*N,(n,g,S0)*>}} is non empty V39() V43() V54() set
[<*(n,g,S0),A0*>,'&'] is non empty pair set
{<*(n,g,S0),A0*>,'&'} is non empty functional V39() V54() set
{<*(n,g,S0),A0*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(n,g,S0),A0*>,'&'},{<*(n,g,S0),A0*>}} is non empty V39() V43() V54() set
<*[<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr (A0,N,(n,g,S0))) +* (1GateCircStr (<*[<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (A0,N,(n,g,S0),'xor')) +* (MajorityStr (A0,N,(n,g,S0))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,g,S0) +* (BitAdderWithOverflowStr (A0,N,(n,g,S0))) is non empty non void V74() 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 V110(((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>))) gate`2=den Boolean MSAlgebra over ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>))
BitAdderWithOverflowCirc (A0,N,(n,g,S0)) is strict non-empty finitely-generated V110( BitAdderWithOverflowStr (A0,N,(n,g,S0))) gate`2=den Boolean MSAlgebra over BitAdderWithOverflowStr (A0,N,(n,g,S0))
BitAdderCirc (A0,N,(n,g,S0)) is strict non-empty finitely-generated V110( 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 V110( 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 V110( 1GateCircStr (<*A0,N*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*A0,N*>,'xor')
1GateCircuit (<*A0,N*>,'xor') is strict non-empty finitely-generated V110( 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 V110( 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 V110( 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 V110((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'))
MajorityCirc (A0,N,(n,g,S0)) is strict non-empty finitely-generated V110( MajorityStr (A0,N,(n,g,S0))) gate`2=den Boolean MSAlgebra over MajorityStr (A0,N,(n,g,S0))
MajorityICirc (A0,N,(n,g,S0)) is strict non-empty finitely-generated V110( MajorityIStr (A0,N,(n,g,S0))) gate`2=den Boolean MSAlgebra over MajorityIStr (A0,N,(n,g,S0))
1GateCircuit (A0,N,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*A0,N*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*A0,N*>,'&')
1GateCircuit (<*A0,N*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*A0,N*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*A0,N*>,'&')
1GateCircuit (N,(n,g,S0),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*N,(n,g,S0)*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*N,(n,g,S0)*>,'&')
1GateCircuit (<*N,(n,g,S0)*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*N,(n,g,S0)*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*N,(n,g,S0)*>,'&')
(1GateCircuit (A0,N,'&')) +* (1GateCircuit (N,(n,g,S0),'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*A0,N*>,'&')) +* (1GateCircStr (<*N,(n,g,S0)*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*A0,N*>,'&')) +* (1GateCircStr (<*N,(n,g,S0)*>,'&'))
1GateCircuit ((n,g,S0),A0,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(n,g,S0),A0*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n,g,S0),A0*>,'&')
1GateCircuit (<*(n,g,S0),A0*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(n,g,S0),A0*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n,g,S0),A0*>,'&')
((1GateCircuit (A0,N,'&')) +* (1GateCircuit (N,(n,g,S0),'&'))) +* (1GateCircuit ((n,g,S0),A0,'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*A0,N*>,'&')) +* (1GateCircStr (<*N,(n,g,S0)*>,'&'))) +* (1GateCircStr (<*(n,g,S0),A0*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*A0,N*>,'&')) +* (1GateCircStr (<*N,(n,g,S0)*>,'&'))) +* (1GateCircStr (<*(n,g,S0),A0*>,'&'))
1GateCircuit ([<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&']*>,or3)
1GateCircuit (<*[<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&']*>,or3)
(MajorityICirc (A0,N,(n,g,S0))) +* (1GateCircuit ([<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr (A0,N,(n,g,S0))) +* (1GateCircStr (<*[<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr (A0,N,(n,g,S0))) +* (1GateCircStr (<*[<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&']*>,or3))
(BitAdderCirc (A0,N,(n,g,S0))) +* (MajorityCirc (A0,N,(n,g,S0))) is strict non-empty finitely-generated V110((2GatesCircStr (A0,N,(n,g,S0),'xor')) +* (MajorityStr (A0,N,(n,g,S0)))) gate`2=den Boolean MSAlgebra over (2GatesCircStr (A0,N,(n,g,S0),'xor')) +* (MajorityStr (A0,N,(n,g,S0)))
(n,g,S0) +* (BitAdderWithOverflowCirc (A0,N,(n,g,S0))) is strict non-empty finitely-generated V110((n,g,S0) +* (BitAdderWithOverflowStr (A0,N,(n,g,S0)))) gate`2=den Boolean MSAlgebra over (n,g,S0) +* (BitAdderWithOverflowStr (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 K23( the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)))
K23( the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>))) is non empty set
the ResultSort of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)) is Relation-like the carrier' of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)) -defined the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)) -valued Function-like V30( the carrier' of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)), the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>))) Element of K23(K24( 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
K24( the carrier' of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)), the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>))) is non empty Relation-like set
K23(K24( the carrier' of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)), the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)))) is non empty set
K497( the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)), the ResultSort of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>))) is Element of K23( the carrier of ((n + 1),(g ^ <*A0*>),(S0 ^ <*N*>)))
MajorityOutput (A0,N,(n,g,S0)) is Element of InnerVertices (MajorityStr (A0,N,(n,g,S0)))
the carrier of (MajorityStr (A0,N,(n,g,S0))) is non empty set
InnerVertices (MajorityStr (A0,N,(n,g,S0))) is non empty Element of K23( the carrier of (MajorityStr (A0,N,(n,g,S0))))
K23( the carrier of (MajorityStr (A0,N,(n,g,S0)))) is non empty set
the ResultSort of (MajorityStr (A0,N,(n,g,S0))) is Relation-like the carrier' of (MajorityStr (A0,N,(n,g,S0))) -defined the carrier of (MajorityStr (A0,N,(n,g,S0))) -valued Function-like V30( the carrier' of (MajorityStr (A0,N,(n,g,S0))), the carrier of (MajorityStr (A0,N,(n,g,S0)))) Element of K23(K24( the carrier' of (MajorityStr (A0,N,(n,g,S0))), the carrier of (MajorityStr (A0,N,(n,g,S0)))))
the carrier' of (MajorityStr (A0,N,(n,g,S0))) is non empty set
K24( the carrier' of (MajorityStr (A0,N,(n,g,S0))), the carrier of (MajorityStr (A0,N,(n,g,S0)))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr (A0,N,(n,g,S0))), the carrier of (MajorityStr (A0,N,(n,g,S0))))) is non empty set
K497( the carrier of (MajorityStr (A0,N,(n,g,S0))), the ResultSort of (MajorityStr (A0,N,(n,g,S0)))) is Element of K23( the carrier of (MajorityStr (A0,N,(n,g,S0))))
[<*[<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&']*>,or3] is non empty pair set
{<*[<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&']*>,or3},{<*[<*A0,N*>,'&'],[<*N,(n,g,S0)*>,'&'],[<*(n,g,S0),A0*>,'&']*>}} is non empty V39() V43() V54() set
(n,(g ^ <*A0*>),(S0 ^ <*N*>)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,(g ^ <*A0*>),(S0 ^ <*N*>)) is strict non-empty finitely-generated V110((n,(g ^ <*A0*>),(S0 ^ <*N*>))) gate`2=den Boolean MSAlgebra over (n,(g ^ <*A0*>),(S0 ^ <*N*>))
An is Relation-like NAT -defined Function-like total set
An . n is set
o0 is Relation-like NAT -defined Function-like total set
o0 . n is set
An . 0 is set
o0 . 0 is set
f1 is Relation-like NAT -defined Function-like total 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 K23( the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>)))
K23( the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>))) is non empty set
the ResultSort of (n,(g ^ <*A0*>),(S0 ^ <*N*>)) is Relation-like the carrier' of (n,(g ^ <*A0*>),(S0 ^ <*N*>)) -defined the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>)) -valued Function-like V30( the carrier' of (n,(g ^ <*A0*>),(S0 ^ <*N*>)), the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>))) Element of K23(K24( 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
K24( the carrier' of (n,(g ^ <*A0*>),(S0 ^ <*N*>)), the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>))) is non empty Relation-like set
K23(K24( the carrier' of (n,(g ^ <*A0*>),(S0 ^ <*N*>)), the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>)))) is non empty set
K497( the carrier of (n,(g ^ <*A0*>),(S0 ^ <*N*>)), the ResultSort of (n,(g ^ <*A0*>),(S0 ^ <*N*>))) is Element of K23( 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 ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
len S0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
(g ^ <*A0*>) . (n + 1) is set
(S0 ^ <*N*>) . (n + 1) is set
g ^ {} is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
S0 ^ {} is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
g is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
((n + 1),f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,f,g) is non empty non void V74() 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 K23( the carrier of (n,f,g))
K23( the carrier of (n,f,g)) is non empty set
the ResultSort of (n,f,g) is Relation-like the carrier' of (n,f,g) -defined the carrier of (n,f,g) -valued Function-like V30( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K24( the carrier' of (n,f,g), the carrier of (n,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g))) is non empty set
K497( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K23( the carrier of (n,f,g))
BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(f . (n + 1)),(g . (n + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'xor'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n,f,g),(f . (n + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(n,f,g),(f . (n + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,'&'))) +* (1GateCircStr (<*(n,f,g),(f . (n + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,'&'] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'&'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (n + 1)),(n,f,g)*>,'&'] is non empty pair set
{<*(g . (n + 1)),(n,f,g)*>,'&'} is non empty functional V39() V54() set
{<*(g . (n + 1)),(n,f,g)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (n + 1)),(n,f,g)*>,'&'},{<*(g . (n + 1)),(n,f,g)*>}} is non empty V39() V43() V54() set
[<*(n,f,g),(f . (n + 1))*>,'&'] is non empty pair set
{<*(n,f,g),(f . (n + 1))*>,'&'} is non empty functional V39() V54() set
{<*(n,f,g),(f . (n + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(n,f,g),(f . (n + 1))*>,'&'},{<*(n,f,g),(f . (n + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (n + 1)),(g . (n + 1)),(n,f,g),'xor')) +* (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(n,f,g) +* (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((n + 1),f,g) is strict non-empty finitely-generated V110(((n + 1),f,g)) gate`2=den Boolean MSAlgebra over ((n + 1),f,g)
(n,f,g) is strict non-empty finitely-generated V110((n,f,g)) gate`2=den Boolean MSAlgebra over (n,f,g)
BitAdderWithOverflowCirc ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is strict non-empty finitely-generated V110( BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) gate`2=den Boolean MSAlgebra over BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))
BitAdderCirc ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is strict non-empty finitely-generated V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110((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'))
MajorityCirc ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is strict non-empty finitely-generated V110( MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) gate`2=den Boolean MSAlgebra over MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))
MajorityICirc ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is strict non-empty finitely-generated V110( MajorityIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) gate`2=den Boolean MSAlgebra over MajorityIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))
1GateCircuit ((f . (n + 1)),(g . (n + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')
1GateCircuit (<*(f . (n + 1)),(g . (n + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')
1GateCircuit ((g . (n + 1)),(n,f,g),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,'&')
1GateCircuit (<*(g . (n + 1)),(n,f,g)*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,'&')
(1GateCircuit ((f . (n + 1)),(g . (n + 1)),'&')) +* (1GateCircuit ((g . (n + 1)),(n,f,g),'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,'&'))
1GateCircuit ((n,f,g),(f . (n + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(n,f,g),(f . (n + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n,f,g),(f . (n + 1))*>,'&')
1GateCircuit (<*(n,f,g),(f . (n + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(n,f,g),(f . (n + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(n,f,g),(f . (n + 1))*>,'&')
((1GateCircuit ((f . (n + 1)),(g . (n + 1)),'&')) +* (1GateCircuit ((g . (n + 1)),(n,f,g),'&'))) +* (1GateCircuit ((n,f,g),(f . (n + 1)),'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,'&'))) +* (1GateCircStr (<*(n,f,g),(f . (n + 1))*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,'&'))) +* (1GateCircStr (<*(n,f,g),(f . (n + 1))*>,'&'))
1GateCircuit ([<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>,or3)
1GateCircuit (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>,or3)
(MajorityICirc ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (1GateCircuit ([<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>,or3))
(BitAdderCirc ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (MajorityCirc ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is strict non-empty finitely-generated V110((2GatesCircStr ((f . (n + 1)),(g . (n + 1)),(n,f,g),'xor')) +* (MajorityStr ((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')) +* (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))
(n,f,g) +* (BitAdderWithOverflowCirc ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is strict non-empty finitely-generated V110((n,f,g) +* (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) gate`2=den Boolean MSAlgebra over (n,f,g) +* (BitAdderWithOverflowStr ((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 K23( the carrier of ((n + 1),f,g))
K23( the carrier of ((n + 1),f,g)) is non empty set
the ResultSort of ((n + 1),f,g) is Relation-like the carrier' of ((n + 1),f,g) -defined the carrier of ((n + 1),f,g) -valued Function-like V30( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) Element of K23(K24( 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
K24( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) is non empty Relation-like set
K23(K24( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g))) is non empty set
K497( the carrier of ((n + 1),f,g), the ResultSort of ((n + 1),f,g)) is Element of K23( the carrier of ((n + 1),f,g))
MajorityOutput ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is Element of InnerVertices (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))
the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty set
InnerVertices (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty Element of K23( the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))
K23( the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is non empty set
the ResultSort of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is Relation-like the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) -defined the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) -valued Function-like V30( the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) Element of K23(K24( the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))))
the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty set
K24( the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))) is non empty set
K497( the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the ResultSort of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is Element of K23( the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))
[<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>,or3] is non empty pair set
{<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>,or3},{<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>}} is non empty V39() V43() V54() set
A0 is Relation-like NAT -defined Function-like total set
A0 . n is set
N is Relation-like NAT -defined Function-like total set
N . n is set
A0 . 0 is set
N . 0 is set
h is Relation-like NAT -defined Function-like total 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 ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
g is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
S0 is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
(n,g,S0) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (n,g,S0) is non empty Element of K23( the carrier of (n,g,S0))
the carrier of (n,g,S0) is non empty set
K23( the carrier of (n,g,S0)) is non empty set
the ResultSort of (n,g,S0) is Relation-like the carrier' of (n,g,S0) -defined the carrier of (n,g,S0) -valued Function-like V30( the carrier' of (n,g,S0), the carrier of (n,g,S0)) Element of K23(K24( the carrier' of (n,g,S0), the carrier of (n,g,S0)))
the carrier' of (n,g,S0) is non empty set
K24( the carrier' of (n,g,S0), the carrier of (n,g,S0)) is non empty Relation-like set
K23(K24( the carrier' of (n,g,S0), the carrier of (n,g,S0))) is non empty set
K497( the carrier of (n,g,S0), the ResultSort of (n,g,S0)) is Element of K23( the carrier of (n,g,S0))
(f,g,S0) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (f,g,S0) is non empty Element of K23( the carrier of (f,g,S0))
the carrier of (f,g,S0) is non empty set
K23( the carrier of (f,g,S0)) is non empty set
the ResultSort of (f,g,S0) is Relation-like the carrier' of (f,g,S0) -defined the carrier of (f,g,S0) -valued Function-like V30( the carrier' of (f,g,S0), the carrier of (f,g,S0)) Element of K23(K24( the carrier' of (f,g,S0), the carrier of (f,g,S0)))
the carrier' of (f,g,S0) is non empty set
K24( the carrier' of (f,g,S0), the carrier of (f,g,S0)) is non empty Relation-like set
K23(K24( the carrier' of (f,g,S0), the carrier of (f,g,S0))) is non empty set
K497( the carrier of (f,g,S0), the ResultSort of (f,g,S0)) is Element of K23( the carrier of (f,g,S0))
A0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
n + A0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
N is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n + N is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n + 0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
((n + 0),g,S0) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + 0),g,S0) is non empty Element of K23( the carrier of ((n + 0),g,S0))
the carrier of ((n + 0),g,S0) is non empty set
K23( the carrier of ((n + 0),g,S0)) is non empty set
the ResultSort of ((n + 0),g,S0) is Relation-like the carrier' of ((n + 0),g,S0) -defined the carrier of ((n + 0),g,S0) -valued Function-like V30( the carrier' of ((n + 0),g,S0), the carrier of ((n + 0),g,S0)) Element of K23(K24( 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
K24( the carrier' of ((n + 0),g,S0), the carrier of ((n + 0),g,S0)) is non empty Relation-like set
K23(K24( the carrier' of ((n + 0),g,S0), the carrier of ((n + 0),g,S0))) is non empty set
K497( the carrier of ((n + 0),g,S0), the ResultSort of ((n + 0),g,S0)) is Element of K23( the carrier of ((n + 0),g,S0))
h is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n + h is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
((n + h),g,S0) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + h),g,S0) is non empty Element of K23( the carrier of ((n + h),g,S0))
the carrier of ((n + h),g,S0) is non empty set
K23( the carrier of ((n + h),g,S0)) is non empty set
the ResultSort of ((n + h),g,S0) is Relation-like the carrier' of ((n + h),g,S0) -defined the carrier of ((n + h),g,S0) -valued Function-like V30( the carrier' of ((n + h),g,S0), the carrier of ((n + h),g,S0)) Element of K23(K24( 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
K24( the carrier' of ((n + h),g,S0), the carrier of ((n + h),g,S0)) is non empty Relation-like set
K23(K24( the carrier' of ((n + h),g,S0), the carrier of ((n + h),g,S0))) is non empty set
K497( the carrier of ((n + h),g,S0), the ResultSort of ((n + h),g,S0)) is Element of K23( the carrier of ((n + h),g,S0))
h + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n + (h + 1) is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
((n + (h + 1)),g,S0) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + (h + 1)),g,S0) is non empty Element of K23( the carrier of ((n + (h + 1)),g,S0))
the carrier of ((n + (h + 1)),g,S0) is non empty set
K23( the carrier of ((n + (h + 1)),g,S0)) is non empty set
the ResultSort of ((n + (h + 1)),g,S0) is Relation-like the carrier' of ((n + (h + 1)),g,S0) -defined the carrier of ((n + (h + 1)),g,S0) -valued Function-like V30( the carrier' of ((n + (h + 1)),g,S0), the carrier of ((n + (h + 1)),g,S0)) Element of K23(K24( 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
K24( the carrier' of ((n + (h + 1)),g,S0), the carrier of ((n + (h + 1)),g,S0)) is non empty Relation-like set
K23(K24( the carrier' of ((n + (h + 1)),g,S0), the carrier of ((n + (h + 1)),g,S0))) is non empty set
K497( the carrier of ((n + (h + 1)),g,S0), the ResultSort of ((n + (h + 1)),g,S0)) is Element of K23( the carrier of ((n + (h + 1)),g,S0))
(n + h) + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
(((n + h) + 1),g,S0) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
g . ((n + h) + 1) is set
S0 . ((n + h) + 1) is set
((n + h),g,S0) is Element of InnerVertices ((n + h),g,S0)
BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'xor'},{<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>}} is non empty V39() V43() V54() set
<*[<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'xor'],((n + h),g,S0)*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'xor'],((n + h),g,S0)*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'&')) +* (1GateCircStr (<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*((n + h),g,S0),(g . ((n + h) + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*((n + h),g,S0),(g . ((n + h) + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'&')) +* (1GateCircStr (<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,'&'))) +* (1GateCircStr (<*((n + h),g,S0),(g . ((n + h) + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'&'] is non empty pair set
{<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'&'},{<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>}} is non empty V39() V43() V54() set
[<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,'&'] is non empty pair set
{<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,'&'} is non empty functional V39() V54() set
{<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,'&'},{<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>}} is non empty V39() V43() V54() set
[<*((n + h),g,S0),(g . ((n + h) + 1))*>,'&'] is non empty pair set
{<*((n + h),g,S0),(g . ((n + h) + 1))*>,'&'} is non empty functional V39() V54() set
{<*((n + h),g,S0),(g . ((n + h) + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*((n + h),g,S0),(g . ((n + h) + 1))*>,'&'},{<*((n + h),g,S0),(g . ((n + h) + 1))*>}} is non empty V39() V43() V54() set
<*[<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'&'],[<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,'&'],[<*((n + h),g,S0),(g . ((n + h) + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'&'],[<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,'&'],[<*((n + h),g,S0),(g . ((n + h) + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) +* (1GateCircStr (<*[<*(g . ((n + h) + 1)),(S0 . ((n + h) + 1))*>,'&'],[<*(S0 . ((n + h) + 1)),((n + h),g,S0)*>,'&'],[<*((n + h),g,S0),(g . ((n + h) + 1))*>,'&']*>,or3)) is non empty non void V74() 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')) +* (MajorityStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is non empty Element of K23( the carrier of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))))
the carrier of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is non empty set
K23( the carrier of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))) is non empty set
the ResultSort of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is Relation-like the carrier' of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) -defined the carrier of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) -valued Function-like V30( the carrier' of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))), the carrier of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))) Element of K23(K24( the carrier' of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))), the carrier of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))))
the carrier' of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is non empty set
K24( the carrier' of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))), the carrier of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))) is non empty Relation-like set
K23(K24( the carrier' of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))), the carrier of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))))) is non empty set
K497( the carrier of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))), the ResultSort of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))) is Element of K23( the carrier of (((n + h),g,S0) +* (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))))
InnerVertices (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) is non empty Element of K23( the carrier of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))
the carrier of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) is non empty set
K23( the carrier of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is non empty set
the ResultSort of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) is Relation-like the carrier' of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) -defined the carrier of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))), the carrier of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))), the carrier of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))))
the carrier' of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))), the carrier of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))), the carrier of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))), the ResultSort of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0))))
(InnerVertices ((n + h),g,S0)) \/ (InnerVertices (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is non empty set
(InnerVertices (n,g,S0)) \/ (InnerVertices (BitAdderWithOverflowStr ((g . ((n + h) + 1)),(S0 . ((n + h) + 1)),((n + h),g,S0)))) is non empty set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
g is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
((n + 1),f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((n + 1),f,g) is non empty Element of K23( the carrier of ((n + 1),f,g))
the carrier of ((n + 1),f,g) is non empty set
K23( the carrier of ((n + 1),f,g)) is non empty set
the ResultSort of ((n + 1),f,g) is Relation-like the carrier' of ((n + 1),f,g) -defined the carrier of ((n + 1),f,g) -valued Function-like V30( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) Element of K23(K24( 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
K24( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) is non empty Relation-like set
K23(K24( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g))) is non empty set
K497( the carrier of ((n + 1),f,g), the ResultSort of ((n + 1),f,g)) is Element of K23( the carrier of ((n + 1),f,g))
(n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (n,f,g) is non empty Element of K23( the carrier of (n,f,g))
the carrier of (n,f,g) is non empty set
K23( the carrier of (n,f,g)) is non empty set
the ResultSort of (n,f,g) is Relation-like the carrier' of (n,f,g) -defined the carrier of (n,f,g) -valued Function-like V30( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K24( the carrier' of (n,f,g), the carrier of (n,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g))) is non empty set
K497( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K23( 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)
BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(f . (n + 1)),(g . (n + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'xor'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(n,f,g)*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n,f,g),(f . (n + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(n,f,g),(f . (n + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),(n,f,g)*>,'&'))) +* (1GateCircStr (<*(n,f,g),(f . (n + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,'&'] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'&'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (n + 1)),(n,f,g)*>,'&'] is non empty pair set
{<*(g . (n + 1)),(n,f,g)*>,'&'} is non empty functional V39() V54() set
{<*(g . (n + 1)),(n,f,g)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (n + 1)),(n,f,g)*>,'&'},{<*(g . (n + 1)),(n,f,g)*>}} is non empty V39() V43() V54() set
[<*(n,f,g),(f . (n + 1))*>,'&'] is non empty pair set
{<*(n,f,g),(f . (n + 1))*>,'&'} is non empty functional V39() V54() set
{<*(n,f,g),(f . (n + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(n,f,g),(f . (n + 1))*>,'&'},{<*(n,f,g),(f . (n + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),(n,f,g)*>,'&'],[<*(n,f,g),(f . (n + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (n + 1)),(g . (n + 1)),(n,f,g),'xor')) +* (MajorityStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty Element of K23( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))
the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty set
K23( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is non empty set
the ResultSort of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is Relation-like the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) -defined the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))))
the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))), the ResultSort of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))))
(InnerVertices (n,f,g)) \/ (InnerVertices (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g)))) is non empty set
(n,f,g) +* (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),(n,f,g))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
f is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
g is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
S0 is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
(f,g,S0) is non empty non void V74() 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 K23( the carrier of (f,g,S0))
K23( the carrier of (f,g,S0)) is non empty set
the ResultSort of (f,g,S0) is Relation-like the carrier' of (f,g,S0) -defined the carrier of (f,g,S0) -valued Function-like V30( the carrier' of (f,g,S0), the carrier of (f,g,S0)) Element of K23(K24( the carrier' of (f,g,S0), the carrier of (f,g,S0)))
the carrier' of (f,g,S0) is non empty set
K24( the carrier' of (f,g,S0), the carrier of (f,g,S0)) is non empty Relation-like set
K23(K24( the carrier' of (f,g,S0), the carrier of (f,g,S0))) is non empty set
K497( the carrier of (f,g,S0), the ResultSort of (f,g,S0)) is Element of K23( the carrier of (f,g,S0))
g . n is set
S0 . n is set
h is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
h + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() 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 V74() 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 K23( the carrier of (h,g,S0))
K23( the carrier of (h,g,S0)) is non empty set
the ResultSort of (h,g,S0) is Relation-like the carrier' of (h,g,S0) -defined the carrier of (h,g,S0) -valued Function-like V30( the carrier' of (h,g,S0), the carrier of (h,g,S0)) Element of K23(K24( the carrier' of (h,g,S0), the carrier of (h,g,S0)))
the carrier' of (h,g,S0) is non empty set
K24( the carrier' of (h,g,S0), the carrier of (h,g,S0)) is non empty Relation-like set
K23(K24( the carrier' of (h,g,S0), the carrier of (h,g,S0))) is non empty set
K497( the carrier of (h,g,S0), the ResultSort of (h,g,S0)) is Element of K23( the carrier of (h,g,S0))
BitAdderOutput ((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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . n),(S0 . n)*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(g . n),(S0 . n)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . n),(S0 . n)*>,'xor'},{<*(g . n),(S0 . n)*>}} is non empty V39() V43() V54() set
<*[<*(g . n),(S0 . n)*>,'xor'],(h,g,S0)*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(g . n),(S0 . n)*>,'xor'],(h,g,S0)*>,'xor') is non empty non void V74() 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 V74() 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 K23( the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')))
K23( the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor'))) is non empty set
the ResultSort of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')) is Relation-like the carrier' of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')) -defined the carrier of (2GatesCircStr ((g . n),(S0 . n),(h,g,S0),'xor')) -valued Function-like V30( 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 K23(K24( 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
K24( 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 Relation-like set
K23(K24( 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
K497( 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 K23( 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 V39() V54() set
{<*[<*(g . n),(S0 . n)*>,'xor'],(h,g,S0)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(g . n),(S0 . n)*>,'xor'],(h,g,S0)*>,'xor'},{<*[<*(g . n),(S0 . n)*>,'xor'],(h,g,S0)*>}} is non empty V39() V43() V54() set
Sn is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
Sn + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() 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 V74() 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 K23( the carrier of (Sn,g,S0))
K23( the carrier of (Sn,g,S0)) is non empty set
the ResultSort of (Sn,g,S0) is Relation-like the carrier' of (Sn,g,S0) -defined the carrier of (Sn,g,S0) -valued Function-like V30( the carrier' of (Sn,g,S0), the carrier of (Sn,g,S0)) Element of K23(K24( the carrier' of (Sn,g,S0), the carrier of (Sn,g,S0)))
the carrier' of (Sn,g,S0) is non empty set
K24( the carrier' of (Sn,g,S0), the carrier of (Sn,g,S0)) is non empty Relation-like set
K23(K24( the carrier' of (Sn,g,S0), the carrier of (Sn,g,S0))) is non empty set
K497( the carrier of (Sn,g,S0), the ResultSort of (Sn,g,S0)) is Element of K23( the carrier of (Sn,g,S0))
BitAdderOutput ((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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*>,'xor') is non empty non void V74() 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 V74() 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 K23( the carrier of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')))
K23( the carrier of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor'))) is non empty set
the ResultSort of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')) is Relation-like the carrier' of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')) -defined the carrier of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')) -valued Function-like V30( 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 K23(K24( 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
K24( 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 Relation-like set
K23(K24( 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
K497( 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 K23( 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 V39() V54() set
{<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*>,'xor'},{<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*>}} is non empty V39() V43() V54() set
A0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
1 + A0 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
Sn is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
(Sn,g,S0) is Element of InnerVertices (Sn,g,S0)
(Sn,g,S0) is non empty non void V74() 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 K23( the carrier of (Sn,g,S0))
K23( the carrier of (Sn,g,S0)) is non empty set
the ResultSort of (Sn,g,S0) is Relation-like the carrier' of (Sn,g,S0) -defined the carrier of (Sn,g,S0) -valued Function-like V30( the carrier' of (Sn,g,S0), the carrier of (Sn,g,S0)) Element of K23(K24( the carrier' of (Sn,g,S0), the carrier of (Sn,g,S0)))
the carrier' of (Sn,g,S0) is non empty set
K24( the carrier' of (Sn,g,S0), the carrier of (Sn,g,S0)) is non empty Relation-like set
K23(K24( the carrier' of (Sn,g,S0), the carrier of (Sn,g,S0))) is non empty set
K497( the carrier of (Sn,g,S0), the ResultSort of (Sn,g,S0)) is Element of K23( the carrier of (Sn,g,S0))
BitAdderOutput ((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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . n),(S0 . n)*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(g . n),(S0 . n)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . n),(S0 . n)*>,'xor'},{<*(g . n),(S0 . n)*>}} is non empty V39() V43() V54() set
<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*>,'xor') is non empty non void V74() 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 V74() 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 K23( the carrier of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')))
K23( the carrier of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor'))) is non empty set
the ResultSort of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')) is Relation-like the carrier' of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')) -defined the carrier of (2GatesCircStr ((g . n),(S0 . n),(Sn,g,S0),'xor')) -valued Function-like V30( 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 K23(K24( 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
K24( 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 Relation-like set
K23(K24( 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
K497( 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 K23( 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 V39() V54() set
{<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*>,'xor'},{<*[<*(g . n),(S0 . n)*>,'xor'],(Sn,g,S0)*>}} is non empty V39() V43() V54() set
h is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
(h,g,S0) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (h,g,S0) is non empty Element of K23( the carrier of (h,g,S0))
the carrier of (h,g,S0) is non empty set
K23( the carrier of (h,g,S0)) is non empty set
the ResultSort of (h,g,S0) is Relation-like the carrier' of (h,g,S0) -defined the carrier of (h,g,S0) -valued Function-like V30( the carrier' of (h,g,S0), the carrier of (h,g,S0)) Element of K23(K24( the carrier' of (h,g,S0), the carrier of (h,g,S0)))
the carrier' of (h,g,S0) is non empty set
K24( the carrier' of (h,g,S0), the carrier of (h,g,S0)) is non empty Relation-like set
K23(K24( the carrier' of (h,g,S0), the carrier of (h,g,S0))) is non empty set
K497( the carrier of (h,g,S0), the ResultSort of (h,g,S0)) is Element of K23( the carrier of (h,g,S0))
N is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
(N,g,S0) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (N,g,S0) is non empty Element of K23( the carrier of (N,g,S0))
the carrier of (N,g,S0) is non empty set
K23( the carrier of (N,g,S0)) is non empty set
the ResultSort of (N,g,S0) is Relation-like the carrier' of (N,g,S0) -defined the carrier of (N,g,S0) -valued Function-like V30( the carrier' of (N,g,S0), the carrier of (N,g,S0)) Element of K23(K24( the carrier' of (N,g,S0), the carrier of (N,g,S0)))
the carrier' of (N,g,S0) is non empty set
K24( the carrier' of (N,g,S0), the carrier of (N,g,S0)) is non empty Relation-like set
K23(K24( the carrier' of (N,g,S0), the carrier of (N,g,S0))) is non empty set
K497( the carrier of (N,g,S0), the ResultSort of (N,g,S0)) is Element of K23( the carrier of (N,g,S0))
Sn + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
g . (Sn + 1) is set
S0 . (Sn + 1) is set
BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0),'xor') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g . (Sn + 1)),(S0 . (Sn + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'xor') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'xor'] is non empty pair set
{<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'xor'} is non empty functional V39() V54() set
{<*(g . (Sn + 1)),(S0 . (Sn + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'xor'},{<*(g . (Sn + 1)),(S0 . (Sn + 1))*>}} is non empty V39() V43() V54() set
<*[<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'xor'],(Sn,g,S0)*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'xor'],(Sn,g,S0)*>,'xor') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'xor')) +* (1GateCircStr (<*[<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'xor'],(Sn,g,S0)*>,'xor')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(S0 . (Sn + 1)),(Sn,g,S0)*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(S0 . (Sn + 1)),(Sn,g,S0)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'&')) +* (1GateCircStr (<*(S0 . (Sn + 1)),(Sn,g,S0)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(Sn,g,S0),(g . (Sn + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(Sn,g,S0),(g . (Sn + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'&')) +* (1GateCircStr (<*(S0 . (Sn + 1)),(Sn,g,S0)*>,'&'))) +* (1GateCircStr (<*(Sn,g,S0),(g . (Sn + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'&'] is non empty pair set
{<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'&'},{<*(g . (Sn + 1)),(S0 . (Sn + 1))*>}} is non empty V39() V43() V54() set
[<*(S0 . (Sn + 1)),(Sn,g,S0)*>,'&'] is non empty pair set
{<*(S0 . (Sn + 1)),(Sn,g,S0)*>,'&'} is non empty functional V39() V54() set
{<*(S0 . (Sn + 1)),(Sn,g,S0)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(S0 . (Sn + 1)),(Sn,g,S0)*>,'&'},{<*(S0 . (Sn + 1)),(Sn,g,S0)*>}} is non empty V39() V43() V54() set
[<*(Sn,g,S0),(g . (Sn + 1))*>,'&'] is non empty pair set
{<*(Sn,g,S0),(g . (Sn + 1))*>,'&'} is non empty functional V39() V54() set
{<*(Sn,g,S0),(g . (Sn + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(Sn,g,S0),(g . (Sn + 1))*>,'&'},{<*(Sn,g,S0),(g . (Sn + 1))*>}} is non empty V39() V43() V54() set
<*[<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'&'],[<*(S0 . (Sn + 1)),(Sn,g,S0)*>,'&'],[<*(Sn,g,S0),(g . (Sn + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'&'],[<*(S0 . (Sn + 1)),(Sn,g,S0)*>,'&'],[<*(Sn,g,S0),(g . (Sn + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))) +* (1GateCircStr (<*[<*(g . (Sn + 1)),(S0 . (Sn + 1))*>,'&'],[<*(S0 . (Sn + 1)),(Sn,g,S0)*>,'&'],[<*(Sn,g,S0),(g . (Sn + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0),'xor')) +* (MajorityStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))) is non empty Element of K23( the carrier of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))))
the carrier of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))) is non empty set
K23( the carrier of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0)))) is non empty set
the ResultSort of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))) is Relation-like the carrier' of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))) -defined the carrier of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))), the carrier of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0)))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))), the carrier of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0)))))
the carrier' of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))), the carrier of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0)))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))), the carrier of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))), the ResultSort of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0)))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))))
(n,g,S0) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(Sn,g,S0) +* (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0))) \/ the carrier of (Sn,g,S0) is non empty set
the carrier of (n,g,S0) is non empty set
o0 is Element of the carrier of (BitAdderWithOverflowStr ((g . (Sn + 1)),(S0 . (Sn + 1)),(Sn,g,S0)))
InnerVertices (n,g,S0) is non empty Element of K23( the carrier of (n,g,S0))
K23( the carrier of (n,g,S0)) is non empty set
the ResultSort of (n,g,S0) is Relation-like the carrier' of (n,g,S0) -defined the carrier of (n,g,S0) -valued Function-like V30( the carrier' of (n,g,S0), the carrier of (n,g,S0)) Element of K23(K24( the carrier' of (n,g,S0), the carrier of (n,g,S0)))
the carrier' of (n,g,S0) is non empty set
K24( the carrier' of (n,g,S0), the carrier of (n,g,S0)) is non empty Relation-like set
K23(K24( the carrier' of (n,g,S0), the carrier of (n,g,S0))) is non empty set
K497( the carrier of (n,g,S0), the ResultSort of (n,g,S0)) is Element of K23( the carrier of (n,g,S0))
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
g is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
S0 is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
((f + 1),n,g,S0) is Element of InnerVertices (n,g,S0)
(n,g,S0) is non empty non void V74() 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 K23( the carrier of (n,g,S0))
K23( the carrier of (n,g,S0)) is non empty set
the ResultSort of (n,g,S0) is Relation-like the carrier' of (n,g,S0) -defined the carrier of (n,g,S0) -valued Function-like V30( the carrier' of (n,g,S0), the carrier of (n,g,S0)) Element of K23(K24( the carrier' of (n,g,S0), the carrier of (n,g,S0)))
the carrier' of (n,g,S0) is non empty set
K24( the carrier' of (n,g,S0), the carrier of (n,g,S0)) is non empty Relation-like set
K23(K24( the carrier' of (n,g,S0), the carrier of (n,g,S0))) is non empty set
K497( the carrier of (n,g,S0), the ResultSort of (n,g,S0)) is Element of K23( 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 V74() 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 K23( the carrier of (f,g,S0))
K23( the carrier of (f,g,S0)) is non empty set
the ResultSort of (f,g,S0) is Relation-like the carrier' of (f,g,S0) -defined the carrier of (f,g,S0) -valued Function-like V30( the carrier' of (f,g,S0), the carrier of (f,g,S0)) Element of K23(K24( the carrier' of (f,g,S0), the carrier of (f,g,S0)))
the carrier' of (f,g,S0) is non empty set
K24( the carrier' of (f,g,S0), the carrier of (f,g,S0)) is non empty Relation-like set
K23(K24( the carrier' of (f,g,S0), the carrier of (f,g,S0))) is non empty set
K497( the carrier of (f,g,S0), the ResultSort of (f,g,S0)) is Element of K23( the carrier of (f,g,S0))
BitAdderOutput ((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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (f + 1)),(S0 . (f + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(g . (f + 1)),(S0 . (f + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'},{<*(g . (f + 1)),(S0 . (f + 1))*>}} is non empty V39() V43() V54() set
<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(f,g,S0)*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(f,g,S0)*>,'xor') is non empty non void V74() 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 V74() 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 K23( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')))
K23( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor'))) is non empty set
the ResultSort of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')) is Relation-like the carrier' of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')) -defined the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(f,g,S0),'xor')) -valued Function-like V30( 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 K23(K24( 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
K24( 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 Relation-like set
K23(K24( 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
K497( 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 K23( 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 V39() V54() set
{<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(f,g,S0)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() 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 V39() V43() V54() set
A0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
A0 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
(A0,g,S0) is Element of InnerVertices (A0,g,S0)
(A0,g,S0) is non empty non void V74() 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 K23( the carrier of (A0,g,S0))
K23( the carrier of (A0,g,S0)) is non empty set
the ResultSort of (A0,g,S0) is Relation-like the carrier' of (A0,g,S0) -defined the carrier of (A0,g,S0) -valued Function-like V30( the carrier' of (A0,g,S0), the carrier of (A0,g,S0)) Element of K23(K24( the carrier' of (A0,g,S0), the carrier of (A0,g,S0)))
the carrier' of (A0,g,S0) is non empty set
K24( the carrier' of (A0,g,S0), the carrier of (A0,g,S0)) is non empty Relation-like set
K23(K24( the carrier' of (A0,g,S0), the carrier of (A0,g,S0))) is non empty set
K497( the carrier of (A0,g,S0), the ResultSort of (A0,g,S0)) is Element of K23( the carrier of (A0,g,S0))
BitAdderOutput ((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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(A0,g,S0)*>,'xor') is non empty non void V74() 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 V74() 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 K23( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')))
K23( the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor'))) is non empty set
the ResultSort of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')) is Relation-like the carrier' of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')) -defined the carrier of (2GatesCircStr ((g . (f + 1)),(S0 . (f + 1)),(A0,g,S0),'xor')) -valued Function-like V30( 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 K23(K24( 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
K24( 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 Relation-like set
K23(K24( 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
K497( 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 K23( 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 V39() V54() set
{<*[<*(g . (f + 1)),(S0 . (f + 1))*>,'xor'],(A0,g,S0)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() 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 V39() V43() V54() set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f is Relation-like NAT -defined Function-like V39() n + 1 -element FinSequence-like FinSubsequence-like V54() set
len f is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
g is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
S0 is set
<*S0*> is non empty V5() Relation-like NAT -defined Function-like constant V39() 1 -element FinSequence-like FinSubsequence-like V54() set
g ^ <*S0*> is non empty Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
len <*S0*> is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
len g is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
(len g) + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
A0 is Relation-like NAT -defined Function-like V39() n -element FinSequence-like FinSubsequence-like V54() set
N is Relation-like NAT -defined Function-like V39() n -element FinSequence-like FinSubsequence-like V54() set
h is set
<*h*> is non empty V5() Relation-like NAT -defined Function-like constant V39() 1 -element FinSequence-like FinSubsequence-like V54() set
N ^ <*h*> is non empty Relation-like NAT -defined Function-like V39() n + 1 -element FinSequence-like FinSubsequence-like V54() set
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f is Relation-like NAT -defined Function-like V39() n + 1 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
g is Relation-like NAT -defined Function-like V39() n -element FinSequence-like FinSubsequence-like V54() set
S0 is set
<*S0*> is non empty V5() Relation-like NAT -defined Function-like constant V39() 1 -element FinSequence-like FinSubsequence-like V54() set
g ^ <*S0*> is non empty Relation-like NAT -defined Function-like V39() n + 1 -element FinSequence-like FinSubsequence-like V54() set
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
dom g is V39() n -element V54() Element of K23(NAT)
dom f is V39() n + 1 -element V54() Element of K23(NAT)
f | (dom g) is Relation-like NAT -defined dom g -defined NAT -defined Function-like V39() FinSubsequence-like V54() set
A0 is set
proj1 g is V39() n -element V54() set
g . A0 is set
f . A0 is set
Seg (n + 1) is non empty V39() n + 1 -element V54() Element of K23(NAT)
len f is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
Seg (len f) is V39() len f -element V54() Element of K23(NAT)
A0 is Relation-like NAT -defined Function-like V39() n -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
len A0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
(len A0) + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . ((len A0) + 1) is set
N is non pair set
h is Relation-like NAT -defined Function-like V39() n -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
Sn is non pair set
<*Sn*> is non empty V5() Relation-like NAT -defined Function-like constant V39() 1 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
h ^ <*Sn*> is non empty Relation-like NAT -defined Function-like V39() n + 1 -element FinSequence-like FinSubsequence-like V54() set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
g is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
(n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (n,f,g) is non empty Element of K23( the carrier of (n,f,g))
the carrier of (n,f,g) is non empty set
K23( the carrier of (n,f,g)) is non empty set
the ResultSort of (n,f,g) is Relation-like the carrier' of (n,f,g) -defined the carrier of (n,f,g) -valued Function-like V30( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K24( the carrier' of (n,f,g), the carrier of (n,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g))) is non empty set
K497( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K23( the carrier of (n,f,g))
(0,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (0,f,g) is non empty Element of K23( the carrier of (0,f,g))
the carrier of (0,f,g) is non empty set
K23( the carrier of (0,f,g)) is non empty set
the ResultSort of (0,f,g) is Relation-like the carrier' of (0,f,g) -defined the carrier of (0,f,g) -valued Function-like V30( the carrier' of (0,f,g), the carrier of (0,f,g)) Element of K23(K24( the carrier' of (0,f,g), the carrier of (0,f,g)))
the carrier' of (0,f,g) is non empty set
K24( the carrier' of (0,f,g), the carrier of (0,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (0,f,g), the carrier of (0,f,g))) is non empty set
K497( the carrier of (0,f,g), the ResultSort of (0,f,g)) is Element of K23( the carrier of (0,f,g))
S0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
(S0,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (S0,f,g) is non empty Element of K23( the carrier of (S0,f,g))
the carrier of (S0,f,g) is non empty set
K23( the carrier of (S0,f,g)) is non empty set
the ResultSort of (S0,f,g) is Relation-like the carrier' of (S0,f,g) -defined the carrier of (S0,f,g) -valued Function-like V30( the carrier' of (S0,f,g), the carrier of (S0,f,g)) Element of K23(K24( the carrier' of (S0,f,g), the carrier of (S0,f,g)))
the carrier' of (S0,f,g) is non empty set
K24( the carrier' of (S0,f,g), the carrier of (S0,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (S0,f,g), the carrier of (S0,f,g))) is non empty set
K497( the carrier of (S0,f,g), the ResultSort of (S0,f,g)) is Element of K23( the carrier of (S0,f,g))
S0 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
((S0 + 1),f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((S0 + 1),f,g) is non empty Element of K23( the carrier of ((S0 + 1),f,g))
the carrier of ((S0 + 1),f,g) is non empty set
K23( the carrier of ((S0 + 1),f,g)) is non empty set
the ResultSort of ((S0 + 1),f,g) is Relation-like the carrier' of ((S0 + 1),f,g) -defined the carrier of ((S0 + 1),f,g) -valued Function-like V30( the carrier' of ((S0 + 1),f,g), the carrier of ((S0 + 1),f,g)) Element of K23(K24( 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
K24( the carrier' of ((S0 + 1),f,g), the carrier of ((S0 + 1),f,g)) is non empty Relation-like set
K23(K24( the carrier' of ((S0 + 1),f,g), the carrier of ((S0 + 1),f,g))) is non empty set
K497( the carrier of ((S0 + 1),f,g), the ResultSort of ((S0 + 1),f,g)) is Element of K23( the carrier of ((S0 + 1),f,g))
f . (S0 + 1) is set
g . (S0 + 1) is set
(S0,f,g) is Element of InnerVertices (S0,f,g)
BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (S0 + 1)),(g . (S0 + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(f . (S0 + 1)),(g . (S0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (S0 + 1)),(g . (S0 + 1))*>,'xor'},{<*(f . (S0 + 1)),(g . (S0 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'xor'],(S0,f,g)*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'xor'],(S0,f,g)*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (S0 + 1)),(S0,f,g)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&')) +* (1GateCircStr (<*(g . (S0 + 1)),(S0,f,g)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(S0,f,g),(f . (S0 + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(S0,f,g),(f . (S0 + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&')) +* (1GateCircStr (<*(g . (S0 + 1)),(S0,f,g)*>,'&'))) +* (1GateCircStr (<*(S0,f,g),(f . (S0 + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'] is non empty pair set
{<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'},{<*(f . (S0 + 1)),(g . (S0 + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (S0 + 1)),(S0,f,g)*>,'&'] is non empty pair set
{<*(g . (S0 + 1)),(S0,f,g)*>,'&'} is non empty functional V39() V54() set
{<*(g . (S0 + 1)),(S0,f,g)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (S0 + 1)),(S0,f,g)*>,'&'},{<*(g . (S0 + 1)),(S0,f,g)*>}} is non empty V39() V43() V54() set
[<*(S0,f,g),(f . (S0 + 1))*>,'&'] is non empty pair set
{<*(S0,f,g),(f . (S0 + 1))*>,'&'} is non empty functional V39() V54() set
{<*(S0,f,g),(f . (S0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(S0,f,g),(f . (S0 + 1))*>,'&'},{<*(S0,f,g),(f . (S0 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'],[<*(g . (S0 + 1)),(S0,f,g)*>,'&'],[<*(S0,f,g),(f . (S0 + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'],[<*(g . (S0 + 1)),(S0,f,g)*>,'&'],[<*(S0,f,g),(f . (S0 + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) +* (1GateCircStr (<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'],[<*(g . (S0 + 1)),(S0,f,g)*>,'&'],[<*(S0,f,g),(f . (S0 + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g),'xor')) +* (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(S0,f,g) +* (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty Element of K23( the carrier of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))))
the carrier of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty set
K23( the carrier of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) is non empty set
the ResultSort of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is Relation-like the carrier' of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) -defined the carrier of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))))
the carrier' of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the ResultSort of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))))
n is set
f is set
g is set
MajorityIStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,f*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*n,f*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f,g*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*f,g*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*g,n*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*g,n*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (MajorityIStr (n,f,g)) is non empty Element of K23( the carrier of (MajorityIStr (n,f,g)))
the carrier of (MajorityIStr (n,f,g)) is non empty set
K23( the carrier of (MajorityIStr (n,f,g))) is non empty set
the ResultSort of (MajorityIStr (n,f,g)) is Relation-like the carrier' of (MajorityIStr (n,f,g)) -defined the carrier of (MajorityIStr (n,f,g)) -valued Function-like V30( the carrier' of (MajorityIStr (n,f,g)), the carrier of (MajorityIStr (n,f,g))) Element of K23(K24( the carrier' of (MajorityIStr (n,f,g)), the carrier of (MajorityIStr (n,f,g))))
the carrier' of (MajorityIStr (n,f,g)) is non empty set
K24( the carrier' of (MajorityIStr (n,f,g)), the carrier of (MajorityIStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityIStr (n,f,g)), the carrier of (MajorityIStr (n,f,g)))) is non empty set
K497( the carrier of (MajorityIStr (n,f,g)), the ResultSort of (MajorityIStr (n,f,g))) is Element of K23( the carrier of (MajorityIStr (n,f,g)))
[<*n,f*>,'&'] is non empty pair set
{<*n,f*>,'&'} is non empty functional V39() V54() set
{<*n,f*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*n,f*>,'&'},{<*n,f*>}} is non empty V39() V43() V54() set
[<*f,g*>,'&'] is non empty pair set
{<*f,g*>,'&'} is non empty functional V39() V54() set
{<*f,g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*f,g*>,'&'},{<*f,g*>}} is non empty V39() V43() V54() set
[<*g,n*>,'&'] is non empty pair set
{<*g,n*>,'&'} is non empty functional V39() V54() set
{<*g,n*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g,n*>,'&'},{<*g,n*>}} is non empty V39() V43() V54() set
{[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']} is non empty Relation-like V39() V54() set
InnerVertices ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) is non empty Element of K23( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))))
the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) is non empty set
K23( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')))) is non empty set
the ResultSort of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) is Relation-like the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) -defined the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) -valued Function-like V30( the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))), the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')))) Element of K23(K24( the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))), the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')))))
the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) is non empty set
K24( the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))), the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')))) is non empty Relation-like set
K23(K24( the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))), the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))))) is non empty set
K497( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))), the ResultSort of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')))) is Element of K23( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))))
InnerVertices (1GateCircStr (<*g,n*>,'&')) is non empty Element of K23( the carrier of (1GateCircStr (<*g,n*>,'&')))
the carrier of (1GateCircStr (<*g,n*>,'&')) is non empty set
K23( the carrier of (1GateCircStr (<*g,n*>,'&'))) is non empty set
the ResultSort of (1GateCircStr (<*g,n*>,'&')) is Relation-like the carrier' of (1GateCircStr (<*g,n*>,'&')) -defined the carrier of (1GateCircStr (<*g,n*>,'&')) -valued Function-like V30( the carrier' of (1GateCircStr (<*g,n*>,'&')), the carrier of (1GateCircStr (<*g,n*>,'&'))) Element of K23(K24( the carrier' of (1GateCircStr (<*g,n*>,'&')), the carrier of (1GateCircStr (<*g,n*>,'&'))))
the carrier' of (1GateCircStr (<*g,n*>,'&')) is non empty set
K24( the carrier' of (1GateCircStr (<*g,n*>,'&')), the carrier of (1GateCircStr (<*g,n*>,'&'))) is non empty Relation-like set
K23(K24( the carrier' of (1GateCircStr (<*g,n*>,'&')), the carrier of (1GateCircStr (<*g,n*>,'&')))) is non empty set
K497( the carrier of (1GateCircStr (<*g,n*>,'&')), the ResultSort of (1GateCircStr (<*g,n*>,'&'))) is Element of K23( the carrier of (1GateCircStr (<*g,n*>,'&')))
(InnerVertices ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')))) \/ (InnerVertices (1GateCircStr (<*g,n*>,'&'))) is non empty set
InnerVertices (1GateCircStr (<*n,f*>,'&')) is non empty Element of K23( the carrier of (1GateCircStr (<*n,f*>,'&')))
the carrier of (1GateCircStr (<*n,f*>,'&')) is non empty set
K23( the carrier of (1GateCircStr (<*n,f*>,'&'))) is non empty set
the ResultSort of (1GateCircStr (<*n,f*>,'&')) is Relation-like the carrier' of (1GateCircStr (<*n,f*>,'&')) -defined the carrier of (1GateCircStr (<*n,f*>,'&')) -valued Function-like V30( the carrier' of (1GateCircStr (<*n,f*>,'&')), the carrier of (1GateCircStr (<*n,f*>,'&'))) Element of K23(K24( the carrier' of (1GateCircStr (<*n,f*>,'&')), the carrier of (1GateCircStr (<*n,f*>,'&'))))
the carrier' of (1GateCircStr (<*n,f*>,'&')) is non empty set
K24( the carrier' of (1GateCircStr (<*n,f*>,'&')), the carrier of (1GateCircStr (<*n,f*>,'&'))) is non empty Relation-like set
K23(K24( the carrier' of (1GateCircStr (<*n,f*>,'&')), the carrier of (1GateCircStr (<*n,f*>,'&')))) is non empty set
K497( the carrier of (1GateCircStr (<*n,f*>,'&')), the ResultSort of (1GateCircStr (<*n,f*>,'&'))) is Element of K23( the carrier of (1GateCircStr (<*n,f*>,'&')))
InnerVertices (1GateCircStr (<*f,g*>,'&')) is non empty Element of K23( the carrier of (1GateCircStr (<*f,g*>,'&')))
the carrier of (1GateCircStr (<*f,g*>,'&')) is non empty set
K23( the carrier of (1GateCircStr (<*f,g*>,'&'))) is non empty set
the ResultSort of (1GateCircStr (<*f,g*>,'&')) is Relation-like the carrier' of (1GateCircStr (<*f,g*>,'&')) -defined the carrier of (1GateCircStr (<*f,g*>,'&')) -valued Function-like V30( the carrier' of (1GateCircStr (<*f,g*>,'&')), the carrier of (1GateCircStr (<*f,g*>,'&'))) Element of K23(K24( the carrier' of (1GateCircStr (<*f,g*>,'&')), the carrier of (1GateCircStr (<*f,g*>,'&'))))
the carrier' of (1GateCircStr (<*f,g*>,'&')) is non empty set
K24( the carrier' of (1GateCircStr (<*f,g*>,'&')), the carrier of (1GateCircStr (<*f,g*>,'&'))) is non empty Relation-like set
K23(K24( the carrier' of (1GateCircStr (<*f,g*>,'&')), the carrier of (1GateCircStr (<*f,g*>,'&')))) is non empty set
K497( the carrier of (1GateCircStr (<*f,g*>,'&')), the ResultSort of (1GateCircStr (<*f,g*>,'&'))) is Element of K23( the carrier of (1GateCircStr (<*f,g*>,'&')))
(InnerVertices (1GateCircStr (<*n,f*>,'&'))) \/ (InnerVertices (1GateCircStr (<*f,g*>,'&'))) is non empty set
((InnerVertices (1GateCircStr (<*n,f*>,'&'))) \/ (InnerVertices (1GateCircStr (<*f,g*>,'&')))) \/ (InnerVertices (1GateCircStr (<*g,n*>,'&'))) is non empty set
{[<*n,f*>,'&']} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
{[<*n,f*>,'&']} \/ (InnerVertices (1GateCircStr (<*f,g*>,'&'))) is non empty set
({[<*n,f*>,'&']} \/ (InnerVertices (1GateCircStr (<*f,g*>,'&')))) \/ (InnerVertices (1GateCircStr (<*g,n*>,'&'))) is non empty set
{[<*f,g*>,'&']} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
{[<*n,f*>,'&']} \/ {[<*f,g*>,'&']} is non empty Relation-like V39() V54() set
({[<*n,f*>,'&']} \/ {[<*f,g*>,'&']}) \/ (InnerVertices (1GateCircStr (<*g,n*>,'&'))) is non empty set
{[<*g,n*>,'&']} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
({[<*n,f*>,'&']} \/ {[<*f,g*>,'&']}) \/ {[<*g,n*>,'&']} is non empty Relation-like V39() V54() set
{[<*n,f*>,'&'],[<*f,g*>,'&']} is non empty Relation-like V39() V54() set
{[<*n,f*>,'&'],[<*f,g*>,'&']} \/ {[<*g,n*>,'&']} is non empty Relation-like V39() V54() set
n is set
f is set
g is set
<*f,g*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*f,g*>,'&'] is non empty pair set
{<*f,g*>,'&'} is non empty functional V39() V54() set
{<*f,g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*f,g*>,'&'},{<*f,g*>}} is non empty V39() V43() V54() set
<*g,n*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*g,n*>,'&'] is non empty pair set
{<*g,n*>,'&'} is non empty functional V39() V54() set
{<*g,n*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g,n*>,'&'},{<*g,n*>}} is non empty V39() V43() V54() set
<*n,f*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*n,f*>,'&'] is non empty pair set
{<*n,f*>,'&'} is non empty functional V39() V54() set
{<*n,f*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*n,f*>,'&'},{<*n,f*>}} is non empty V39() V43() V54() set
MajorityIStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*f,g*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*g,n*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (MajorityIStr (n,f,g)) is Element of K23( the carrier of (MajorityIStr (n,f,g)))
the carrier of (MajorityIStr (n,f,g)) is non empty set
K23( the carrier of (MajorityIStr (n,f,g))) is non empty set
the ResultSort of (MajorityIStr (n,f,g)) is Relation-like the carrier' of (MajorityIStr (n,f,g)) -defined the carrier of (MajorityIStr (n,f,g)) -valued Function-like V30( the carrier' of (MajorityIStr (n,f,g)), the carrier of (MajorityIStr (n,f,g))) Element of K23(K24( the carrier' of (MajorityIStr (n,f,g)), the carrier of (MajorityIStr (n,f,g))))
the carrier' of (MajorityIStr (n,f,g)) is non empty set
K24( the carrier' of (MajorityIStr (n,f,g)), the carrier of (MajorityIStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityIStr (n,f,g)), the carrier of (MajorityIStr (n,f,g)))) is non empty set
K497( the carrier of (MajorityIStr (n,f,g)), the ResultSort of (MajorityIStr (n,f,g))) is Element of K23( the carrier of (MajorityIStr (n,f,g)))
the carrier of (MajorityIStr (n,f,g)) \ K497( the carrier of (MajorityIStr (n,f,g)), the ResultSort of (MajorityIStr (n,f,g))) is Element of K23( the carrier of (MajorityIStr (n,f,g)))
{n,f,g} is non empty V39() V54() set
{1,f} is non empty V39() V54() set
{2,f} is non empty V39() V54() set
[1,f] is non empty pair set
{1} is non empty V5() V39() V43() 1 -element V54() non with_pair set
{{1,f},{1}} is non empty V39() V43() V54() set
[2,f] is non empty pair set
{2} is non empty V5() V39() V43() 1 -element V54() non with_pair set
{{2,f},{2}} is non empty V39() V43() V54() set
<*f*> is non empty V5() Relation-like NAT -defined Function-like constant V39() 1 -element FinSequence-like FinSubsequence-like V54() set
<*g*> is non empty V5() Relation-like NAT -defined Function-like constant V39() 1 -element FinSequence-like FinSubsequence-like V54() set
<*f*> ^ <*g*> is non empty Relation-like NAT -defined Function-like V39() 1 + 1 -element FinSequence-like FinSubsequence-like V54() set
1 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
{[1,f]} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
{2,g} is non empty V39() V54() set
[2,g] is non empty pair set
{{2,g},{2}} is non empty V39() V43() V54() set
dom <*f,g*> is non empty V39() 2 -element V54() Element of K23(NAT)
Seg 2 is non empty V39() 2 -element V54() Element of K23(NAT)
<*f,g*> . 2 is set
dom <*n,f*> is non empty V39() 2 -element V54() Element of K23(NAT)
<*n,f*> . 2 is set
{f,g} is non empty V39() V54() set
{1,n} is non empty V39() V54() set
[1,n] is non empty pair set
{{1,n},{1}} is non empty V39() V43() V54() set
<*n*> is non empty V5() Relation-like NAT -defined Function-like constant V39() 1 -element FinSequence-like FinSubsequence-like V54() set
<*n*> ^ <*f*> is non empty Relation-like NAT -defined Function-like V39() 1 + 1 -element FinSequence-like FinSubsequence-like V54() set
{[1,n]} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
{[<*n,f*>,'&'],[<*f,g*>,'&']} is non empty Relation-like V39() V54() set
{2,n} is non empty V39() V54() set
[2,n] is non empty pair set
{{2,n},{2}} is non empty V39() V43() V54() set
dom <*g,n*> is non empty V39() 2 -element V54() Element of K23(NAT)
<*g,n*> . 2 is set
{1,g} is non empty V39() V54() set
[1,g] is non empty pair set
{{1,g},{1}} is non empty V39() V43() V54() set
<*g*> ^ <*n*> is non empty Relation-like NAT -defined Function-like V39() 1 + 1 -element FinSequence-like FinSubsequence-like V54() set
{[1,g]} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) is non empty set
InputVertices ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) is Element of K23( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))))
K23( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')))) is non empty set
the ResultSort of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) is Relation-like the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) -defined the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) -valued Function-like V30( the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))), the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')))) Element of K23(K24( the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))), the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')))))
the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) is non empty set
K24( the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))), the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')))) is non empty Relation-like set
K23(K24( the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))), the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))))) is non empty set
K497( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))), the ResultSort of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')))) is Element of K23( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))))
the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) \ K497( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))), the ResultSort of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')))) is Element of K23( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))))
InnerVertices (1GateCircStr (<*g,n*>,'&')) is non empty Element of K23( the carrier of (1GateCircStr (<*g,n*>,'&')))
the carrier of (1GateCircStr (<*g,n*>,'&')) is non empty set
K23( the carrier of (1GateCircStr (<*g,n*>,'&'))) is non empty set
the ResultSort of (1GateCircStr (<*g,n*>,'&')) is Relation-like the carrier' of (1GateCircStr (<*g,n*>,'&')) -defined the carrier of (1GateCircStr (<*g,n*>,'&')) -valued Function-like V30( the carrier' of (1GateCircStr (<*g,n*>,'&')), the carrier of (1GateCircStr (<*g,n*>,'&'))) Element of K23(K24( the carrier' of (1GateCircStr (<*g,n*>,'&')), the carrier of (1GateCircStr (<*g,n*>,'&'))))
the carrier' of (1GateCircStr (<*g,n*>,'&')) is non empty set
K24( the carrier' of (1GateCircStr (<*g,n*>,'&')), the carrier of (1GateCircStr (<*g,n*>,'&'))) is non empty Relation-like set
K23(K24( the carrier' of (1GateCircStr (<*g,n*>,'&')), the carrier of (1GateCircStr (<*g,n*>,'&')))) is non empty set
K497( the carrier of (1GateCircStr (<*g,n*>,'&')), the ResultSort of (1GateCircStr (<*g,n*>,'&'))) is Element of K23( the carrier of (1GateCircStr (<*g,n*>,'&')))
(InputVertices ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')))) \ (InnerVertices (1GateCircStr (<*g,n*>,'&'))) is Element of K23( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))))
InputVertices (1GateCircStr (<*g,n*>,'&')) is Element of K23( the carrier of (1GateCircStr (<*g,n*>,'&')))
the carrier of (1GateCircStr (<*g,n*>,'&')) \ K497( the carrier of (1GateCircStr (<*g,n*>,'&')), the ResultSort of (1GateCircStr (<*g,n*>,'&'))) is Element of K23( the carrier of (1GateCircStr (<*g,n*>,'&')))
InnerVertices ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) is non empty Element of K23( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))))
(InputVertices (1GateCircStr (<*g,n*>,'&'))) \ (InnerVertices ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')))) is Element of K23( the carrier of (1GateCircStr (<*g,n*>,'&')))
((InputVertices ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')))) \ (InnerVertices (1GateCircStr (<*g,n*>,'&')))) \/ ((InputVertices (1GateCircStr (<*g,n*>,'&'))) \ (InnerVertices ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))))) is set
the carrier of (1GateCircStr (<*n,f*>,'&')) is non empty set
InputVertices (1GateCircStr (<*n,f*>,'&')) is Element of K23( the carrier of (1GateCircStr (<*n,f*>,'&')))
K23( the carrier of (1GateCircStr (<*n,f*>,'&'))) is non empty set
the ResultSort of (1GateCircStr (<*n,f*>,'&')) is Relation-like the carrier' of (1GateCircStr (<*n,f*>,'&')) -defined the carrier of (1GateCircStr (<*n,f*>,'&')) -valued Function-like V30( the carrier' of (1GateCircStr (<*n,f*>,'&')), the carrier of (1GateCircStr (<*n,f*>,'&'))) Element of K23(K24( the carrier' of (1GateCircStr (<*n,f*>,'&')), the carrier of (1GateCircStr (<*n,f*>,'&'))))
the carrier' of (1GateCircStr (<*n,f*>,'&')) is non empty set
K24( the carrier' of (1GateCircStr (<*n,f*>,'&')), the carrier of (1GateCircStr (<*n,f*>,'&'))) is non empty Relation-like set
K23(K24( the carrier' of (1GateCircStr (<*n,f*>,'&')), the carrier of (1GateCircStr (<*n,f*>,'&')))) is non empty set
K497( the carrier of (1GateCircStr (<*n,f*>,'&')), the ResultSort of (1GateCircStr (<*n,f*>,'&'))) is Element of K23( the carrier of (1GateCircStr (<*n,f*>,'&')))
the carrier of (1GateCircStr (<*n,f*>,'&')) \ K497( the carrier of (1GateCircStr (<*n,f*>,'&')), the ResultSort of (1GateCircStr (<*n,f*>,'&'))) is Element of K23( the carrier of (1GateCircStr (<*n,f*>,'&')))
InnerVertices (1GateCircStr (<*f,g*>,'&')) is non empty Element of K23( the carrier of (1GateCircStr (<*f,g*>,'&')))
the carrier of (1GateCircStr (<*f,g*>,'&')) is non empty set
K23( the carrier of (1GateCircStr (<*f,g*>,'&'))) is non empty set
the ResultSort of (1GateCircStr (<*f,g*>,'&')) is Relation-like the carrier' of (1GateCircStr (<*f,g*>,'&')) -defined the carrier of (1GateCircStr (<*f,g*>,'&')) -valued Function-like V30( the carrier' of (1GateCircStr (<*f,g*>,'&')), the carrier of (1GateCircStr (<*f,g*>,'&'))) Element of K23(K24( the carrier' of (1GateCircStr (<*f,g*>,'&')), the carrier of (1GateCircStr (<*f,g*>,'&'))))
the carrier' of (1GateCircStr (<*f,g*>,'&')) is non empty set
K24( the carrier' of (1GateCircStr (<*f,g*>,'&')), the carrier of (1GateCircStr (<*f,g*>,'&'))) is non empty Relation-like set
K23(K24( the carrier' of (1GateCircStr (<*f,g*>,'&')), the carrier of (1GateCircStr (<*f,g*>,'&')))) is non empty set
K497( the carrier of (1GateCircStr (<*f,g*>,'&')), the ResultSort of (1GateCircStr (<*f,g*>,'&'))) is Element of K23( the carrier of (1GateCircStr (<*f,g*>,'&')))
(InputVertices (1GateCircStr (<*n,f*>,'&'))) \ (InnerVertices (1GateCircStr (<*f,g*>,'&'))) is Element of K23( the carrier of (1GateCircStr (<*n,f*>,'&')))
InputVertices (1GateCircStr (<*f,g*>,'&')) is Element of K23( the carrier of (1GateCircStr (<*f,g*>,'&')))
the carrier of (1GateCircStr (<*f,g*>,'&')) \ K497( the carrier of (1GateCircStr (<*f,g*>,'&')), the ResultSort of (1GateCircStr (<*f,g*>,'&'))) is Element of K23( the carrier of (1GateCircStr (<*f,g*>,'&')))
InnerVertices (1GateCircStr (<*n,f*>,'&')) is non empty Element of K23( the carrier of (1GateCircStr (<*n,f*>,'&')))
(InputVertices (1GateCircStr (<*f,g*>,'&'))) \ (InnerVertices (1GateCircStr (<*n,f*>,'&'))) is Element of K23( the carrier of (1GateCircStr (<*f,g*>,'&')))
((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ (InnerVertices (1GateCircStr (<*f,g*>,'&')))) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ (InnerVertices (1GateCircStr (<*n,f*>,'&')))) is set
(((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ (InnerVertices (1GateCircStr (<*f,g*>,'&')))) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ (InnerVertices (1GateCircStr (<*n,f*>,'&'))))) \ (InnerVertices (1GateCircStr (<*g,n*>,'&'))) is Element of K23((((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ (InnerVertices (1GateCircStr (<*f,g*>,'&')))) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ (InnerVertices (1GateCircStr (<*n,f*>,'&'))))))
K23((((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ (InnerVertices (1GateCircStr (<*f,g*>,'&')))) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ (InnerVertices (1GateCircStr (<*n,f*>,'&')))))) is non empty set
((((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ (InnerVertices (1GateCircStr (<*f,g*>,'&')))) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ (InnerVertices (1GateCircStr (<*n,f*>,'&'))))) \ (InnerVertices (1GateCircStr (<*g,n*>,'&')))) \/ ((InputVertices (1GateCircStr (<*g,n*>,'&'))) \ (InnerVertices ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))))) is set
(InnerVertices (1GateCircStr (<*n,f*>,'&'))) \/ (InnerVertices (1GateCircStr (<*f,g*>,'&'))) is non empty set
(InputVertices (1GateCircStr (<*g,n*>,'&'))) \ ((InnerVertices (1GateCircStr (<*n,f*>,'&'))) \/ (InnerVertices (1GateCircStr (<*f,g*>,'&')))) is Element of K23( the carrier of (1GateCircStr (<*g,n*>,'&')))
((((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ (InnerVertices (1GateCircStr (<*f,g*>,'&')))) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ (InnerVertices (1GateCircStr (<*n,f*>,'&'))))) \ (InnerVertices (1GateCircStr (<*g,n*>,'&')))) \/ ((InputVertices (1GateCircStr (<*g,n*>,'&'))) \ ((InnerVertices (1GateCircStr (<*n,f*>,'&'))) \/ (InnerVertices (1GateCircStr (<*f,g*>,'&'))))) is set
{[<*f,g*>,'&']} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
(InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']} is Element of K23( the carrier of (1GateCircStr (<*n,f*>,'&')))
((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ (InnerVertices (1GateCircStr (<*n,f*>,'&')))) is set
(((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ (InnerVertices (1GateCircStr (<*n,f*>,'&'))))) \ (InnerVertices (1GateCircStr (<*g,n*>,'&'))) is Element of K23((((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ (InnerVertices (1GateCircStr (<*n,f*>,'&'))))))
K23((((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ (InnerVertices (1GateCircStr (<*n,f*>,'&')))))) is non empty set
((((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ (InnerVertices (1GateCircStr (<*n,f*>,'&'))))) \ (InnerVertices (1GateCircStr (<*g,n*>,'&')))) \/ ((InputVertices (1GateCircStr (<*g,n*>,'&'))) \ ((InnerVertices (1GateCircStr (<*n,f*>,'&'))) \/ (InnerVertices (1GateCircStr (<*f,g*>,'&'))))) is set
{[<*n,f*>,'&']} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
(InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']} is Element of K23( the carrier of (1GateCircStr (<*f,g*>,'&')))
((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']}) is set
(((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']})) \ (InnerVertices (1GateCircStr (<*g,n*>,'&'))) is Element of K23((((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']})))
K23((((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']}))) is non empty set
((((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']})) \ (InnerVertices (1GateCircStr (<*g,n*>,'&')))) \/ ((InputVertices (1GateCircStr (<*g,n*>,'&'))) \ ((InnerVertices (1GateCircStr (<*n,f*>,'&'))) \/ (InnerVertices (1GateCircStr (<*f,g*>,'&'))))) is set
{[<*g,n*>,'&']} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
(((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']})) \ {[<*g,n*>,'&']} is Element of K23((((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']})))
((((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']})) \ {[<*g,n*>,'&']}) \/ ((InputVertices (1GateCircStr (<*g,n*>,'&'))) \ ((InnerVertices (1GateCircStr (<*n,f*>,'&'))) \/ (InnerVertices (1GateCircStr (<*f,g*>,'&'))))) is set
{[<*n,f*>,'&']} \/ (InnerVertices (1GateCircStr (<*f,g*>,'&'))) is non empty set
(InputVertices (1GateCircStr (<*g,n*>,'&'))) \ ({[<*n,f*>,'&']} \/ (InnerVertices (1GateCircStr (<*f,g*>,'&')))) is Element of K23( the carrier of (1GateCircStr (<*g,n*>,'&')))
((((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']})) \ {[<*g,n*>,'&']}) \/ ((InputVertices (1GateCircStr (<*g,n*>,'&'))) \ ({[<*n,f*>,'&']} \/ (InnerVertices (1GateCircStr (<*f,g*>,'&'))))) is set
{[<*n,f*>,'&']} \/ {[<*f,g*>,'&']} is non empty Relation-like V39() V54() set
(InputVertices (1GateCircStr (<*g,n*>,'&'))) \ ({[<*n,f*>,'&']} \/ {[<*f,g*>,'&']}) is Element of K23( the carrier of (1GateCircStr (<*g,n*>,'&')))
((((InputVertices (1GateCircStr (<*n,f*>,'&'))) \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']})) \ {[<*g,n*>,'&']}) \/ ((InputVertices (1GateCircStr (<*g,n*>,'&'))) \ ({[<*n,f*>,'&']} \/ {[<*f,g*>,'&']})) is set
{n,f} is non empty V39() V54() set
{n,f} \ {[<*f,g*>,'&']} is V39() V54() Element of K23({n,f})
K23({n,f}) is non empty V39() V43() V54() set
({n,f} \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']}) is set
(({n,f} \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']})) \ {[<*g,n*>,'&']} is Element of K23((({n,f} \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']})))
K23((({n,f} \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']}))) is non empty set
((({n,f} \ {[<*f,g*>,'&']}) \/ ((InputVertices (1GateCircStr (<*f,g*>,'&'))) \ {[<*n,f*>,'&']})) \ {[<*g,n*>,'&']}) \/ ((InputVertices (1GateCircStr (<*g,n*>,'&'))) \ ({[<*n,f*>,'&']} \/ {[<*f,g*>,'&']})) is set
{f,g} \ {[<*n,f*>,'&']} is V39() V54() Element of K23({f,g})
K23({f,g}) is non empty V39() V43() V54() set
({n,f} \ {[<*f,g*>,'&']}) \/ ({f,g} \ {[<*n,f*>,'&']}) is V39() V54() set
(({n,f} \ {[<*f,g*>,'&']}) \/ ({f,g} \ {[<*n,f*>,'&']})) \ {[<*g,n*>,'&']} is V39() V54() Element of K23((({n,f} \ {[<*f,g*>,'&']}) \/ ({f,g} \ {[<*n,f*>,'&']})))
K23((({n,f} \ {[<*f,g*>,'&']}) \/ ({f,g} \ {[<*n,f*>,'&']}))) is non empty V39() V43() V54() set
((({n,f} \ {[<*f,g*>,'&']}) \/ ({f,g} \ {[<*n,f*>,'&']})) \ {[<*g,n*>,'&']}) \/ ((InputVertices (1GateCircStr (<*g,n*>,'&'))) \ ({[<*n,f*>,'&']} \/ {[<*f,g*>,'&']})) is set
{g,n} is non empty V39() V54() set
{g,n} \ ({[<*n,f*>,'&']} \/ {[<*f,g*>,'&']}) is V39() V54() Element of K23({g,n})
K23({g,n}) is non empty V39() V43() V54() set
((({n,f} \ {[<*f,g*>,'&']}) \/ ({f,g} \ {[<*n,f*>,'&']})) \ {[<*g,n*>,'&']}) \/ ({g,n} \ ({[<*n,f*>,'&']} \/ {[<*f,g*>,'&']})) is V39() V54() set
{g,n} \ {[<*n,f*>,'&'],[<*f,g*>,'&']} is V39() V54() Element of K23({g,n})
((({n,f} \ {[<*f,g*>,'&']}) \/ ({f,g} \ {[<*n,f*>,'&']})) \ {[<*g,n*>,'&']}) \/ ({g,n} \ {[<*n,f*>,'&'],[<*f,g*>,'&']}) is V39() V54() set
{n,f} \/ ({f,g} \ {[<*n,f*>,'&']}) is non empty V39() V54() set
({n,f} \/ ({f,g} \ {[<*n,f*>,'&']})) \ {[<*g,n*>,'&']} is V39() V54() Element of K23(({n,f} \/ ({f,g} \ {[<*n,f*>,'&']})))
K23(({n,f} \/ ({f,g} \ {[<*n,f*>,'&']}))) is non empty V39() V43() V54() set
(({n,f} \/ ({f,g} \ {[<*n,f*>,'&']})) \ {[<*g,n*>,'&']}) \/ ({g,n} \ {[<*n,f*>,'&'],[<*f,g*>,'&']}) is V39() V54() set
{n,f} \/ {f,g} is non empty V39() V54() set
({n,f} \/ {f,g}) \ {[<*g,n*>,'&']} is V39() V54() Element of K23(({n,f} \/ {f,g}))
K23(({n,f} \/ {f,g})) is non empty V39() V43() V54() set
(({n,f} \/ {f,g}) \ {[<*g,n*>,'&']}) \/ ({g,n} \ {[<*n,f*>,'&'],[<*f,g*>,'&']}) is V39() V54() set
(({n,f} \/ {f,g}) \ {[<*g,n*>,'&']}) \/ {g,n} is non empty V39() V54() set
{n,f,f,g} is non empty V39() V54() set
{n,f,f,g} \ {[<*g,n*>,'&']} is V39() V54() Element of K23({n,f,f,g})
K23({n,f,f,g}) is non empty V39() V43() V54() set
({n,f,f,g} \ {[<*g,n*>,'&']}) \/ {g,n} is non empty V39() V54() set
{f,f,n,g} is non empty V39() V54() set
{f,f,n,g} \ {[<*g,n*>,'&']} is V39() V54() Element of K23({f,f,n,g})
K23({f,f,n,g}) is non empty V39() V43() V54() set
({f,f,n,g} \ {[<*g,n*>,'&']}) \/ {g,n} is non empty V39() V54() set
{f,n,g} is non empty V39() V54() set
{f,n,g} \ {[<*g,n*>,'&']} is V39() V54() Element of K23({f,n,g})
K23({f,n,g}) is non empty V39() V43() V54() set
({f,n,g} \ {[<*g,n*>,'&']}) \/ {g,n} is non empty V39() V54() set
{n,f,g} \ {[<*g,n*>,'&']} is V39() V54() Element of K23({n,f,g})
K23({n,f,g}) is non empty V39() V43() V54() set
({n,f,g} \ {[<*g,n*>,'&']}) \/ {g,n} is non empty V39() V54() set
{n,f,g} \/ {g,n} is non empty V39() V54() set
{n,f,g,g,n} is non empty V39() V54() set
{n,f,g,g} is non empty V39() V54() set
{n} is non empty V5() V39() 1 -element V54() set
{n,f,g,g} \/ {n} is non empty V39() V54() set
{g,g,n,f} is non empty V39() V54() set
{g,g,n,f} \/ {n} is non empty V39() V54() set
{g,n,f} is non empty V39() V54() set
{g,n,f} \/ {n} is non empty V39() V54() set
{g,n,f,n} is non empty V39() V54() set
{n,n,f,g} is non empty V39() V54() set
n is set
f is set
g is set
MajorityStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,f*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*n,f*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f,g*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*f,g*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*g,n*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*g,n*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*n,f*>,'&'] is non empty pair set
{<*n,f*>,'&'} is non empty functional V39() V54() set
{<*n,f*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*n,f*>,'&'},{<*n,f*>}} is non empty V39() V43() V54() set
[<*f,g*>,'&'] is non empty pair set
{<*f,g*>,'&'} is non empty functional V39() V54() set
{<*f,g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*f,g*>,'&'},{<*f,g*>}} is non empty V39() V43() V54() set
[<*g,n*>,'&'] is non empty pair set
{<*g,n*>,'&'} is non empty functional V39() V54() set
{<*g,n*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g,n*>,'&'},{<*g,n*>}} is non empty V39() V43() V54() set
<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (MajorityStr (n,f,g)) is non empty Element of K23( the carrier of (MajorityStr (n,f,g)))
the carrier of (MajorityStr (n,f,g)) is non empty set
K23( the carrier of (MajorityStr (n,f,g))) is non empty set
the ResultSort of (MajorityStr (n,f,g)) is Relation-like the carrier' of (MajorityStr (n,f,g)) -defined the carrier of (MajorityStr (n,f,g)) -valued Function-like V30( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) Element of K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))))
the carrier' of (MajorityStr (n,f,g)) is non empty set
K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g)))) is non empty set
K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
{[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']} is non empty Relation-like V39() V54() set
MajorityOutput (n,f,g) is Element of InnerVertices (MajorityStr (n,f,g))
[<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3] is non empty pair set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3},{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>}} is non empty V39() V43() V54() set
{(MajorityOutput (n,f,g))} is non empty V5() V39() 1 -element V54() set
{[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']} \/ {(MajorityOutput (n,f,g))} is non empty V39() V54() set
(1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty Element of K23( the carrier of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))))
the carrier of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty set
K23( the carrier of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))) is non empty set
the ResultSort of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is Relation-like the carrier' of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) -defined the carrier of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) -valued Function-like V30( the carrier' of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))), the carrier of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))) Element of K23(K24( the carrier' of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))), the carrier of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))))
the carrier' of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty set
K24( the carrier' of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))), the carrier of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))) is non empty Relation-like set
K23(K24( the carrier' of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))), the carrier of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))))) is non empty set
K497( the carrier of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))), the ResultSort of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))) is Element of K23( the carrier of ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))))
InnerVertices (1GateCircStr (<*f,g*>,'&')) is non empty Element of K23( the carrier of (1GateCircStr (<*f,g*>,'&')))
the carrier of (1GateCircStr (<*f,g*>,'&')) is non empty set
K23( the carrier of (1GateCircStr (<*f,g*>,'&'))) is non empty set
the ResultSort of (1GateCircStr (<*f,g*>,'&')) is Relation-like the carrier' of (1GateCircStr (<*f,g*>,'&')) -defined the carrier of (1GateCircStr (<*f,g*>,'&')) -valued Function-like V30( the carrier' of (1GateCircStr (<*f,g*>,'&')), the carrier of (1GateCircStr (<*f,g*>,'&'))) Element of K23(K24( the carrier' of (1GateCircStr (<*f,g*>,'&')), the carrier of (1GateCircStr (<*f,g*>,'&'))))
the carrier' of (1GateCircStr (<*f,g*>,'&')) is non empty set
K24( the carrier' of (1GateCircStr (<*f,g*>,'&')), the carrier of (1GateCircStr (<*f,g*>,'&'))) is non empty Relation-like set
K23(K24( the carrier' of (1GateCircStr (<*f,g*>,'&')), the carrier of (1GateCircStr (<*f,g*>,'&')))) is non empty set
K497( the carrier of (1GateCircStr (<*f,g*>,'&')), the ResultSort of (1GateCircStr (<*f,g*>,'&'))) is Element of K23( the carrier of (1GateCircStr (<*f,g*>,'&')))
InnerVertices ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty Element of K23( the carrier of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))
the carrier of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty set
K23( the carrier of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty set
the ResultSort of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is Relation-like the carrier' of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) -defined the carrier of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) -valued Function-like V30( the carrier' of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))), the carrier of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) Element of K23(K24( the carrier' of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))), the carrier of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))))
the carrier' of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty set
K24( the carrier' of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))), the carrier of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty Relation-like set
K23(K24( the carrier' of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))), the carrier of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))) is non empty set
K497( the carrier of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))), the ResultSort of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is Element of K23( the carrier of ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))
(InnerVertices (1GateCircStr (<*f,g*>,'&'))) \/ (InnerVertices ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty set
InnerVertices (1GateCircStr (<*g,n*>,'&')) is non empty Element of K23( the carrier of (1GateCircStr (<*g,n*>,'&')))
the carrier of (1GateCircStr (<*g,n*>,'&')) is non empty set
K23( the carrier of (1GateCircStr (<*g,n*>,'&'))) is non empty set
the ResultSort of (1GateCircStr (<*g,n*>,'&')) is Relation-like the carrier' of (1GateCircStr (<*g,n*>,'&')) -defined the carrier of (1GateCircStr (<*g,n*>,'&')) -valued Function-like V30( the carrier' of (1GateCircStr (<*g,n*>,'&')), the carrier of (1GateCircStr (<*g,n*>,'&'))) Element of K23(K24( the carrier' of (1GateCircStr (<*g,n*>,'&')), the carrier of (1GateCircStr (<*g,n*>,'&'))))
the carrier' of (1GateCircStr (<*g,n*>,'&')) is non empty set
K24( the carrier' of (1GateCircStr (<*g,n*>,'&')), the carrier of (1GateCircStr (<*g,n*>,'&'))) is non empty Relation-like set
K23(K24( the carrier' of (1GateCircStr (<*g,n*>,'&')), the carrier of (1GateCircStr (<*g,n*>,'&')))) is non empty set
K497( the carrier of (1GateCircStr (<*g,n*>,'&')), the ResultSort of (1GateCircStr (<*g,n*>,'&'))) is Element of K23( the carrier of (1GateCircStr (<*g,n*>,'&')))
InnerVertices (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty Element of K23( the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))
the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty set
K23( the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty set
the ResultSort of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is Relation-like the carrier' of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) -defined the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) -valued Function-like V30( the carrier' of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) Element of K23(K24( the carrier' of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))
the carrier' of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty set
K24( the carrier' of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty Relation-like set
K23(K24( the carrier' of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty set
K497( the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)), the ResultSort of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is Element of K23( the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))
(InnerVertices (1GateCircStr (<*g,n*>,'&'))) \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty set
(1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty Element of K23( the carrier of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))
the carrier of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty set
K23( the carrier of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty set
the ResultSort of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is Relation-like the carrier' of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) -defined the carrier of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) -valued Function-like V30( the carrier' of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))), the carrier of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) Element of K23(K24( the carrier' of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))), the carrier of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))))
the carrier' of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty set
K24( the carrier' of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))), the carrier of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty Relation-like set
K23(K24( the carrier' of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))), the carrier of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))) is non empty set
K497( the carrier of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))), the ResultSort of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is Element of K23( the carrier of (((1GateCircStr (<*n,f*>,'&')) +* ((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&')))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))
(1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty Element of K23( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))))
the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty set
K23( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))) is non empty set
the ResultSort of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is Relation-like the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) -defined the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) -valued Function-like V30( the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))), the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))) Element of K23(K24( the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))), the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))))
the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty set
K24( the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))), the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))) is non empty Relation-like set
K23(K24( the carrier' of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))), the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))))) is non empty set
K497( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))), the ResultSort of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))) is Element of K23( the carrier of ((1GateCircStr (<*n,f*>,'&')) +* (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))))
InnerVertices (1GateCircStr (<*n,f*>,'&')) is non empty Element of K23( the carrier of (1GateCircStr (<*n,f*>,'&')))
the carrier of (1GateCircStr (<*n,f*>,'&')) is non empty set
K23( the carrier of (1GateCircStr (<*n,f*>,'&'))) is non empty set
the ResultSort of (1GateCircStr (<*n,f*>,'&')) is Relation-like the carrier' of (1GateCircStr (<*n,f*>,'&')) -defined the carrier of (1GateCircStr (<*n,f*>,'&')) -valued Function-like V30( the carrier' of (1GateCircStr (<*n,f*>,'&')), the carrier of (1GateCircStr (<*n,f*>,'&'))) Element of K23(K24( the carrier' of (1GateCircStr (<*n,f*>,'&')), the carrier of (1GateCircStr (<*n,f*>,'&'))))
the carrier' of (1GateCircStr (<*n,f*>,'&')) is non empty set
K24( the carrier' of (1GateCircStr (<*n,f*>,'&')), the carrier of (1GateCircStr (<*n,f*>,'&'))) is non empty Relation-like set
K23(K24( the carrier' of (1GateCircStr (<*n,f*>,'&')), the carrier of (1GateCircStr (<*n,f*>,'&')))) is non empty set
K497( the carrier of (1GateCircStr (<*n,f*>,'&')), the ResultSort of (1GateCircStr (<*n,f*>,'&'))) is Element of K23( the carrier of (1GateCircStr (<*n,f*>,'&')))
InnerVertices (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty Element of K23( the carrier of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))
the carrier of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty set
K23( the carrier of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty set
the ResultSort of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is Relation-like the carrier' of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) -defined the carrier of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) -valued Function-like V30( the carrier' of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))), the carrier of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) Element of K23(K24( the carrier' of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))), the carrier of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))))
the carrier' of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty set
K24( the carrier' of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))), the carrier of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty Relation-like set
K23(K24( the carrier' of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))), the carrier of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))) is non empty set
K497( the carrier of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))), the ResultSort of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is Element of K23( the carrier of (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))
(InnerVertices (1GateCircStr (<*n,f*>,'&'))) \/ (InnerVertices (((1GateCircStr (<*f,g*>,'&')) +* (1GateCircStr (<*g,n*>,'&'))) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty set
(InnerVertices (1GateCircStr (<*n,f*>,'&'))) \/ (InnerVertices ((1GateCircStr (<*f,g*>,'&')) +* ((1GateCircStr (<*g,n*>,'&')) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))) is non empty set
(InnerVertices (1GateCircStr (<*n,f*>,'&'))) \/ (InnerVertices (1GateCircStr (<*f,g*>,'&'))) is non empty set
((InnerVertices (1GateCircStr (<*n,f*>,'&'))) \/ (InnerVertices (1GateCircStr (<*f,g*>,'&')))) \/ ((InnerVertices (1GateCircStr (<*g,n*>,'&'))) \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty set
((InnerVertices (1GateCircStr (<*n,f*>,'&'))) \/ (InnerVertices (1GateCircStr (<*f,g*>,'&')))) \/ (InnerVertices (1GateCircStr (<*g,n*>,'&'))) is non empty set
(((InnerVertices (1GateCircStr (<*n,f*>,'&'))) \/ (InnerVertices (1GateCircStr (<*f,g*>,'&')))) \/ (InnerVertices (1GateCircStr (<*g,n*>,'&')))) \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty set
{[<*n,f*>,'&']} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
{[<*n,f*>,'&']} \/ (InnerVertices (1GateCircStr (<*f,g*>,'&'))) is non empty set
({[<*n,f*>,'&']} \/ (InnerVertices (1GateCircStr (<*f,g*>,'&')))) \/ (InnerVertices (1GateCircStr (<*g,n*>,'&'))) is non empty set
(({[<*n,f*>,'&']} \/ (InnerVertices (1GateCircStr (<*f,g*>,'&')))) \/ (InnerVertices (1GateCircStr (<*g,n*>,'&')))) \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty set
{[<*f,g*>,'&']} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
{[<*n,f*>,'&']} \/ {[<*f,g*>,'&']} is non empty Relation-like V39() V54() set
({[<*n,f*>,'&']} \/ {[<*f,g*>,'&']}) \/ (InnerVertices (1GateCircStr (<*g,n*>,'&'))) is non empty set
(({[<*n,f*>,'&']} \/ {[<*f,g*>,'&']}) \/ (InnerVertices (1GateCircStr (<*g,n*>,'&')))) \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty set
{[<*g,n*>,'&']} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
({[<*n,f*>,'&']} \/ {[<*f,g*>,'&']}) \/ {[<*g,n*>,'&']} is non empty Relation-like V39() V54() set
(({[<*n,f*>,'&']} \/ {[<*f,g*>,'&']}) \/ {[<*g,n*>,'&']}) \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty set
{[<*n,f*>,'&'],[<*f,g*>,'&']} is non empty Relation-like V39() V54() set
{[<*n,f*>,'&'],[<*f,g*>,'&']} \/ {[<*g,n*>,'&']} is non empty Relation-like V39() V54() set
({[<*n,f*>,'&'],[<*f,g*>,'&']} \/ {[<*g,n*>,'&']}) \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty set
{[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']} \/ (InnerVertices (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*f,g*>,'&'] is non empty pair set
{<*f,g*>,'&'} is non empty functional V39() V54() set
{<*f,g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*f,g*>,'&'},{<*f,g*>}} is non empty V39() V43() V54() set
<*g,n*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*g,n*>,'&'] is non empty pair set
{<*g,n*>,'&'} is non empty functional V39() V54() set
{<*g,n*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g,n*>,'&'},{<*g,n*>}} is non empty V39() V43() V54() set
<*n,f*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*n,f*>,'&'] is non empty pair set
{<*n,f*>,'&'} is non empty functional V39() V54() set
{<*n,f*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*n,f*>,'&'},{<*n,f*>}} is non empty V39() V43() V54() set
MajorityStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*f,g*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*g,n*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (MajorityStr (n,f,g)) is Element of K23( the carrier of (MajorityStr (n,f,g)))
the carrier of (MajorityStr (n,f,g)) is non empty set
K23( the carrier of (MajorityStr (n,f,g))) is non empty set
the ResultSort of (MajorityStr (n,f,g)) is Relation-like the carrier' of (MajorityStr (n,f,g)) -defined the carrier of (MajorityStr (n,f,g)) -valued Function-like V30( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) Element of K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))))
the carrier' of (MajorityStr (n,f,g)) is non empty set
K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g)))) is non empty set
K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
the carrier of (MajorityStr (n,f,g)) \ K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
{n,f,g} is non empty V39() V54() set
InnerVertices (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty Element of K23( the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))
the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty set
K23( the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty set
the ResultSort of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is Relation-like the carrier' of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) -defined the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) -valued Function-like V30( the carrier' of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) Element of K23(K24( the carrier' of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))))
the carrier' of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty set
K24( the carrier' of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is non empty Relation-like set
K23(K24( the carrier' of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)), the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) is non empty set
K497( the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)), the ResultSort of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is Element of K23( the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))
[<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3] is non empty pair set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3},{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>}} is non empty V39() V43() V54() set
{[<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3]} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
InputVertices (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is Element of K23( the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))
the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) \ K497( the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)), the ResultSort of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is Element of K23( the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))
proj2 <*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> is non empty V39() V54() set
{[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']} is non empty Relation-like V39() V54() set
proj2 <*g,n*> is non empty V39() V54() set
{g,n} is non empty V39() V54() set
len <*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
Seg 3 is non empty V39() 3 -element V54() Element of K23(NAT)
dom <*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> is non empty V39() 3 -element V54() Element of K23(NAT)
<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> . 3 is set
[3,[<*g,n*>,'&']] is non empty pair set
{3,[<*g,n*>,'&']} is non empty V39() V54() set
{3} is non empty V5() V39() V43() 1 -element V54() non with_pair set
{{3,[<*g,n*>,'&']},{3}} is non empty V39() V43() V54() set
the_rank_of [<*g,n*>,'&'] is V12() V13() V14() set
the_rank_of [<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3] is V12() V13() V14() set
proj2 <*n,f*> is non empty V39() V54() set
{n,f} is non empty V39() V54() set
<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> . 1 is set
[1,[<*n,f*>,'&']] is non empty pair set
{1,[<*n,f*>,'&']} is non empty V39() V54() set
{1} is non empty V5() V39() V43() 1 -element V54() non with_pair set
{{1,[<*n,f*>,'&']},{1}} is non empty V39() V43() V54() set
the_rank_of [<*n,f*>,'&'] is V12() V13() V14() set
proj2 <*f,g*> is non empty V39() V54() set
{f,g} is non empty V39() V54() set
<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> . 2 is set
[2,[<*f,g*>,'&']] is non empty pair set
{2,[<*f,g*>,'&']} is non empty V39() V54() set
{2} is non empty V5() V39() V43() 1 -element V54() non with_pair set
{{2,[<*f,g*>,'&']},{2}} is non empty V39() V43() V54() set
the_rank_of [<*f,g*>,'&'] is V12() V13() V14() set
{[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']} \ {[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']} is Relation-like V39() V54() Element of K23({[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']})
K23({[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']}) is non empty V39() V43() V54() set
{n,f,g} \ {[<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3]} is V39() V54() Element of K23({n,f,g})
K23({n,f,g}) is non empty V39() V43() V54() set
An is set
the carrier of (MajorityIStr (n,f,g)) is non empty set
InputVertices (MajorityIStr (n,f,g)) is Element of K23( the carrier of (MajorityIStr (n,f,g)))
K23( the carrier of (MajorityIStr (n,f,g))) is non empty set
the ResultSort of (MajorityIStr (n,f,g)) is Relation-like the carrier' of (MajorityIStr (n,f,g)) -defined the carrier of (MajorityIStr (n,f,g)) -valued Function-like V30( the carrier' of (MajorityIStr (n,f,g)), the carrier of (MajorityIStr (n,f,g))) Element of K23(K24( the carrier' of (MajorityIStr (n,f,g)), the carrier of (MajorityIStr (n,f,g))))
the carrier' of (MajorityIStr (n,f,g)) is non empty set
K24( the carrier' of (MajorityIStr (n,f,g)), the carrier of (MajorityIStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityIStr (n,f,g)), the carrier of (MajorityIStr (n,f,g)))) is non empty set
K497( the carrier of (MajorityIStr (n,f,g)), the ResultSort of (MajorityIStr (n,f,g))) is Element of K23( the carrier of (MajorityIStr (n,f,g)))
the carrier of (MajorityIStr (n,f,g)) \ K497( the carrier of (MajorityIStr (n,f,g)), the ResultSort of (MajorityIStr (n,f,g))) is Element of K23( the carrier of (MajorityIStr (n,f,g)))
(InputVertices (MajorityIStr (n,f,g))) \ (InnerVertices (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) is Element of K23( the carrier of (MajorityIStr (n,f,g)))
InnerVertices (MajorityIStr (n,f,g)) is non empty Element of K23( the carrier of (MajorityIStr (n,f,g)))
(InputVertices (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) \ (InnerVertices (MajorityIStr (n,f,g))) is Element of K23( the carrier of (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))
((InputVertices (MajorityIStr (n,f,g))) \ (InnerVertices (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)))) \/ ((InputVertices (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) \ (InnerVertices (MajorityIStr (n,f,g)))) is set
{[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']} \ (InnerVertices (MajorityIStr (n,f,g))) is Relation-like V39() V54() Element of K23({[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']})
{n,f,g} \/ ({[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']} \ (InnerVertices (MajorityIStr (n,f,g)))) is non empty V39() V54() set
{n,f,g} \/ {} is non empty V39() V54() set
n is non empty V74() ManySortedSign
f is non empty V74() ManySortedSign
InputVertices n is Element of K23( the carrier of n)
the carrier of n is non empty set
K23( the carrier of n) is non empty set
the ResultSort of n is Relation-like the carrier' of n -defined the carrier of n -valued Function-like V30( the carrier' of n, the carrier of n) Element of K23(K24( the carrier' of n, the carrier of n))
the carrier' of n is set
K24( the carrier' of n, the carrier of n) is Relation-like set
K23(K24( the carrier' of n, the carrier of n)) is non empty set
K497( the carrier of n, the ResultSort of n) is Element of K23( the carrier of n)
the carrier of n \ K497( the carrier of n, the ResultSort of n) is Element of K23( the carrier of n)
InputVertices f is Element of K23( the carrier of f)
the carrier of f is non empty set
K23( the carrier of f) is non empty set
the ResultSort of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V30( the carrier' of f, the carrier of f) Element of K23(K24( the carrier' of f, the carrier of f))
the carrier' of f is set
K24( the carrier' of f, the carrier of f) is Relation-like set
K23(K24( the carrier' of f, the carrier of f)) is non empty set
K497( the carrier of f, the ResultSort of f) is Element of K23( the carrier of f)
the carrier of f \ K497( the carrier of f, the ResultSort of f) is Element of K23( the carrier of f)
n +* f is non empty V74() strict ManySortedSign
InputVertices (n +* f) is Element of K23( the carrier of (n +* f))
the carrier of (n +* f) is non empty set
K23( the carrier of (n +* f)) is non empty set
the ResultSort of (n +* f) is Relation-like the carrier' of (n +* f) -defined the carrier of (n +* f) -valued Function-like V30( the carrier' of (n +* f), the carrier of (n +* f)) Element of K23(K24( the carrier' of (n +* f), the carrier of (n +* f)))
the carrier' of (n +* f) is set
K24( the carrier' of (n +* f), the carrier of (n +* f)) is Relation-like set
K23(K24( the carrier' of (n +* f), the carrier of (n +* f))) is non empty set
K497( the carrier of (n +* f), the ResultSort of (n +* f)) is Element of K23( the carrier of (n +* f))
the carrier of (n +* f) \ K497( the carrier of (n +* f), the ResultSort of (n +* f)) is Element of K23( the carrier of (n +* f))
InnerVertices n is Element of K23( the carrier of n)
InnerVertices f is Element of K23( the carrier of f)
(InputVertices n) \ (InnerVertices f) is Element of K23( the carrier of n)
(InputVertices f) \ (InnerVertices n) is Element of K23( the carrier of f)
((InputVertices n) \ (InnerVertices f)) \/ ((InputVertices f) \ (InnerVertices n)) is set
(InputVertices n) \/ ((InputVertices f) \ (InnerVertices n)) is set
(InputVertices n) \/ (InputVertices f) is set
n is set
f is set
g is set
<*f,g*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*f,g*>,'&'] is non empty pair set
{<*f,g*>,'&'} is non empty functional V39() V54() set
{<*f,g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*f,g*>,'&'},{<*f,g*>}} is non empty V39() V43() V54() set
<*g,n*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*g,n*>,'&'] is non empty pair set
{<*g,n*>,'&'} is non empty functional V39() V54() set
{<*g,n*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g,n*>,'&'},{<*g,n*>}} is non empty V39() V43() V54() set
<*n,f*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*n,f*>,'&'] is non empty pair set
{<*n,f*>,'&'} is non empty functional V39() V54() set
{<*n,f*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*n,f*>,'&'},{<*n,f*>}} is non empty V39() V43() V54() set
[<*n,f*>,'xor'] is non empty pair set
{<*n,f*>,'xor'} is non empty functional V39() V54() set
{{<*n,f*>,'xor'},{<*n,f*>}} is non empty V39() V43() V54() set
BitAdderWithOverflowStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (n,f,g,'xor') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,'xor') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*f,g*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*g,n*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (BitAdderWithOverflowStr (n,f,g)) is Element of K23( the carrier of (BitAdderWithOverflowStr (n,f,g)))
the carrier of (BitAdderWithOverflowStr (n,f,g)) is non empty set
K23( the carrier of (BitAdderWithOverflowStr (n,f,g))) is non empty set
the ResultSort of (BitAdderWithOverflowStr (n,f,g)) is Relation-like the carrier' of (BitAdderWithOverflowStr (n,f,g)) -defined the carrier of (BitAdderWithOverflowStr (n,f,g)) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr (n,f,g)), the carrier of (BitAdderWithOverflowStr (n,f,g))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr (n,f,g)), the carrier of (BitAdderWithOverflowStr (n,f,g))))
the carrier' of (BitAdderWithOverflowStr (n,f,g)) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr (n,f,g)), the carrier of (BitAdderWithOverflowStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr (n,f,g)), the carrier of (BitAdderWithOverflowStr (n,f,g)))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr (n,f,g)), the ResultSort of (BitAdderWithOverflowStr (n,f,g))) is Element of K23( the carrier of (BitAdderWithOverflowStr (n,f,g)))
the carrier of (BitAdderWithOverflowStr (n,f,g)) \ K497( the carrier of (BitAdderWithOverflowStr (n,f,g)), the ResultSort of (BitAdderWithOverflowStr (n,f,g))) is Element of K23( the carrier of (BitAdderWithOverflowStr (n,f,g)))
{n,f,g} is non empty V39() V54() set
InputVertices (2GatesCircStr (n,f,g,'xor')) is Element of K23( the carrier of (2GatesCircStr (n,f,g,'xor')))
the carrier of (2GatesCircStr (n,f,g,'xor')) is non empty set
K23( the carrier of (2GatesCircStr (n,f,g,'xor'))) is non empty set
the ResultSort of (2GatesCircStr (n,f,g,'xor')) is Relation-like the carrier' of (2GatesCircStr (n,f,g,'xor')) -defined the carrier of (2GatesCircStr (n,f,g,'xor')) -valued Function-like V30( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) Element of K23(K24( 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
K24( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) is non empty Relation-like set
K23(K24( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor')))) is non empty set
K497( the carrier of (2GatesCircStr (n,f,g,'xor')), the ResultSort of (2GatesCircStr (n,f,g,'xor'))) is Element of K23( the carrier of (2GatesCircStr (n,f,g,'xor')))
the carrier of (2GatesCircStr (n,f,g,'xor')) \ K497( the carrier of (2GatesCircStr (n,f,g,'xor')), the ResultSort of (2GatesCircStr (n,f,g,'xor'))) is Element of K23( the carrier of (2GatesCircStr (n,f,g,'xor')))
InputVertices (MajorityStr (n,f,g)) is Element of K23( the carrier of (MajorityStr (n,f,g)))
the carrier of (MajorityStr (n,f,g)) is non empty set
K23( the carrier of (MajorityStr (n,f,g))) is non empty set
the ResultSort of (MajorityStr (n,f,g)) is Relation-like the carrier' of (MajorityStr (n,f,g)) -defined the carrier of (MajorityStr (n,f,g)) -valued Function-like V30( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) Element of K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))))
the carrier' of (MajorityStr (n,f,g)) is non empty set
K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g)))) is non empty set
K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
the carrier of (MajorityStr (n,f,g)) \ K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
n is set
f is set
g is set
BitAdderWithOverflowStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (n,f,g,'xor') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,f*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*n,f*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*n,f*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*n,f*>,'xor'},{<*n,f*>}} is non empty V39() V43() V54() set
<*[<*n,f*>,'xor'],g*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f,g*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*f,g*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*g,n*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*g,n*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*n,f*>,'&'] is non empty pair set
{<*n,f*>,'&'} is non empty functional V39() V54() set
{{<*n,f*>,'&'},{<*n,f*>}} is non empty V39() V43() V54() set
[<*f,g*>,'&'] is non empty pair set
{<*f,g*>,'&'} is non empty functional V39() V54() set
{<*f,g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*f,g*>,'&'},{<*f,g*>}} is non empty V39() V43() V54() set
[<*g,n*>,'&'] is non empty pair set
{<*g,n*>,'&'} is non empty functional V39() V54() set
{<*g,n*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g,n*>,'&'},{<*g,n*>}} is non empty V39() V43() V54() set
<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitAdderWithOverflowStr (n,f,g)) is non empty Element of K23( the carrier of (BitAdderWithOverflowStr (n,f,g)))
the carrier of (BitAdderWithOverflowStr (n,f,g)) is non empty set
K23( the carrier of (BitAdderWithOverflowStr (n,f,g))) is non empty set
the ResultSort of (BitAdderWithOverflowStr (n,f,g)) is Relation-like the carrier' of (BitAdderWithOverflowStr (n,f,g)) -defined the carrier of (BitAdderWithOverflowStr (n,f,g)) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr (n,f,g)), the carrier of (BitAdderWithOverflowStr (n,f,g))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr (n,f,g)), the carrier of (BitAdderWithOverflowStr (n,f,g))))
the carrier' of (BitAdderWithOverflowStr (n,f,g)) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr (n,f,g)), the carrier of (BitAdderWithOverflowStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr (n,f,g)), the carrier of (BitAdderWithOverflowStr (n,f,g)))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr (n,f,g)), the ResultSort of (BitAdderWithOverflowStr (n,f,g))) is Element of K23( the carrier of (BitAdderWithOverflowStr (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 K23( the carrier of (2GatesCircStr (n,f,g,'xor')))
K23( the carrier of (2GatesCircStr (n,f,g,'xor'))) is non empty set
the ResultSort of (2GatesCircStr (n,f,g,'xor')) is Relation-like the carrier' of (2GatesCircStr (n,f,g,'xor')) -defined the carrier of (2GatesCircStr (n,f,g,'xor')) -valued Function-like V30( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) Element of K23(K24( 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
K24( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) is non empty Relation-like set
K23(K24( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor')))) is non empty set
K497( the carrier of (2GatesCircStr (n,f,g,'xor')), the ResultSort of (2GatesCircStr (n,f,g,'xor'))) is Element of K23( 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 V39() V54() set
{<*[<*n,f*>,'xor'],g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*n,f*>,'xor'],g*>,'xor'},{<*[<*n,f*>,'xor'],g*>}} is non empty V39() V43() V54() set
{[<*n,f*>,'xor'],(2GatesCircOutput (n,f,g,'xor'))} is non empty Relation-like V39() V54() set
{[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']} is non empty Relation-like V39() V54() set
{[<*n,f*>,'xor'],(2GatesCircOutput (n,f,g,'xor'))} \/ {[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']} is non empty Relation-like V39() V54() set
MajorityOutput (n,f,g) is Element of InnerVertices (MajorityStr (n,f,g))
the carrier of (MajorityStr (n,f,g)) is non empty set
InnerVertices (MajorityStr (n,f,g)) is non empty Element of K23( the carrier of (MajorityStr (n,f,g)))
K23( the carrier of (MajorityStr (n,f,g))) is non empty set
the ResultSort of (MajorityStr (n,f,g)) is Relation-like the carrier' of (MajorityStr (n,f,g)) -defined the carrier of (MajorityStr (n,f,g)) -valued Function-like V30( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) Element of K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))))
the carrier' of (MajorityStr (n,f,g)) is non empty set
K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g)))) is non empty set
K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
[<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3] is non empty pair set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3},{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>}} is non empty V39() V43() V54() set
{(MajorityOutput (n,f,g))} is non empty V5() V39() 1 -element V54() set
({[<*n,f*>,'xor'],(2GatesCircOutput (n,f,g,'xor'))} \/ {[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']}) \/ {(MajorityOutput (n,f,g))} is non empty V39() V54() set
(InnerVertices (2GatesCircStr (n,f,g,'xor'))) \/ (InnerVertices (MajorityStr (n,f,g))) is non empty set
{[<*n,f*>,'xor'],(2GatesCircOutput (n,f,g,'xor'))} \/ (InnerVertices (MajorityStr (n,f,g))) is non empty set
{[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']} \/ {(MajorityOutput (n,f,g))} is non empty V39() V54() set
{[<*n,f*>,'xor'],(2GatesCircOutput (n,f,g,'xor'))} \/ ({[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']} \/ {(MajorityOutput (n,f,g))}) is non empty V39() V54() set
n is set
n is Relation-like Function-like set
f is set
proj1 n is set
n . f is set
n is Relation-like Function-like nonpair-yielding set
f is set
n . f is set
proj1 n is set
proj1 n is set
proj1 n is set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
g is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
(n,f,g) is Element of InnerVertices (n,f,g)
(n,f,g) is non empty non void V74() 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 K23( the carrier of (n,f,g))
K23( the carrier of (n,f,g)) is non empty set
the ResultSort of (n,f,g) is Relation-like the carrier' of (n,f,g) -defined the carrier of (n,f,g) -valued Function-like V30( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K24( the carrier' of (n,f,g), the carrier of (n,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g))) is non empty set
K497( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K23( the carrier of (n,f,g))
(0,f,g) is Element of InnerVertices (0,f,g)
(0,f,g) is non empty non void V74() 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 K23( the carrier of (0,f,g))
K23( the carrier of (0,f,g)) is non empty set
the ResultSort of (0,f,g) is Relation-like the carrier' of (0,f,g) -defined the carrier of (0,f,g) -valued Function-like V30( the carrier' of (0,f,g), the carrier of (0,f,g)) Element of K23(K24( the carrier' of (0,f,g), the carrier of (0,f,g)))
the carrier' of (0,f,g) is non empty set
K24( the carrier' of (0,f,g), the carrier of (0,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (0,f,g), the carrier of (0,f,g))) is non empty set
K497( the carrier of (0,f,g), the ResultSort of (0,f,g)) is Element of K23( the carrier of (0,f,g))
S0 is Relation-like NAT -defined Function-like total set
S0 . 0 is set
S0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
(S0,f,g) is Element of InnerVertices (S0,f,g)
(S0,f,g) is non empty non void V74() 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 K23( the carrier of (S0,f,g))
K23( the carrier of (S0,f,g)) is non empty set
the ResultSort of (S0,f,g) is Relation-like the carrier' of (S0,f,g) -defined the carrier of (S0,f,g) -valued Function-like V30( the carrier' of (S0,f,g), the carrier of (S0,f,g)) Element of K23(K24( the carrier' of (S0,f,g), the carrier of (S0,f,g)))
the carrier' of (S0,f,g) is non empty set
K24( the carrier' of (S0,f,g), the carrier of (S0,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (S0,f,g), the carrier of (S0,f,g))) is non empty set
K497( the carrier of (S0,f,g), the ResultSort of (S0,f,g)) is Element of K23( the carrier of (S0,f,g))
S0 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
((S0 + 1),f,g) is Element of InnerVertices ((S0 + 1),f,g)
((S0 + 1),f,g) is non empty non void V74() 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 K23( the carrier of ((S0 + 1),f,g))
K23( the carrier of ((S0 + 1),f,g)) is non empty set
the ResultSort of ((S0 + 1),f,g) is Relation-like the carrier' of ((S0 + 1),f,g) -defined the carrier of ((S0 + 1),f,g) -valued Function-like V30( the carrier' of ((S0 + 1),f,g), the carrier of ((S0 + 1),f,g)) Element of K23(K24( 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
K24( the carrier' of ((S0 + 1),f,g), the carrier of ((S0 + 1),f,g)) is non empty Relation-like set
K23(K24( the carrier' of ((S0 + 1),f,g), the carrier of ((S0 + 1),f,g))) is non empty set
K497( the carrier of ((S0 + 1),f,g), the ResultSort of ((S0 + 1),f,g)) is Element of K23( the carrier of ((S0 + 1),f,g))
f . (S0 + 1) is set
g . (S0 + 1) is set
MajorityOutput ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)) is Element of InnerVertices (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))
MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)) is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (S0 + 1)),(S0,f,g)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&')) +* (1GateCircStr (<*(g . (S0 + 1)),(S0,f,g)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(S0,f,g),(f . (S0 + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(S0,f,g),(f . (S0 + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&')) +* (1GateCircStr (<*(g . (S0 + 1)),(S0,f,g)*>,'&'))) +* (1GateCircStr (<*(S0,f,g),(f . (S0 + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'] is non empty pair set
{<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'} is non empty functional V39() V54() set
{<*(f . (S0 + 1)),(g . (S0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'},{<*(f . (S0 + 1)),(g . (S0 + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (S0 + 1)),(S0,f,g)*>,'&'] is non empty pair set
{<*(g . (S0 + 1)),(S0,f,g)*>,'&'} is non empty functional V39() V54() set
{<*(g . (S0 + 1)),(S0,f,g)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (S0 + 1)),(S0,f,g)*>,'&'},{<*(g . (S0 + 1)),(S0,f,g)*>}} is non empty V39() V43() V54() set
[<*(S0,f,g),(f . (S0 + 1))*>,'&'] is non empty pair set
{<*(S0,f,g),(f . (S0 + 1))*>,'&'} is non empty functional V39() V54() set
{<*(S0,f,g),(f . (S0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(S0,f,g),(f . (S0 + 1))*>,'&'},{<*(S0,f,g),(f . (S0 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'],[<*(g . (S0 + 1)),(S0,f,g)*>,'&'],[<*(S0,f,g),(f . (S0 + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'],[<*(g . (S0 + 1)),(S0,f,g)*>,'&'],[<*(S0,f,g),(f . (S0 + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) +* (1GateCircStr (<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'],[<*(g . (S0 + 1)),(S0,f,g)*>,'&'],[<*(S0,f,g),(f . (S0 + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty set
InnerVertices (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty Element of K23( the carrier of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))))
K23( the carrier of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) is non empty set
the ResultSort of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is Relation-like the carrier' of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) -defined the carrier of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) -valued Function-like V30( the carrier' of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) Element of K23(K24( the carrier' of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))))
the carrier' of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))) is non empty set
K24( the carrier' of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the carrier of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))))) is non empty set
K497( the carrier of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))), the ResultSort of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g)))) is Element of K23( the carrier of (MajorityStr ((f . (S0 + 1)),(g . (S0 + 1)),(S0,f,g))))
[<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'],[<*(g . (S0 + 1)),(S0,f,g)*>,'&'],[<*(S0,f,g),(f . (S0 + 1))*>,'&']*>,or3] is non empty pair set
{<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'],[<*(g . (S0 + 1)),(S0,f,g)*>,'&'],[<*(S0,f,g),(f . (S0 + 1))*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'],[<*(g . (S0 + 1)),(S0,f,g)*>,'&'],[<*(S0,f,g),(f . (S0 + 1))*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'],[<*(g . (S0 + 1)),(S0,f,g)*>,'&'],[<*(S0,f,g),(f . (S0 + 1))*>,'&']*>,or3},{<*[<*(f . (S0 + 1)),(g . (S0 + 1))*>,'&'],[<*(g . (S0 + 1)),(S0,f,g)*>,'&'],[<*(S0,f,g),(f . (S0 + 1))*>,'&']*>}} is non empty V39() V43() V54() set
n is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
f is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
proj1 ((0 -tuples_on BOOLEAN) --> FALSE) is set
(0,n,f) is non empty pair Element of InnerVertices (0,n,f)
(0,n,f) is non empty non void V74() 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 K23( the carrier of (0,n,f))
K23( the carrier of (0,n,f)) is non empty set
the ResultSort of (0,n,f) is Relation-like the carrier' of (0,n,f) -defined the carrier of (0,n,f) -valued Function-like V30( the carrier' of (0,n,f), the carrier of (0,n,f)) Element of K23(K24( the carrier' of (0,n,f), the carrier of (0,n,f)))
the carrier' of (0,n,f) is non empty set
K24( the carrier' of (0,n,f), the carrier of (0,n,f)) is non empty Relation-like set
K23(K24( the carrier' of (0,n,f), the carrier of (0,n,f))) is non empty set
K497( the carrier of (0,n,f), the ResultSort of (0,n,f)) is Element of K23( 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 V12() V13() V14() cardinal set
g is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
(g,n,f) is non empty pair Element of InnerVertices (g,n,f)
(g,n,f) is non empty non void V74() 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 K23( the carrier of (g,n,f))
K23( the carrier of (g,n,f)) is non empty set
the ResultSort of (g,n,f) is Relation-like the carrier' of (g,n,f) -defined the carrier of (g,n,f) -valued Function-like V30( the carrier' of (g,n,f), the carrier of (g,n,f)) Element of K23(K24( the carrier' of (g,n,f), the carrier of (g,n,f)))
the carrier' of (g,n,f) is non empty set
K24( the carrier' of (g,n,f), the carrier of (g,n,f)) is non empty Relation-like set
K23(K24( the carrier' of (g,n,f), the carrier of (g,n,f))) is non empty set
K497( the carrier of (g,n,f), the ResultSort of (g,n,f)) is Element of K23( 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 V12() V13() V14() cardinal set
g + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() 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 V74() 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 K23( the carrier of ((g + 1),n,f))
K23( the carrier of ((g + 1),n,f)) is non empty set
the ResultSort of ((g + 1),n,f) is Relation-like the carrier' of ((g + 1),n,f) -defined the carrier of ((g + 1),n,f) -valued Function-like V30( the carrier' of ((g + 1),n,f), the carrier of ((g + 1),n,f)) Element of K23(K24( 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
K24( the carrier' of ((g + 1),n,f), the carrier of ((g + 1),n,f)) is non empty Relation-like set
K23(K24( the carrier' of ((g + 1),n,f), the carrier of ((g + 1),n,f))) is non empty set
K497( the carrier of ((g + 1),n,f), the ResultSort of ((g + 1),n,f)) is Element of K23( the carrier of ((g + 1),n,f))
n . (g + 1) is set
f . (g + 1) is set
MajorityOutput ((n . (g + 1)),(f . (g + 1)),(g,n,f)) is Element of InnerVertices (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)))
MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)) is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(n . (g + 1)),(f . (g + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (g + 1)),(g,n,f)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (g + 1)),(f . (g + 1))*>,'&')) +* (1GateCircStr (<*(f . (g + 1)),(g,n,f)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(g,n,f),(n . (g + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g,n,f),(n . (g + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (g + 1)),(f . (g + 1))*>,'&')) +* (1GateCircStr (<*(f . (g + 1)),(g,n,f)*>,'&'))) +* (1GateCircStr (<*(g,n,f),(n . (g + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (g + 1)),(f . (g + 1))*>,'&'] is non empty pair set
{<*(n . (g + 1)),(f . (g + 1))*>,'&'} is non empty functional V39() V54() set
{<*(n . (g + 1)),(f . (g + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(n . (g + 1)),(f . (g + 1))*>,'&'},{<*(n . (g + 1)),(f . (g + 1))*>}} is non empty V39() V43() V54() set
[<*(f . (g + 1)),(g,n,f)*>,'&'] is non empty pair set
{<*(f . (g + 1)),(g,n,f)*>,'&'} is non empty functional V39() V54() set
{<*(f . (g + 1)),(g,n,f)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (g + 1)),(g,n,f)*>,'&'},{<*(f . (g + 1)),(g,n,f)*>}} is non empty V39() V43() V54() set
[<*(g,n,f),(n . (g + 1))*>,'&'] is non empty pair set
{<*(g,n,f),(n . (g + 1))*>,'&'} is non empty functional V39() V54() set
{<*(g,n,f),(n . (g + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g,n,f),(n . (g + 1))*>,'&'},{<*(g,n,f),(n . (g + 1))*>}} is non empty V39() V43() V54() set
<*[<*(n . (g + 1)),(f . (g + 1))*>,'&'],[<*(f . (g + 1)),(g,n,f)*>,'&'],[<*(g,n,f),(n . (g + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . (g + 1)),(f . (g + 1))*>,'&'],[<*(f . (g + 1)),(g,n,f)*>,'&'],[<*(g,n,f),(n . (g + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))) +* (1GateCircStr (<*[<*(n . (g + 1)),(f . (g + 1))*>,'&'],[<*(f . (g + 1)),(g,n,f)*>,'&'],[<*(g,n,f),(n . (g + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))) is non empty set
InnerVertices (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))) is non empty Element of K23( the carrier of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))))
K23( the carrier of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)))) is non empty set
the ResultSort of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))) is Relation-like the carrier' of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))) -defined the carrier of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))) -valued Function-like V30( the carrier' of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))), the carrier of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)))) Element of K23(K24( the carrier' of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))), the carrier of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)))))
the carrier' of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))) is non empty set
K24( the carrier' of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))), the carrier of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))), the carrier of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))))) is non empty set
K497( the carrier of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))), the ResultSort of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f)))) is Element of K23( the carrier of (MajorityStr ((n . (g + 1)),(f . (g + 1)),(g,n,f))))
[<*[<*(n . (g + 1)),(f . (g + 1))*>,'&'],[<*(f . (g + 1)),(g,n,f)*>,'&'],[<*(g,n,f),(n . (g + 1))*>,'&']*>,or3] is non empty pair set
{<*[<*(n . (g + 1)),(f . (g + 1))*>,'&'],[<*(f . (g + 1)),(g,n,f)*>,'&'],[<*(g,n,f),(n . (g + 1))*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*(n . (g + 1)),(f . (g + 1))*>,'&'],[<*(f . (g + 1)),(g,n,f)*>,'&'],[<*(g,n,f),(n . (g + 1))*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(n . (g + 1)),(f . (g + 1))*>,'&'],[<*(f . (g + 1)),(g,n,f)*>,'&'],[<*(g,n,f),(n . (g + 1))*>,'&']*>,or3},{<*[<*(n . (g + 1)),(f . (g + 1))*>,'&'],[<*(f . (g + 1)),(g,n,f)*>,'&'],[<*(g,n,f),(n . (g + 1))*>,'&']*>}} is non empty V39() V43() V54() 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 V12() V13() V14() cardinal set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
g is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
(n,f,g) is non empty pair Element of InnerVertices (n,f,g)
(n,f,g) is non empty non void V74() 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 K23( the carrier of (n,f,g))
K23( the carrier of (n,f,g)) is non empty set
the ResultSort of (n,f,g) is Relation-like the carrier' of (n,f,g) -defined the carrier of (n,f,g) -valued Function-like V30( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K24( the carrier' of (n,f,g), the carrier of (n,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g))) is non empty set
K497( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K23( the carrier of (n,f,g))
S0 is set
[S0,'&'] is non empty pair set
{S0,'&'} is non empty V39() V54() set
{S0} is non empty V5() V39() 1 -element V54() set
{{S0,'&'},{S0}} is non empty V39() V43() V54() set
[S0,'xor'] is non empty pair set
{S0,'xor'} is non empty V39() V54() set
{{S0,'xor'},{S0}} is non empty V39() V43() V54() set
proj1 '&' is set
proj1 'xor' is set
[S0,'&'] `2 is set
proj1 ([S0,'&'] `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 V39() FinSequence-like FinSubsequence-like V54() nonpair-yielding set
f is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() nonpair-yielding set
g is Relation-like NAT -defined Function-like total set
(0,n,f) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices H₁( 0 ) is non empty Element of K23( the carrier of H₁( 0 ))
the carrier of H₁( 0 ) is non empty set
K23( the carrier of H₁( 0 )) is non empty set
the carrier of (0,n,f) is non empty set
the ResultSort of (0,n,f) is Relation-like the carrier' of (0,n,f) -defined the carrier of (0,n,f) -valued Function-like V30( the carrier' of (0,n,f), the carrier of (0,n,f)) Element of K23(K24( the carrier' of (0,n,f), the carrier of (0,n,f)))
the carrier' of (0,n,f) is non empty set
K24( the carrier' of (0,n,f), the carrier of (0,n,f)) is non empty Relation-like set
K23(K24( the carrier' of (0,n,f), the carrier of (0,n,f))) is non empty set
K497( the carrier of (0,n,f), the ResultSort of (0,n,f)) is Element of K23( the carrier of (0,n,f))
K23( the carrier of (0,n,f)) is non empty set
InputVertices H₁( 0 ) is Element of K23( the carrier of H₁( 0 ))
the carrier of (0,n,f) \ K497( the carrier of (0,n,f), the ResultSort of (0,n,f)) is Element of K23( 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 K23( the carrier of (0,n,f))
A0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
A0 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n . (A0 + 1) is non pair set
f . (A0 + 1) is non pair set
N is set
BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],N*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],N*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (A0 + 1)),N*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&')) +* (1GateCircStr (<*(f . (A0 + 1)),N*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*N,(n . (A0 + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*N,(n . (A0 + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&')) +* (1GateCircStr (<*(f . (A0 + 1)),N*>,'&'))) +* (1GateCircStr (<*N,(n . (A0 + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V39() V43() V54() set
[<*(f . (A0 + 1)),N*>,'&'] is non empty pair set
{<*(f . (A0 + 1)),N*>,'&'} is non empty functional V39() V54() set
{<*(f . (A0 + 1)),N*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (A0 + 1)),N*>,'&'},{<*(f . (A0 + 1)),N*>}} is non empty V39() V43() V54() set
[<*N,(n . (A0 + 1))*>,'&'] is non empty pair set
{<*N,(n . (A0 + 1))*>,'&'} is non empty functional V39() V54() set
{<*N,(n . (A0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*N,(n . (A0 + 1))*>,'&'},{<*N,(n . (A0 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),N*>,'&'],[<*N,(n . (A0 + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),N*>,'&'],[<*N,(n . (A0 + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) +* (1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),N*>,'&'],[<*N,(n . (A0 + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),N,'xor')) +* (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty Element of K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))
the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty set
K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is non empty set
the ResultSort of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is Relation-like the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) -defined the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))))
the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the ResultSort of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))
N is set
A0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
g . A0 is set
(A0,n,f) is Element of InnerVertices (A0,n,f)
(A0,n,f) is non empty non void V74() 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 K23( the carrier of (A0,n,f))
K23( the carrier of (A0,n,f)) is non empty set
the ResultSort of (A0,n,f) is Relation-like the carrier' of (A0,n,f) -defined the carrier of (A0,n,f) -valued Function-like V30( the carrier' of (A0,n,f), the carrier of (A0,n,f)) Element of K23(K24( the carrier' of (A0,n,f), the carrier of (A0,n,f)))
the carrier' of (A0,n,f) is non empty set
K24( the carrier' of (A0,n,f), the carrier of (A0,n,f)) is non empty Relation-like set
K23(K24( the carrier' of (A0,n,f), the carrier of (A0,n,f))) is non empty set
K497( the carrier of (A0,n,f), the ResultSort of (A0,n,f)) is Element of K23( the carrier of (A0,n,f))
A0 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'} is non empty functional V39() V54() set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V39() V43() V54() set
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'} is non empty functional V39() V54() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V39() V43() V54() set
BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],N*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],N*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (A0 + 1)),N*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&')) +* (1GateCircStr (<*(f . (A0 + 1)),N*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*N,(n . (A0 + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*N,(n . (A0 + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&')) +* (1GateCircStr (<*(f . (A0 + 1)),N*>,'&'))) +* (1GateCircStr (<*N,(n . (A0 + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (A0 + 1)),N*>,'&'] is non empty pair set
{<*(f . (A0 + 1)),N*>,'&'} is non empty functional V39() V54() set
{<*(f . (A0 + 1)),N*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (A0 + 1)),N*>,'&'},{<*(f . (A0 + 1)),N*>}} is non empty V39() V43() V54() set
[<*N,(n . (A0 + 1))*>,'&'] is non empty pair set
{<*N,(n . (A0 + 1))*>,'&'} is non empty functional V39() V54() set
{<*N,(n . (A0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*N,(n . (A0 + 1))*>,'&'},{<*N,(n . (A0 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),N*>,'&'],[<*N,(n . (A0 + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),N*>,'&'],[<*N,(n . (A0 + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) +* (1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),N*>,'&'],[<*N,(n . (A0 + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),N,'xor')) +* (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices H<sub>2</sub>(N,A0) is Element of K23( the carrier of H<sub>2</sub>(N,A0))
the carrier of H<sub>2</sub>(N,A0) is non empty set
K23( the carrier of H<sub>2</sub>(N,A0)) is non empty set
the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty set
the ResultSort of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is Relation-like the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) -defined the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))))
the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the ResultSort of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))
K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is non empty set
the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) \ K497( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the ResultSort of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))
{(n . (A0 + 1)),(f . (A0 + 1)),N} is non empty V39() V54() set
A0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
g . A0 is set
A0 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n . (A0 + 1) is non pair set
f . (A0 + 1) is non pair set
N is set
BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],N*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],N*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((n . (A0 + 1)),(f . (A0 + 1)),N) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (A0 + 1)),N*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&')) +* (1GateCircStr (<*(f . (A0 + 1)),N*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*N,(n . (A0 + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*N,(n . (A0 + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&')) +* (1GateCircStr (<*(f . (A0 + 1)),N*>,'&'))) +* (1GateCircStr (<*N,(n . (A0 + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V39() V43() V54() set
[<*(f . (A0 + 1)),N*>,'&'] is non empty pair set
{<*(f . (A0 + 1)),N*>,'&'} is non empty functional V39() V54() set
{<*(f . (A0 + 1)),N*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (A0 + 1)),N*>,'&'},{<*(f . (A0 + 1)),N*>}} is non empty V39() V43() V54() set
[<*N,(n . (A0 + 1))*>,'&'] is non empty pair set
{<*N,(n . (A0 + 1))*>,'&'} is non empty functional V39() V54() set
{<*N,(n . (A0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*N,(n . (A0 + 1))*>,'&'},{<*N,(n . (A0 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),N*>,'&'],[<*N,(n . (A0 + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),N*>,'&'],[<*N,(n . (A0 + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) +* (1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),N*>,'&'],[<*N,(n . (A0 + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),N,'xor')) +* (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty non void V74() 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 K23( the carrier of H₂(N,A0))
K23( the carrier of H₂(N,A0)) is non empty set
the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty set
the ResultSort of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is Relation-like the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) -defined the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))))
the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the ResultSort of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))
K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is non empty set
the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)) \ K497( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)), the ResultSort of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),N)))
{N} is non empty V5() V39() 1 -element V54() set
(InputVertices H₂(N,A0)) \ {N} is Element of K23( the carrier of H₂(N,A0))
{(n . (A0 + 1)),(f . (A0 + 1)),N} is non empty V39() V54() set
h is non empty pair set
A0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
N is non empty V74() ManySortedSign
(A0,n,f) is non empty non void V74() 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 K23( the carrier of (A0,n,f))
K23( the carrier of (A0,n,f)) is non empty set
the ResultSort of (A0,n,f) is Relation-like the carrier' of (A0,n,f) -defined the carrier of (A0,n,f) -valued Function-like V30( the carrier' of (A0,n,f), the carrier of (A0,n,f)) Element of K23(K24( the carrier' of (A0,n,f), the carrier of (A0,n,f)))
the carrier' of (A0,n,f) is non empty set
K24( the carrier' of (A0,n,f), the carrier of (A0,n,f)) is non empty Relation-like set
K23(K24( the carrier' of (A0,n,f), the carrier of (A0,n,f))) is non empty set
K497( the carrier of (A0,n,f), the ResultSort of (A0,n,f)) is Element of K23( the carrier of (A0,n,f))
A0 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() 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 V74() 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 K23( the carrier of ((A0 + 1),n,f))
K23( the carrier of ((A0 + 1),n,f)) is non empty set
the ResultSort of ((A0 + 1),n,f) is Relation-like the carrier' of ((A0 + 1),n,f) -defined the carrier of ((A0 + 1),n,f) -valued Function-like V30( the carrier' of ((A0 + 1),n,f), the carrier of ((A0 + 1),n,f)) Element of K23(K24( 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
K24( the carrier' of ((A0 + 1),n,f), the carrier of ((A0 + 1),n,f)) is non empty Relation-like set
K23(K24( the carrier' of ((A0 + 1),n,f), the carrier of ((A0 + 1),n,f))) is non empty set
K497( the carrier of ((A0 + 1),n,f), the ResultSort of ((A0 + 1),n,f)) is Element of K23( the carrier of ((A0 + 1),n,f))
n . (A0 + 1) is non pair set
f . (A0 + 1) is non pair set
BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],h*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],h*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((n . (A0 + 1)),(f . (A0 + 1)),h) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (A0 + 1)),h*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&')) +* (1GateCircStr (<*(f . (A0 + 1)),h*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*h,(n . (A0 + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*h,(n . (A0 + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&')) +* (1GateCircStr (<*(f . (A0 + 1)),h*>,'&'))) +* (1GateCircStr (<*h,(n . (A0 + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V39() V43() V54() set
[<*(f . (A0 + 1)),h*>,'&'] is non empty pair set
{<*(f . (A0 + 1)),h*>,'&'} is non empty functional V39() V54() set
{<*(f . (A0 + 1)),h*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (A0 + 1)),h*>,'&'},{<*(f . (A0 + 1)),h*>}} is non empty V39() V43() V54() set
[<*h,(n . (A0 + 1))*>,'&'] is non empty pair set
{<*h,(n . (A0 + 1))*>,'&'} is non empty functional V39() V54() set
{<*h,(n . (A0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*h,(n . (A0 + 1))*>,'&'},{<*h,(n . (A0 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),h*>,'&'],[<*h,(n . (A0 + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),h*>,'&'],[<*h,(n . (A0 + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) +* (1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),h*>,'&'],[<*h,(n . (A0 + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')) +* (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is non empty non void V74() 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 V74() strict ManySortedSign
MajorityOutput ((n . (A0 + 1)),(f . (A0 + 1)),h) is Element of InnerVertices (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h))
the carrier of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is non empty set
InnerVertices (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is non empty Element of K23( the carrier of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h)))
K23( the carrier of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) is non empty set
the ResultSort of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is Relation-like the carrier' of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) -defined the carrier of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) -valued Function-like V30( the carrier' of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) Element of K23(K24( the carrier' of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h))))
the carrier' of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is non empty set
K24( the carrier' of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h)))) is non empty set
K497( the carrier of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the ResultSort of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) is Element of K23( the carrier of (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),h)))
[<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),h*>,'&'],[<*h,(n . (A0 + 1))*>,'&']*>,or3] is non empty pair set
{<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),h*>,'&'],[<*h,(n . (A0 + 1))*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),h*>,'&'],[<*h,(n . (A0 + 1))*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),h*>,'&'],[<*h,(n . (A0 + 1))*>,'&']*>,or3},{<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),h*>,'&'],[<*h,(n . (A0 + 1))*>,'&']*>}} is non empty V39() V43() V54() set
InputVertices H<sub>2</sub>(h,A0) is Element of K23( the carrier of H<sub>2</sub>(h,A0))
the carrier of H<sub>2</sub>(h,A0) is non empty set
K23( the carrier of H<sub>2</sub>(h,A0)) is non empty set
the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is non empty set
the ResultSort of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is Relation-like the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) -defined the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))))
the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the ResultSort of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)))
K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) is non empty set
the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)) \ K497( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)), the ResultSort of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),h)))
{(n . (A0 + 1)),(f . (A0 + 1)),h} is non empty V39() V54() set
InnerVertices H<sub>2</sub>(h,A0) is non empty Element of K23( 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 K23( the carrier of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')))
K23( the carrier of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor'))) is non empty set
the ResultSort of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')) is Relation-like the carrier' of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')) -defined the carrier of (2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor')) -valued Function-like V30( 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 K23(K24( 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
K24( 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 Relation-like set
K23(K24( 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
K497( 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 K23( 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 V39() V54() set
{<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],h*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],h*>,'xor'},{<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],h*>}} is non empty V39() V43() V54() set
{[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],(2GatesCircOutput ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor'))} is non empty Relation-like V39() V54() set
{[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),h*>,'&'],[<*h,(n . (A0 + 1))*>,'&']} is non empty Relation-like V39() V54() set
{[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],(2GatesCircOutput ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor'))} \/ {[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),h*>,'&'],[<*h,(n . (A0 + 1))*>,'&']} is non empty Relation-like V39() V54() set
{(MajorityOutput ((n . (A0 + 1)),(f . (A0 + 1)),h))} is non empty V5() V39() 1 -element V54() set
({[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],(2GatesCircOutput ((n . (A0 + 1)),(f . (A0 + 1)),h,'xor'))} \/ {[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),h*>,'&'],[<*h,(n . (A0 + 1))*>,'&']}) \/ {(MajorityOutput ((n . (A0 + 1)),(f . (A0 + 1)),h))} is non empty V39() V54() set
{H<sub>5</sub>(h,A0)} is non empty V5() V39() 1 -element V54() set
A0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
A0 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
((A0 + 1),n,f) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices ((A0 + 1),n,f) is Element of K23( the carrier of ((A0 + 1),n,f))
the carrier of ((A0 + 1),n,f) is non empty set
K23( the carrier of ((A0 + 1),n,f)) is non empty set
the ResultSort of ((A0 + 1),n,f) is Relation-like the carrier' of ((A0 + 1),n,f) -defined the carrier of ((A0 + 1),n,f) -valued Function-like V30( the carrier' of ((A0 + 1),n,f), the carrier of ((A0 + 1),n,f)) Element of K23(K24( 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
K24( the carrier' of ((A0 + 1),n,f), the carrier of ((A0 + 1),n,f)) is non empty Relation-like set
K23(K24( the carrier' of ((A0 + 1),n,f), the carrier of ((A0 + 1),n,f))) is non empty set
K497( the carrier of ((A0 + 1),n,f), the ResultSort of ((A0 + 1),n,f)) is Element of K23( the carrier of ((A0 + 1),n,f))
the carrier of ((A0 + 1),n,f) \ K497( the carrier of ((A0 + 1),n,f), the ResultSort of ((A0 + 1),n,f)) is Element of K23( the carrier of ((A0 + 1),n,f))
(A0,n,f) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (A0,n,f) is Element of K23( the carrier of (A0,n,f))
the carrier of (A0,n,f) is non empty set
K23( the carrier of (A0,n,f)) is non empty set
the ResultSort of (A0,n,f) is Relation-like the carrier' of (A0,n,f) -defined the carrier of (A0,n,f) -valued Function-like V30( the carrier' of (A0,n,f), the carrier of (A0,n,f)) Element of K23(K24( the carrier' of (A0,n,f), the carrier of (A0,n,f)))
the carrier' of (A0,n,f) is non empty set
K24( the carrier' of (A0,n,f), the carrier of (A0,n,f)) is non empty Relation-like set
K23(K24( the carrier' of (A0,n,f), the carrier of (A0,n,f))) is non empty set
K497( the carrier of (A0,n,f), the ResultSort of (A0,n,f)) is Element of K23( the carrier of (A0,n,f))
the carrier of (A0,n,f) \ K497( the carrier of (A0,n,f), the ResultSort of (A0,n,f)) is Element of K23( 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 K23( the carrier of (A0,n,f))
BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],(A0,n,f)*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'xor'],(A0,n,f)*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(f . (A0 + 1)),(A0,n,f)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&')) +* (1GateCircStr (<*(f . (A0 + 1)),(A0,n,f)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(A0,n,f),(n . (A0 + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(A0,n,f),(n . (A0 + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&')) +* (1GateCircStr (<*(f . (A0 + 1)),(A0,n,f)*>,'&'))) +* (1GateCircStr (<*(A0,n,f),(n . (A0 + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'] is non empty pair set
{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'},{<*(n . (A0 + 1)),(f . (A0 + 1))*>}} is non empty V39() V43() V54() set
[<*(f . (A0 + 1)),(A0,n,f)*>,'&'] is non empty pair set
{<*(f . (A0 + 1)),(A0,n,f)*>,'&'} is non empty functional V39() V54() set
{<*(f . (A0 + 1)),(A0,n,f)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (A0 + 1)),(A0,n,f)*>,'&'},{<*(f . (A0 + 1)),(A0,n,f)*>}} is non empty V39() V43() V54() set
[<*(A0,n,f),(n . (A0 + 1))*>,'&'] is non empty pair set
{<*(A0,n,f),(n . (A0 + 1))*>,'&'} is non empty functional V39() V54() set
{<*(A0,n,f),(n . (A0 + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(A0,n,f),(n . (A0 + 1))*>,'&'},{<*(A0,n,f),(n . (A0 + 1))*>}} is non empty V39() V43() V54() set
<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),(A0,n,f)*>,'&'],[<*(A0,n,f),(n . (A0 + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),(A0,n,f)*>,'&'],[<*(A0,n,f),(n . (A0 + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) +* (1GateCircStr (<*[<*(n . (A0 + 1)),(f . (A0 + 1))*>,'&'],[<*(f . (A0 + 1)),(A0,n,f)*>,'&'],[<*(A0,n,f),(n . (A0 + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f),'xor')) +* (MajorityStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) is non empty set
InputVertices (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))))
K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))) is non empty set
the ResultSort of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) is Relation-like the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) -defined the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))))
the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))), the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))), the ResultSort of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))))
the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))) \ K497( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))), the ResultSort of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))))
{(A0,n,f)} is non empty V5() Relation-like V39() 1 -element V54() set
(InputVertices (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))) \ {(A0,n,f)} is Element of K23( the carrier of (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f))))
(InputVertices (A0,n,f)) \/ ((InputVertices (BitAdderWithOverflowStr ((n . (A0 + 1)),(f . (A0 + 1)),(A0,n,f)))) \ {(A0,n,f)}) is set
g . A0 is set
n is ext-real non positive non negative empty Relation-like non-empty empty-yielding NAT -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair nonpair-yielding set
f is ext-real non positive non negative empty Relation-like non-empty empty-yielding NAT -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair nonpair-yielding set
(0,n,f) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (0,n,f) is Element of K23( the carrier of (0,n,f))
the carrier of (0,n,f) is non empty set
K23( the carrier of (0,n,f)) is non empty set
the ResultSort of (0,n,f) is Relation-like the carrier' of (0,n,f) -defined the carrier of (0,n,f) -valued Function-like V30( the carrier' of (0,n,f), the carrier of (0,n,f)) Element of K23(K24( the carrier' of (0,n,f), the carrier of (0,n,f)))
the carrier' of (0,n,f) is non empty set
K24( the carrier' of (0,n,f), the carrier of (0,n,f)) is non empty Relation-like set
K23(K24( the carrier' of (0,n,f), the carrier of (0,n,f))) is non empty set
K497( the carrier of (0,n,f), the ResultSort of (0,n,f)) is Element of K23( the carrier of (0,n,f))
the carrier of (0,n,f) \ K497( the carrier of (0,n,f), the ResultSort of (0,n,f)) is Element of K23( the carrier of (0,n,f))
proj2 n is ext-real non positive non negative empty V5() Relation-like non-empty empty-yielding NAT -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair nonpair-yielding set
proj2 f is ext-real non positive non negative empty V5() Relation-like non-empty empty-yielding NAT -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair nonpair-yielding set
(proj2 n) \/ (proj2 f) is ext-real non positive non negative empty Relation-like non-empty empty-yielding NAT -defined V12() V13() V14() V16() V17() V18() Function-like one-to-one constant functional non pair V33() V34() V39() V40() V43() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V51() V52() V54() non with_pair nonpair-yielding set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f is Relation-like NAT -defined Function-like V39() n + 1 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
g is Relation-like NAT -defined Function-like V39() n + 1 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
((n + 1),f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices ((n + 1),f,g) is Element of K23( the carrier of ((n + 1),f,g))
the carrier of ((n + 1),f,g) is non empty set
K23( the carrier of ((n + 1),f,g)) is non empty set
the ResultSort of ((n + 1),f,g) is Relation-like the carrier' of ((n + 1),f,g) -defined the carrier of ((n + 1),f,g) -valued Function-like V30( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) Element of K23(K24( 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
K24( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) is non empty Relation-like set
K23(K24( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g))) is non empty set
K497( the carrier of ((n + 1),f,g), the ResultSort of ((n + 1),f,g)) is Element of K23( the carrier of ((n + 1),f,g))
the carrier of ((n + 1),f,g) \ K497( the carrier of ((n + 1),f,g), the ResultSort of ((n + 1),f,g)) is Element of K23( the carrier of ((n + 1),f,g))
proj2 f is V39() V54() non with_pair set
proj2 g is V39() V54() non with_pair set
(proj2 f) \/ (proj2 g) is V39() V54() non with_pair set
S0 is Relation-like NAT -defined Function-like V39() n -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
A0 is non pair set
<*A0*> is non empty V5() Relation-like NAT -defined Function-like constant V39() 1 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
S0 ^ <*A0*> is non empty Relation-like NAT -defined Function-like V39() n + 1 -element FinSequence-like FinSubsequence-like V54() set
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
N is Relation-like NAT -defined Function-like V39() n -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
h is non pair set
<*h*> is non empty V5() Relation-like NAT -defined Function-like constant V39() 1 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
N ^ <*h*> is non empty Relation-like NAT -defined Function-like V39() n + 1 -element FinSequence-like FinSubsequence-like V54() set
dom <*A0*> is non empty V5() V39() 1 -element V54() Element of K23(NAT)
<*A0*> . 1 is non pair set
len S0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . (n + 1) is non pair set
dom <*h*> is non empty V5() V39() 1 -element V54() Element of K23(NAT)
<*h*> . 1 is non pair set
len N is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
g . (n + 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 V74() 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 K23( the carrier of (n,f,g))
K23( the carrier of (n,f,g)) is non empty set
the ResultSort of (n,f,g) is Relation-like the carrier' of (n,f,g) -defined the carrier of (n,f,g) -valued Function-like V30( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K24( the carrier' of (n,f,g), the carrier of (n,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g))) is non empty set
K497( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K23( the carrier of (n,f,g))
{A0,h,(n,f,g)} is non empty V39() V54() set
{(n,f,g),A0,h} is non empty V39() V54() set
proj2 S0 is V39() V54() non with_pair set
proj2 <*A0*> is non empty V5() V39() 1 -element V54() non with_pair set
(proj2 S0) \/ (proj2 <*A0*>) is non empty V39() V54() non with_pair set
{A0} is non empty V5() V39() 1 -element V54() non with_pair set
(proj2 S0) \/ {A0} is non empty V39() V54() non with_pair set
proj2 N is V39() V54() non with_pair set
proj2 <*h*> is non empty V5() V39() 1 -element V54() non with_pair set
(proj2 N) \/ (proj2 <*h*>) is non empty V39() V54() non with_pair set
{h} is non empty V5() V39() 1 -element V54() non with_pair set
(proj2 N) \/ {h} is non empty V39() V54() non with_pair set
<*A0,h*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
[<*A0,h*>,'&'] is non empty pair set
{<*A0,h*>,'&'} is non empty functional V39() V54() set
{<*A0,h*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*A0,h*>,'&'},{<*A0,h*>}} is non empty V39() V43() V54() set
[<*A0,h*>,'xor'] is non empty pair set
{<*A0,h*>,'xor'} is non empty functional V39() V54() set
{{<*A0,h*>,'xor'},{<*A0,h*>}} is non empty V39() V43() V54() set
S0 ^ {} is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
N ^ {} is Relation-like NAT -defined Function-like V39() FinSequence-like FinSubsequence-like V54() set
(n,S0,N) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices (n,S0,N) is Element of K23( the carrier of (n,S0,N))
the carrier of (n,S0,N) is non empty set
K23( the carrier of (n,S0,N)) is non empty set
the ResultSort of (n,S0,N) is Relation-like the carrier' of (n,S0,N) -defined the carrier of (n,S0,N) -valued Function-like V30( the carrier' of (n,S0,N), the carrier of (n,S0,N)) Element of K23(K24( the carrier' of (n,S0,N), the carrier of (n,S0,N)))
the carrier' of (n,S0,N) is non empty set
K24( the carrier' of (n,S0,N), the carrier of (n,S0,N)) is non empty Relation-like set
K23(K24( the carrier' of (n,S0,N), the carrier of (n,S0,N))) is non empty set
K497( the carrier of (n,S0,N), the ResultSort of (n,S0,N)) is Element of K23( the carrier of (n,S0,N))
the carrier of (n,S0,N) \ K497( the carrier of (n,S0,N), the ResultSort of (n,S0,N)) is Element of K23( the carrier of (n,S0,N))
BitAdderWithOverflowStr (A0,h,(n,f,g)) is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*A0,h*>,'xor') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*A0,h*>,'xor'],(n,f,g)*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr (A0,h,(n,f,g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr (A0,h,(n,f,g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*A0,h*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*h,(n,f,g)*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*A0,h*>,'&')) +* (1GateCircStr (<*h,(n,f,g)*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*(n,f,g),A0*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(n,f,g),A0*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*A0,h*>,'&')) +* (1GateCircStr (<*h,(n,f,g)*>,'&'))) +* (1GateCircStr (<*(n,f,g),A0*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*h,(n,f,g)*>,'&'] is non empty pair set
{<*h,(n,f,g)*>,'&'} is non empty functional V39() V54() set
{<*h,(n,f,g)*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*h,(n,f,g)*>,'&'},{<*h,(n,f,g)*>}} is non empty V39() V43() V54() set
[<*(n,f,g),A0*>,'&'] is non empty pair set
{<*(n,f,g),A0*>,'&'} is non empty functional V39() V54() set
{<*(n,f,g),A0*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(n,f,g),A0*>,'&'},{<*(n,f,g),A0*>}} is non empty V39() V43() V54() set
<*[<*A0,h*>,'&'],[<*h,(n,f,g)*>,'&'],[<*(n,f,g),A0*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*A0,h*>,'&'],[<*h,(n,f,g)*>,'&'],[<*(n,f,g),A0*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr (A0,h,(n,f,g))) +* (1GateCircStr (<*[<*A0,h*>,'&'],[<*h,(n,f,g)*>,'&'],[<*(n,f,g),A0*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (A0,h,(n,f,g),'xor')) +* (MajorityStr (A0,h,(n,f,g))) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BitAdderWithOverflowStr (A0,h,(n,f,g))) is non empty set
InputVertices (BitAdderWithOverflowStr (A0,h,(n,f,g))) is Element of K23( the carrier of (BitAdderWithOverflowStr (A0,h,(n,f,g))))
K23( the carrier of (BitAdderWithOverflowStr (A0,h,(n,f,g)))) is non empty set
the ResultSort of (BitAdderWithOverflowStr (A0,h,(n,f,g))) is Relation-like the carrier' of (BitAdderWithOverflowStr (A0,h,(n,f,g))) -defined the carrier of (BitAdderWithOverflowStr (A0,h,(n,f,g))) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr (A0,h,(n,f,g))), the carrier of (BitAdderWithOverflowStr (A0,h,(n,f,g)))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr (A0,h,(n,f,g))), the carrier of (BitAdderWithOverflowStr (A0,h,(n,f,g)))))
the carrier' of (BitAdderWithOverflowStr (A0,h,(n,f,g))) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr (A0,h,(n,f,g))), the carrier of (BitAdderWithOverflowStr (A0,h,(n,f,g)))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr (A0,h,(n,f,g))), the carrier of (BitAdderWithOverflowStr (A0,h,(n,f,g))))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr (A0,h,(n,f,g))), the ResultSort of (BitAdderWithOverflowStr (A0,h,(n,f,g)))) is Element of K23( the carrier of (BitAdderWithOverflowStr (A0,h,(n,f,g))))
the carrier of (BitAdderWithOverflowStr (A0,h,(n,f,g))) \ K497( the carrier of (BitAdderWithOverflowStr (A0,h,(n,f,g))), the ResultSort of (BitAdderWithOverflowStr (A0,h,(n,f,g)))) is Element of K23( the carrier of (BitAdderWithOverflowStr (A0,h,(n,f,g))))
{(n,f,g)} is non empty V5() Relation-like V39() 1 -element V54() set
(InputVertices (BitAdderWithOverflowStr (A0,h,(n,f,g)))) \ {(n,f,g)} is Element of K23( the carrier of (BitAdderWithOverflowStr (A0,h,(n,f,g))))
(InputVertices (n,S0,N)) \/ ((InputVertices (BitAdderWithOverflowStr (A0,h,(n,f,g)))) \ {(n,f,g)}) is set
(proj2 S0) \/ (proj2 N) is V39() V54() non with_pair set
((proj2 S0) \/ (proj2 N)) \/ ((InputVertices (BitAdderWithOverflowStr (A0,h,(n,f,g)))) \ {(n,f,g)}) is set
{A0,h,(n,f,g)} \ {(n,f,g)} is V39() V54() Element of K23({A0,h,(n,f,g)})
K23({A0,h,(n,f,g)}) is non empty V39() V43() V54() set
((proj2 S0) \/ (proj2 N)) \/ ({A0,h,(n,f,g)} \ {(n,f,g)}) is V39() V54() set
{A0,h} is non empty V39() V54() non with_pair set
((proj2 S0) \/ (proj2 N)) \/ {A0,h} is non empty V39() V54() non with_pair set
{A0} \/ {h} is non empty V39() V54() non with_pair set
((proj2 S0) \/ (proj2 N)) \/ ({A0} \/ {h}) is non empty V39() V54() non with_pair set
((proj2 S0) \/ (proj2 N)) \/ {A0} is non empty V39() V54() non with_pair set
(((proj2 S0) \/ (proj2 N)) \/ {A0}) \/ {h} is non empty V39() V54() non with_pair set
((proj2 S0) \/ {A0}) \/ (proj2 N) is non empty V39() V54() non with_pair set
(((proj2 S0) \/ {A0}) \/ (proj2 N)) \/ {h} is non empty V39() V54() non with_pair set
n is set
f is set
g is set
MajorityStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,f*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*n,f*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f,g*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*f,g*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*g,n*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*g,n*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*n,f*>,'&'] is non empty pair set
{<*n,f*>,'&'} is non empty functional V39() V54() set
{<*n,f*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*n,f*>,'&'},{<*n,f*>}} is non empty V39() V43() V54() set
[<*f,g*>,'&'] is non empty pair set
{<*f,g*>,'&'} is non empty functional V39() V54() set
{<*f,g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*f,g*>,'&'},{<*f,g*>}} is non empty V39() V43() V54() set
[<*g,n*>,'&'] is non empty pair set
{<*g,n*>,'&'} is non empty functional V39() V54() set
{<*g,n*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g,n*>,'&'},{<*g,n*>}} is non empty V39() V43() V54() set
<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (MajorityStr (n,f,g)) is non empty set
MajorityCirc (n,f,g) is strict non-empty finitely-generated V110( MajorityStr (n,f,g)) gate`2=den Boolean MSAlgebra over MajorityStr (n,f,g)
MajorityICirc (n,f,g) is strict non-empty finitely-generated V110( MajorityIStr (n,f,g)) gate`2=den Boolean MSAlgebra over MajorityIStr (n,f,g)
1GateCircuit (n,f,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*n,f*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'&')
1GateCircuit (<*n,f*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*n,f*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'&')
1GateCircuit (f,g,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f,g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,'&')
1GateCircuit (<*f,g*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f,g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,'&')
(1GateCircuit (n,f,'&')) +* (1GateCircuit (f,g,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))
1GateCircuit (g,n,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,n*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,'&')
1GateCircuit (<*g,n*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,n*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,'&')
((1GateCircuit (n,f,'&')) +* (1GateCircuit (f,g,'&'))) +* (1GateCircuit (g,n,'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&'))
1GateCircuit ([<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)
1GateCircuit (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)
(MajorityICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))
the Sorts of (MajorityCirc (n,f,g)) is Relation-like non-empty the carrier of (MajorityStr (n,f,g)) -defined Function-like total set
K235( the Sorts of (MajorityCirc (n,f,g))) is non empty functional V52() V53() set
S0 is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
S0 . n is set
S0 . f is set
S0 . g is set
Following S0 is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
(Following S0) . [<*n,f*>,'&'] is set
(Following S0) . [<*f,g*>,'&'] is set
(Following S0) . [<*g,n*>,'&'] is set
A0 is boolean Element of BOOLEAN
N is boolean Element of BOOLEAN
h is boolean Element of BOOLEAN
A0 '&' N is boolean Element of BOOLEAN
N '&' h is boolean Element of BOOLEAN
h '&' A0 is boolean Element of BOOLEAN
InnerVertices (MajorityStr (n,f,g)) is non empty Element of K23( the carrier of (MajorityStr (n,f,g)))
K23( the carrier of (MajorityStr (n,f,g))) is non empty set
the ResultSort of (MajorityStr (n,f,g)) is Relation-like the carrier' of (MajorityStr (n,f,g)) -defined the carrier of (MajorityStr (n,f,g)) -valued Function-like V30( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) Element of K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))))
the carrier' of (MajorityStr (n,f,g)) is non empty set
K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g)))) is non empty set
K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
proj1 S0 is set
<*n,f*> * S0 is Relation-like NAT -defined Function-like V39() V54() set
'&' . (<*n,f*> * S0) is boolean set
<*A0,N*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
'&' . <*A0,N*> is boolean set
<*f,g*> * S0 is Relation-like NAT -defined Function-like V39() V54() set
'&' . (<*f,g*> * S0) is boolean set
<*N,h*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
'&' . <*N,h*> is boolean set
<*g,n*> * S0 is Relation-like NAT -defined Function-like V39() V54() set
'&' . (<*g,n*> * S0) is boolean set
<*h,A0*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
'&' . <*h,A0*> is boolean set
n is set
f is set
g is set
MajorityStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*n,f*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*n,f*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*f,g*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*f,g*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*g,n*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*g,n*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*n,f*>,'&'] is non empty pair set
{<*n,f*>,'&'} is non empty functional V39() V54() set
{<*n,f*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*n,f*>,'&'},{<*n,f*>}} is non empty V39() V43() V54() set
[<*f,g*>,'&'] is non empty pair set
{<*f,g*>,'&'} is non empty functional V39() V54() set
{<*f,g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*f,g*>,'&'},{<*f,g*>}} is non empty V39() V43() V54() set
[<*g,n*>,'&'] is non empty pair set
{<*g,n*>,'&'} is non empty functional V39() V54() set
{<*g,n*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g,n*>,'&'},{<*g,n*>}} is non empty V39() V43() V54() set
<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (MajorityStr (n,f,g)) is non empty set
MajorityCirc (n,f,g) is strict non-empty finitely-generated V110( MajorityStr (n,f,g)) gate`2=den Boolean MSAlgebra over MajorityStr (n,f,g)
MajorityICirc (n,f,g) is strict non-empty finitely-generated V110( MajorityIStr (n,f,g)) gate`2=den Boolean MSAlgebra over MajorityIStr (n,f,g)
1GateCircuit (n,f,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*n,f*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'&')
1GateCircuit (<*n,f*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*n,f*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'&')
1GateCircuit (f,g,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f,g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,'&')
1GateCircuit (<*f,g*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f,g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,'&')
(1GateCircuit (n,f,'&')) +* (1GateCircuit (f,g,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))
1GateCircuit (g,n,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,n*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,'&')
1GateCircuit (<*g,n*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,n*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,'&')
((1GateCircuit (n,f,'&')) +* (1GateCircuit (f,g,'&'))) +* (1GateCircuit (g,n,'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&'))
1GateCircuit ([<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)
1GateCircuit (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)
(MajorityICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))
the Sorts of (MajorityCirc (n,f,g)) is Relation-like non-empty the carrier of (MajorityStr (n,f,g)) -defined Function-like total set
K235( the Sorts of (MajorityCirc (n,f,g))) is non empty functional V52() V53() set
MajorityOutput (n,f,g) is Element of InnerVertices (MajorityStr (n,f,g))
InnerVertices (MajorityStr (n,f,g)) is non empty Element of K23( the carrier of (MajorityStr (n,f,g)))
K23( the carrier of (MajorityStr (n,f,g))) is non empty set
the ResultSort of (MajorityStr (n,f,g)) is Relation-like the carrier' of (MajorityStr (n,f,g)) -defined the carrier of (MajorityStr (n,f,g)) -valued Function-like V30( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) Element of K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))))
the carrier' of (MajorityStr (n,f,g)) is non empty set
K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g)))) is non empty set
K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
[<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3] is non empty pair set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3},{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>}} is non empty V39() V43() V54() set
S0 is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
S0 . [<*n,f*>,'&'] is set
S0 . [<*f,g*>,'&'] is set
S0 . [<*g,n*>,'&'] is set
Following S0 is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
(Following S0) . (MajorityOutput (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 (MajorityStr (n,f,g))
h1 is Element of InnerVertices (MajorityStr (n,f,g))
n is Element of InnerVertices (MajorityStr (n,f,g))
<*g1,h1,n*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
<*g1,h1,n*> * S0 is Relation-like NAT -defined Function-like V39() V54() set
or3 . (<*g1,h1,n*> * S0) is boolean set
<*A0,N,h*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*f,g*>,'&'] is non empty pair set
{<*f,g*>,'&'} is non empty functional V39() V54() set
{<*f,g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*f,g*>,'&'},{<*f,g*>}} is non empty V39() V43() V54() set
<*g,n*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*g,n*>,'&'] is non empty pair set
{<*g,n*>,'&'} is non empty functional V39() V54() set
{<*g,n*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g,n*>,'&'},{<*g,n*>}} is non empty V39() V43() V54() set
<*n,f*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*n,f*>,'&'] is non empty pair set
{<*n,f*>,'&'} is non empty functional V39() V54() set
{<*n,f*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*n,f*>,'&'},{<*n,f*>}} is non empty V39() V43() V54() set
MajorityStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*f,g*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*g,n*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (MajorityStr (n,f,g)) is non empty set
MajorityCirc (n,f,g) is strict non-empty finitely-generated V110( MajorityStr (n,f,g)) gate`2=den Boolean MSAlgebra over MajorityStr (n,f,g)
MajorityICirc (n,f,g) is strict non-empty finitely-generated V110( MajorityIStr (n,f,g)) gate`2=den Boolean MSAlgebra over MajorityIStr (n,f,g)
1GateCircuit (n,f,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*n,f*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'&')
1GateCircuit (<*n,f*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*n,f*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'&')
1GateCircuit (f,g,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f,g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,'&')
1GateCircuit (<*f,g*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f,g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,'&')
(1GateCircuit (n,f,'&')) +* (1GateCircuit (f,g,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))
1GateCircuit (g,n,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,n*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,'&')
1GateCircuit (<*g,n*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,n*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,'&')
((1GateCircuit (n,f,'&')) +* (1GateCircuit (f,g,'&'))) +* (1GateCircuit (g,n,'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&'))
1GateCircuit ([<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)
1GateCircuit (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)
(MajorityICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))
the Sorts of (MajorityCirc (n,f,g)) is Relation-like non-empty the carrier of (MajorityStr (n,f,g)) -defined Function-like total set
K235( the Sorts of (MajorityCirc (n,f,g))) is non empty functional V52() V53() set
MajorityOutput (n,f,g) is Element of InnerVertices (MajorityStr (n,f,g))
InnerVertices (MajorityStr (n,f,g)) is non empty Element of K23( the carrier of (MajorityStr (n,f,g)))
K23( the carrier of (MajorityStr (n,f,g))) is non empty set
the ResultSort of (MajorityStr (n,f,g)) is Relation-like the carrier' of (MajorityStr (n,f,g)) -defined the carrier of (MajorityStr (n,f,g)) -valued Function-like V30( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) Element of K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))))
the carrier' of (MajorityStr (n,f,g)) is non empty set
K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g)))) is non empty set
K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
[<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3] is non empty pair set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3},{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>}} is non empty V39() V43() V54() set
S0 is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
S0 . n is set
S0 . f is set
S0 . g is set
Following (S0,2) is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
(Following (S0,2)) . (MajorityOutput (n,f,g)) is boolean Element of BOOLEAN
(Following (S0,2)) . [<*n,f*>,'&'] is set
(Following (S0,2)) . [<*f,g*>,'&'] is set
(Following (S0,2)) . [<*g,n*>,'&'] is set
A0 is boolean Element of BOOLEAN
N is boolean Element of BOOLEAN
h is boolean Element of BOOLEAN
A0 '&' N is boolean Element of BOOLEAN
N '&' h is boolean Element of BOOLEAN
(A0 '&' N) 'or' (N '&' h) is boolean Element of BOOLEAN
h '&' A0 is boolean Element of BOOLEAN
((A0 '&' N) 'or' (N '&' h)) 'or' (h '&' A0) is boolean Element of BOOLEAN
InputVertices (MajorityStr (n,f,g)) is Element of K23( the carrier of (MajorityStr (n,f,g)))
the carrier of (MajorityStr (n,f,g)) \ K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
{n,f,g} is non empty V39() V54() set
Following S0 is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
g1 is Element of the carrier of (MajorityStr (n,f,g))
(Following S0) . g1 is boolean Element of BOOLEAN
h1 is Element of the carrier of (MajorityStr (n,f,g))
(Following S0) . h1 is boolean Element of BOOLEAN
n is Element of the carrier of (MajorityStr (n,f,g))
(Following S0) . n is boolean Element of BOOLEAN
Following (Following S0) is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
(Following S0) . [<*n,f*>,'&'] is set
(Following S0) . [<*f,g*>,'&'] is set
(Following S0) . [<*g,n*>,'&'] is set
n is set
f is set
g is set
<*f,g*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*f,g*>,'&'] is non empty pair set
{<*f,g*>,'&'} is non empty functional V39() V54() set
{<*f,g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*f,g*>,'&'},{<*f,g*>}} is non empty V39() V43() V54() set
<*g,n*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*g,n*>,'&'] is non empty pair set
{<*g,n*>,'&'} is non empty functional V39() V54() set
{<*g,n*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g,n*>,'&'},{<*g,n*>}} is non empty V39() V43() V54() set
<*n,f*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*n,f*>,'&'] is non empty pair set
{<*n,f*>,'&'} is non empty functional V39() V54() set
{<*n,f*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*n,f*>,'&'},{<*n,f*>}} is non empty V39() V43() V54() set
MajorityStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*f,g*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*g,n*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (MajorityStr (n,f,g)) is non empty set
MajorityCirc (n,f,g) is strict non-empty finitely-generated V110( MajorityStr (n,f,g)) gate`2=den Boolean MSAlgebra over MajorityStr (n,f,g)
MajorityICirc (n,f,g) is strict non-empty finitely-generated V110( MajorityIStr (n,f,g)) gate`2=den Boolean MSAlgebra over MajorityIStr (n,f,g)
1GateCircuit (n,f,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*n,f*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'&')
1GateCircuit (<*n,f*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*n,f*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'&')
1GateCircuit (f,g,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f,g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,'&')
1GateCircuit (<*f,g*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f,g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,'&')
(1GateCircuit (n,f,'&')) +* (1GateCircuit (f,g,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))
1GateCircuit (g,n,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,n*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,'&')
1GateCircuit (<*g,n*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,n*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,'&')
((1GateCircuit (n,f,'&')) +* (1GateCircuit (f,g,'&'))) +* (1GateCircuit (g,n,'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&'))
1GateCircuit ([<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)
1GateCircuit (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)
(MajorityICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))
the Sorts of (MajorityCirc (n,f,g)) is Relation-like non-empty the carrier of (MajorityStr (n,f,g)) -defined Function-like total set
K235( the Sorts of (MajorityCirc (n,f,g))) is non empty functional V52() V53() set
A0 is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
Following (A0,2) is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
Following (Following (A0,2)) is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
proj1 (Following (Following (A0,2))) is set
proj1 (Following (A0,2)) is set
N is Element of the carrier of (MajorityStr (n,f,g))
A0 . N is boolean Element of BOOLEAN
h is Element of the carrier of (MajorityStr (n,f,g))
A0 . h is boolean Element of BOOLEAN
Sn is Element of the carrier of (MajorityStr (n,f,g))
A0 . Sn is boolean Element of BOOLEAN
A0 . n is set
A0 . f is set
A0 . g is set
MajorityOutput (n,f,g) is Element of InnerVertices (MajorityStr (n,f,g))
InnerVertices (MajorityStr (n,f,g)) is non empty Element of K23( the carrier of (MajorityStr (n,f,g)))
K23( the carrier of (MajorityStr (n,f,g))) is non empty set
the ResultSort of (MajorityStr (n,f,g)) is Relation-like the carrier' of (MajorityStr (n,f,g)) -defined the carrier of (MajorityStr (n,f,g)) -valued Function-like V30( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) Element of K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))))
the carrier' of (MajorityStr (n,f,g)) is non empty set
K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g)))) is non empty set
K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
[<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3] is non empty pair set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3},{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>}} is non empty V39() V43() V54() set
(Following (A0,2)) . (MajorityOutput (n,f,g)) is boolean Element of BOOLEAN
(A0 . N) '&' (A0 . h) is boolean Element of BOOLEAN
(A0 . h) '&' (A0 . Sn) is boolean Element of BOOLEAN
((A0 . N) '&' (A0 . h)) 'or' ((A0 . h) '&' (A0 . Sn)) is boolean Element of BOOLEAN
(A0 . Sn) '&' (A0 . N) is boolean Element of BOOLEAN
(((A0 . N) '&' (A0 . h)) 'or' ((A0 . h) '&' (A0 . Sn))) 'or' ((A0 . Sn) '&' (A0 . N)) is boolean Element of BOOLEAN
(Following (A0,2)) . [<*n,f*>,'&'] is set
(Following (A0,2)) . [<*f,g*>,'&'] is set
(Following (A0,2)) . [<*g,n*>,'&'] is set
Following A0 is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
Following (Following A0) is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
InputVertices (MajorityStr (n,f,g)) is Element of K23( the carrier of (MajorityStr (n,f,g)))
the carrier of (MajorityStr (n,f,g)) \ K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
{n,f,g} is non empty V39() V54() 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 (MajorityStr (n,f,g))
(InputVertices (MajorityStr (n,f,g))) \/ (InnerVertices (MajorityStr (n,f,g))) is non empty Element of K23( the carrier of (MajorityStr (n,f,g)))
(Following (A0,2)) . n is set
(Following (Following (A0,2))) . n is set
{[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']} is non empty Relation-like V39() V54() set
{(MajorityOutput (n,f,g))} is non empty V5() V39() 1 -element V54() set
{[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']} \/ {(MajorityOutput (n,f,g))} is non empty V39() V54() set
n is set
f is set
g is set
<*f,g*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*f,g*>,'&'] is non empty pair set
{<*f,g*>,'&'} is non empty functional V39() V54() set
{<*f,g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*f,g*>,'&'},{<*f,g*>}} is non empty V39() V43() V54() set
<*g,n*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*g,n*>,'&'] is non empty pair set
{<*g,n*>,'&'} is non empty functional V39() V54() set
{<*g,n*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g,n*>,'&'},{<*g,n*>}} is non empty V39() V43() V54() set
<*n,f*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*n,f*>,'&'] is non empty pair set
{<*n,f*>,'&'} is non empty functional V39() V54() set
{<*n,f*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*n,f*>,'&'},{<*n,f*>}} is non empty V39() V43() V54() set
[<*n,f*>,'xor'] is non empty pair set
{<*n,f*>,'xor'} is non empty functional V39() V54() set
{{<*n,f*>,'xor'},{<*n,f*>}} is non empty V39() V43() V54() set
BitAdderWithOverflowStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (n,f,g,'xor') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,'xor') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*f,g*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*g,n*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BitAdderWithOverflowStr (n,f,g)) is non empty set
BitAdderWithOverflowCirc (n,f,g) is strict non-empty finitely-generated V110( BitAdderWithOverflowStr (n,f,g)) gate`2=den Boolean MSAlgebra over BitAdderWithOverflowStr (n,f,g)
BitAdderCirc (n,f,g) is strict non-empty finitely-generated V110( 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 V110( 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 V110( 1GateCircStr (<*n,f*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'xor')
1GateCircuit (<*n,f*>,'xor') is strict non-empty finitely-generated V110( 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 V110( 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 V110( 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 V110((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'))
MajorityCirc (n,f,g) is strict non-empty finitely-generated V110( MajorityStr (n,f,g)) gate`2=den Boolean MSAlgebra over MajorityStr (n,f,g)
MajorityICirc (n,f,g) is strict non-empty finitely-generated V110( MajorityIStr (n,f,g)) gate`2=den Boolean MSAlgebra over MajorityIStr (n,f,g)
1GateCircuit (n,f,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*n,f*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'&')
1GateCircuit (<*n,f*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*n,f*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'&')
1GateCircuit (f,g,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f,g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,'&')
1GateCircuit (<*f,g*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f,g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,'&')
(1GateCircuit (n,f,'&')) +* (1GateCircuit (f,g,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))
1GateCircuit (g,n,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,n*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,'&')
1GateCircuit (<*g,n*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,n*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,'&')
((1GateCircuit (n,f,'&')) +* (1GateCircuit (f,g,'&'))) +* (1GateCircuit (g,n,'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&'))
1GateCircuit ([<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)
1GateCircuit (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)
(MajorityICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))
(BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g)) is strict non-empty finitely-generated V110((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) gate`2=den Boolean MSAlgebra over (2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))
the Sorts of (BitAdderWithOverflowCirc (n,f,g)) is Relation-like non-empty the carrier of (BitAdderWithOverflowStr (n,f,g)) -defined Function-like total set
K235( the Sorts of (BitAdderWithOverflowCirc (n,f,g))) is non empty functional V52() V53() set
BitAdderOutput (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 K23( the carrier of (2GatesCircStr (n,f,g,'xor')))
K23( the carrier of (2GatesCircStr (n,f,g,'xor'))) is non empty set
the ResultSort of (2GatesCircStr (n,f,g,'xor')) is Relation-like the carrier' of (2GatesCircStr (n,f,g,'xor')) -defined the carrier of (2GatesCircStr (n,f,g,'xor')) -valued Function-like V30( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) Element of K23(K24( 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
K24( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) is non empty Relation-like set
K23(K24( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor')))) is non empty set
K497( the carrier of (2GatesCircStr (n,f,g,'xor')), the ResultSort of (2GatesCircStr (n,f,g,'xor'))) is Element of K23( 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 V39() V54() set
{<*[<*n,f*>,'xor'],g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*n,f*>,'xor'],g*>,'xor'},{<*[<*n,f*>,'xor'],g*>}} is non empty V39() V43() V54() set
MajorityOutput (n,f,g) is Element of InnerVertices (MajorityStr (n,f,g))
the carrier of (MajorityStr (n,f,g)) is non empty set
InnerVertices (MajorityStr (n,f,g)) is non empty Element of K23( the carrier of (MajorityStr (n,f,g)))
K23( the carrier of (MajorityStr (n,f,g))) is non empty set
the ResultSort of (MajorityStr (n,f,g)) is Relation-like the carrier' of (MajorityStr (n,f,g)) -defined the carrier of (MajorityStr (n,f,g)) -valued Function-like V30( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) Element of K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))))
the carrier' of (MajorityStr (n,f,g)) is non empty set
K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g)))) is non empty set
K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
[<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3] is non empty pair set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3},{<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>}} is non empty V39() V43() V54() set
o0 is Relation-like the carrier of (BitAdderWithOverflowStr (n,f,g)) -defined Function-like the Sorts of (BitAdderWithOverflowCirc (n,f,g)) -compatible total Element of K235( the Sorts of (BitAdderWithOverflowCirc (n,f,g)))
o0 . n is set
o0 . f is set
o0 . g is set
Following (o0,2) is Relation-like the carrier of (BitAdderWithOverflowStr (n,f,g)) -defined Function-like the Sorts of (BitAdderWithOverflowCirc (n,f,g)) -compatible total Element of K235( the Sorts of (BitAdderWithOverflowCirc (n,f,g)))
(Following (o0,2)) . (BitAdderOutput (n,f,g)) is set
(Following (o0,2)) . (MajorityOutput (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
f1 '&' g1 is boolean Element of BOOLEAN
g1 '&' h1 is boolean Element of BOOLEAN
(f1 '&' g1) 'or' (g1 '&' h1) is boolean Element of BOOLEAN
h1 '&' f1 is boolean Element of BOOLEAN
((f1 '&' g1) 'or' (g1 '&' h1)) 'or' (h1 '&' f1) is boolean Element of BOOLEAN
the Sorts of (BitAdderCirc (n,f,g)) is Relation-like non-empty the carrier of (2GatesCircStr (n,f,g,'xor')) -defined Function-like total set
K235( the Sorts of (BitAdderCirc (n,f,g))) is non empty functional V52() V53() set
o0 | the carrier of (2GatesCircStr (n,f,g,'xor')) is Relation-like the carrier of (2GatesCircStr (n,f,g,'xor')) -defined the carrier of (BitAdderWithOverflowStr (n,f,g)) -defined Function-like the Sorts of (BitAdderWithOverflowCirc (n,f,g)) -compatible set
the Sorts of (MajorityCirc (n,f,g)) is Relation-like non-empty the carrier of (MajorityStr (n,f,g)) -defined Function-like total set
K235( the Sorts of (MajorityCirc (n,f,g))) is non empty functional V52() V53() set
o0 | the carrier of (MajorityStr (n,f,g)) is Relation-like the carrier of (MajorityStr (n,f,g)) -defined the carrier of (BitAdderWithOverflowStr (n,f,g)) -defined Function-like the Sorts of (BitAdderWithOverflowCirc (n,f,g)) -compatible set
the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) is non empty set
the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))) is Relation-like non-empty the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) -defined Function-like total set
K235( the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g)))) is non empty functional V52() V53() set
InputVertices (2GatesCircStr (n,f,g,'xor')) is Element of K23( the carrier of (2GatesCircStr (n,f,g,'xor')))
the carrier of (2GatesCircStr (n,f,g,'xor')) \ K497( the carrier of (2GatesCircStr (n,f,g,'xor')), the ResultSort of (2GatesCircStr (n,f,g,'xor'))) is Element of K23( the carrier of (2GatesCircStr (n,f,g,'xor')))
{n,f,g} is non empty V39() V54() set
InputVertices (MajorityStr (n,f,g)) is Element of K23( the carrier of (MajorityStr (n,f,g)))
the carrier of (MajorityStr (n,f,g)) \ K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
n is Relation-like the carrier of (2GatesCircStr (n,f,g,'xor')) -defined Function-like the Sorts of (BitAdderCirc (n,f,g)) -compatible total Element of K235( the Sorts of (BitAdderCirc (n,f,g)))
proj1 n is set
n . n is set
n . f is set
n . g is set
xx is Relation-like the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) -defined Function-like the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))) -compatible total Element of K235( the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))))
Following (xx,2) is Relation-like the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) -defined Function-like the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))) -compatible total Element of K235( the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))))
(Following (xx,2)) . (2GatesCircOutput (n,f,g,'xor')) is set
Following (n,2) is Relation-like the carrier of (2GatesCircStr (n,f,g,'xor')) -defined Function-like the Sorts of (BitAdderCirc (n,f,g)) -compatible total Element of K235( the Sorts of (BitAdderCirc (n,f,g)))
(Following (n,2)) . (2GatesCircOutput (n,f,g,'xor')) is boolean Element of BOOLEAN
x is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
proj1 x is set
x . n is set
x . f is set
x . g is set
(Following (xx,2)) . (MajorityOutput (n,f,g)) is set
Following (x,2) is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
(Following (x,2)) . (MajorityOutput (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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*f,g*>,'&'] is non empty pair set
{<*f,g*>,'&'} is non empty functional V39() V54() set
{<*f,g*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*f,g*>,'&'},{<*f,g*>}} is non empty V39() V43() V54() set
<*g,n*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*g,n*>,'&'] is non empty pair set
{<*g,n*>,'&'} is non empty functional V39() V54() set
{<*g,n*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*g,n*>,'&'},{<*g,n*>}} is non empty V39() V43() V54() set
<*n,f*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
[<*n,f*>,'&'] is non empty pair set
{<*n,f*>,'&'} is non empty functional V39() V54() set
{<*n,f*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*n,f*>,'&'},{<*n,f*>}} is non empty V39() V43() V54() set
[<*n,f*>,'xor'] is non empty pair set
{<*n,f*>,'xor'} is non empty functional V39() V54() set
{{<*n,f*>,'xor'},{<*n,f*>}} is non empty V39() V43() V54() set
BitAdderWithOverflowStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
2GatesCircStr (n,f,g,'xor') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,'xor') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'xor'],g*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr (n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*n,f*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*f,g*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*g,n*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (BitAdderWithOverflowStr (n,f,g)) is non empty set
BitAdderWithOverflowCirc (n,f,g) is strict non-empty finitely-generated V110( BitAdderWithOverflowStr (n,f,g)) gate`2=den Boolean MSAlgebra over BitAdderWithOverflowStr (n,f,g)
BitAdderCirc (n,f,g) is strict non-empty finitely-generated V110( 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 V110( 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 V110( 1GateCircStr (<*n,f*>,'xor')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'xor')
1GateCircuit (<*n,f*>,'xor') is strict non-empty finitely-generated V110( 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 V110( 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 V110( 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 V110((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'))
MajorityCirc (n,f,g) is strict non-empty finitely-generated V110( MajorityStr (n,f,g)) gate`2=den Boolean MSAlgebra over MajorityStr (n,f,g)
MajorityICirc (n,f,g) is strict non-empty finitely-generated V110( MajorityIStr (n,f,g)) gate`2=den Boolean MSAlgebra over MajorityIStr (n,f,g)
1GateCircuit (n,f,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*n,f*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'&')
1GateCircuit (<*n,f*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*n,f*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*n,f*>,'&')
1GateCircuit (f,g,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f,g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,'&')
1GateCircuit (<*f,g*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*f,g*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*f,g*>,'&')
(1GateCircuit (n,f,'&')) +* (1GateCircuit (f,g,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))
1GateCircuit (g,n,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,n*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,'&')
1GateCircuit (<*g,n*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*g,n*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*g,n*>,'&')
((1GateCircuit (n,f,'&')) +* (1GateCircuit (f,g,'&'))) +* (1GateCircuit (g,n,'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*n,f*>,'&')) +* (1GateCircStr (<*f,g*>,'&'))) +* (1GateCircStr (<*g,n*>,'&'))
1GateCircuit ([<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)
1GateCircuit (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3)
(MajorityICirc (n,f,g)) +* (1GateCircuit ([<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr (n,f,g)) +* (1GateCircStr (<*[<*n,f*>,'&'],[<*f,g*>,'&'],[<*g,n*>,'&']*>,or3))
(BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g)) is strict non-empty finitely-generated V110((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) gate`2=den Boolean MSAlgebra over (2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))
the Sorts of (BitAdderWithOverflowCirc (n,f,g)) is Relation-like non-empty the carrier of (BitAdderWithOverflowStr (n,f,g)) -defined Function-like total set
K235( the Sorts of (BitAdderWithOverflowCirc (n,f,g))) is non empty functional V52() V53() set
o0 is Relation-like the carrier of (BitAdderWithOverflowStr (n,f,g)) -defined Function-like the Sorts of (BitAdderWithOverflowCirc (n,f,g)) -compatible total Element of K235( the Sorts of (BitAdderWithOverflowCirc (n,f,g)))
Following (o0,2) is Relation-like the carrier of (BitAdderWithOverflowStr (n,f,g)) -defined Function-like the Sorts of (BitAdderWithOverflowCirc (n,f,g)) -compatible total Element of K235( the Sorts of (BitAdderWithOverflowCirc (n,f,g)))
the carrier of (2GatesCircStr (n,f,g,'xor')) is non empty set
the Sorts of (BitAdderCirc (n,f,g)) is Relation-like non-empty the carrier of (2GatesCircStr (n,f,g,'xor')) -defined Function-like total set
K235( the Sorts of (BitAdderCirc (n,f,g))) is non empty functional V52() V53() set
o0 | the carrier of (2GatesCircStr (n,f,g,'xor')) is Relation-like the carrier of (2GatesCircStr (n,f,g,'xor')) -defined the carrier of (BitAdderWithOverflowStr (n,f,g)) -defined Function-like the Sorts of (BitAdderWithOverflowCirc (n,f,g)) -compatible set
the carrier of (MajorityStr (n,f,g)) is non empty set
the Sorts of (MajorityCirc (n,f,g)) is Relation-like non-empty the carrier of (MajorityStr (n,f,g)) -defined Function-like total set
K235( the Sorts of (MajorityCirc (n,f,g))) is non empty functional V52() V53() set
o0 | the carrier of (MajorityStr (n,f,g)) is Relation-like the carrier of (MajorityStr (n,f,g)) -defined the carrier of (BitAdderWithOverflowStr (n,f,g)) -defined Function-like the Sorts of (BitAdderWithOverflowCirc (n,f,g)) -compatible set
the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) is non empty set
the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))) is Relation-like non-empty the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) -defined Function-like total set
K235( the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g)))) is non empty functional V52() V53() set
InputVertices (2GatesCircStr (n,f,g,'xor')) is Element of K23( the carrier of (2GatesCircStr (n,f,g,'xor')))
K23( the carrier of (2GatesCircStr (n,f,g,'xor'))) is non empty set
the ResultSort of (2GatesCircStr (n,f,g,'xor')) is Relation-like the carrier' of (2GatesCircStr (n,f,g,'xor')) -defined the carrier of (2GatesCircStr (n,f,g,'xor')) -valued Function-like V30( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) Element of K23(K24( 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
K24( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor'))) is non empty Relation-like set
K23(K24( the carrier' of (2GatesCircStr (n,f,g,'xor')), the carrier of (2GatesCircStr (n,f,g,'xor')))) is non empty set
K497( the carrier of (2GatesCircStr (n,f,g,'xor')), the ResultSort of (2GatesCircStr (n,f,g,'xor'))) is Element of K23( the carrier of (2GatesCircStr (n,f,g,'xor')))
the carrier of (2GatesCircStr (n,f,g,'xor')) \ K497( the carrier of (2GatesCircStr (n,f,g,'xor')), the ResultSort of (2GatesCircStr (n,f,g,'xor'))) is Element of K23( the carrier of (2GatesCircStr (n,f,g,'xor')))
{n,f,g} is non empty V39() V54() set
InputVertices (MajorityStr (n,f,g)) is Element of K23( the carrier of (MajorityStr (n,f,g)))
K23( the carrier of (MajorityStr (n,f,g))) is non empty set
the ResultSort of (MajorityStr (n,f,g)) is Relation-like the carrier' of (MajorityStr (n,f,g)) -defined the carrier of (MajorityStr (n,f,g)) -valued Function-like V30( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) Element of K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))))
the carrier' of (MajorityStr (n,f,g)) is non empty set
K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr (n,f,g)), the carrier of (MajorityStr (n,f,g)))) is non empty set
K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
the carrier of (MajorityStr (n,f,g)) \ K497( the carrier of (MajorityStr (n,f,g)), the ResultSort of (MajorityStr (n,f,g))) is Element of K23( the carrier of (MajorityStr (n,f,g)))
InnerVertices (2GatesCircStr (n,f,g,'xor')) is non empty Element of K23( the carrier of (2GatesCircStr (n,f,g,'xor')))
InnerVertices (MajorityStr (n,f,g)) is non empty Element of K23( the carrier of (MajorityStr (n,f,g)))
f1 is Relation-like the carrier of (2GatesCircStr (n,f,g,'xor')) -defined Function-like the Sorts of (BitAdderCirc (n,f,g)) -compatible total Element of K235( the Sorts of (BitAdderCirc (n,f,g)))
Following (f1,2) is Relation-like the carrier of (2GatesCircStr (n,f,g,'xor')) -defined Function-like the Sorts of (BitAdderCirc (n,f,g)) -compatible total Element of K235( the Sorts of (BitAdderCirc (n,f,g)))
h1 is Relation-like the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) -defined Function-like the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))) -compatible total Element of K235( the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))))
Following (h1,2) is Relation-like the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) -defined Function-like the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))) -compatible total Element of K235( the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))))
(Following (h1,2)) | the carrier of (2GatesCircStr (n,f,g,'xor')) is Relation-like the carrier of (2GatesCircStr (n,f,g,'xor')) -defined the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) -defined Function-like the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))) -compatible set
Following (f1,3) is Relation-like the carrier of (2GatesCircStr (n,f,g,'xor')) -defined Function-like the Sorts of (BitAdderCirc (n,f,g)) -compatible total Element of K235( the Sorts of (BitAdderCirc (n,f,g)))
Following (h1,3) is Relation-like the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) -defined Function-like the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))) -compatible total Element of K235( the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))))
(Following (h1,3)) | the carrier of (2GatesCircStr (n,f,g,'xor')) is Relation-like the carrier of (2GatesCircStr (n,f,g,'xor')) -defined the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) -defined Function-like the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))) -compatible set
g1 is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
Following (g1,2) is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
(Following (h1,2)) | the carrier of (MajorityStr (n,f,g)) is Relation-like the carrier of (MajorityStr (n,f,g)) -defined the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) -defined Function-like the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))) -compatible set
Following (g1,3) is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
(Following (h1,3)) | the carrier of (MajorityStr (n,f,g)) is Relation-like the carrier of (MajorityStr (n,f,g)) -defined the carrier of ((2GatesCircStr (n,f,g,'xor')) +* (MajorityStr (n,f,g))) -defined Function-like the Sorts of ((BitAdderCirc (n,f,g)) +* (MajorityCirc (n,f,g))) -compatible set
Following (Following (f1,2)) is Relation-like the carrier of (2GatesCircStr (n,f,g,'xor')) -defined Function-like the Sorts of (BitAdderCirc (n,f,g)) -compatible total Element of K235( the Sorts of (BitAdderCirc (n,f,g)))
2 + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
Following (f1,(2 + 1)) is Relation-like the carrier of (2GatesCircStr (n,f,g,'xor')) -defined Function-like the Sorts of (BitAdderCirc (n,f,g)) -compatible total Element of K235( the Sorts of (BitAdderCirc (n,f,g)))
Following (Following (g1,2)) is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
Following (g1,(2 + 1)) is Relation-like the carrier of (MajorityStr (n,f,g)) -defined Function-like the Sorts of (MajorityCirc (n,f,g)) -compatible total Element of K235( the Sorts of (MajorityCirc (n,f,g)))
Following (o0,(2 + 1)) is Relation-like the carrier of (BitAdderWithOverflowStr (n,f,g)) -defined Function-like the Sorts of (BitAdderWithOverflowCirc (n,f,g)) -compatible total Element of K235( the Sorts of (BitAdderWithOverflowCirc (n,f,g)))
Following (Following (o0,2)) is Relation-like the carrier of (BitAdderWithOverflowStr (n,f,g)) -defined Function-like the Sorts of (BitAdderWithOverflowCirc (n,f,g)) -compatible total Element of K235( the Sorts of (BitAdderWithOverflowCirc (n,f,g)))
proj1 (Following (o0,2)) is set
Following (o0,3) is Relation-like the carrier of (BitAdderWithOverflowStr (n,f,g)) -defined Function-like the Sorts of (BitAdderWithOverflowCirc (n,f,g)) -compatible total Element of K235( the Sorts of (BitAdderWithOverflowCirc (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 (MajorityStr (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
K23(K24(NAT,NAT)) is non empty V5() V39() set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f is Relation-like Function-like set
proj1 f is set
g is Relation-like Function-like set
proj1 g is set
proj2 g is set
S0 is set
A0 is set
g . A0 is set
N is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . N is set
S0 is Relation-like NAT -defined NAT -valued Function-like V30( NAT , NAT ) Element of K23(K24(NAT,NAT))
S0 . 0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
S0 . 1 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
S0 . 2 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . 0 is set
f . 1 is set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
2 * n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
1 + (2 * n) is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f is Relation-like NAT -defined Function-like V39() n -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
g is Relation-like NAT -defined Function-like V39() n -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
(n,f,g) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (n,f,g) is non empty set
(n,f,g) is strict non-empty finitely-generated V110((n,f,g)) gate`2=den Boolean MSAlgebra over (n,f,g)
the Sorts of (n,f,g) is Relation-like non-empty the carrier of (n,f,g) -defined Function-like total set
K235( the Sorts of (n,f,g)) is non empty functional V52() V53() set
N is Relation-like NAT -defined NAT -valued Function-like V30( NAT , NAT ) Element of K23(K24(NAT,NAT))
N . 0 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
N . 1 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
N . 2 is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
Sn is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
Sn + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . (Sn + 1) is non pair set
g . (Sn + 1) is non pair set
h is set
BitAdderWithOverflowCirc ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V110( BitAdderWithOverflowStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) gate`2=den Boolean MSAlgebra over BitAdderWithOverflowStr ((f . (Sn + 1)),(g . (Sn + 1)),h)
BitAdderWithOverflowStr ((f . (Sn + 1)),(g . (Sn + 1)),h) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(f . (Sn + 1)),(g . (Sn + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'},{<*(f . (Sn + 1)),(g . (Sn + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],h*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],h*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (Sn + 1)),(g . (Sn + 1)),h) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (Sn + 1)),(g . (Sn + 1)),h) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (Sn + 1)),h*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*h,(f . (Sn + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*h,(f . (Sn + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,'&'))) +* (1GateCircStr (<*h,(f . (Sn + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'] is non empty pair set
{<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'},{<*(f . (Sn + 1)),(g . (Sn + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (Sn + 1)),h*>,'&'] is non empty pair set
{<*(g . (Sn + 1)),h*>,'&'} is non empty functional V39() V54() set
{<*(g . (Sn + 1)),h*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (Sn + 1)),h*>,'&'},{<*(g . (Sn + 1)),h*>}} is non empty V39() V43() V54() set
[<*h,(f . (Sn + 1))*>,'&'] is non empty pair set
{<*h,(f . (Sn + 1))*>,'&'} is non empty functional V39() V54() set
{<*h,(f . (Sn + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*h,(f . (Sn + 1))*>,'&'},{<*h,(f . (Sn + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),h*>,'&'],[<*h,(f . (Sn + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),h*>,'&'],[<*h,(f . (Sn + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),h*>,'&'],[<*h,(f . (Sn + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,'xor')) +* (MajorityStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitAdderCirc ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110((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'))
MajorityCirc ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V110( MajorityStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) gate`2=den Boolean MSAlgebra over MajorityStr ((f . (Sn + 1)),(g . (Sn + 1)),h)
MajorityICirc ((f . (Sn + 1)),(g . (Sn + 1)),h) is strict non-empty finitely-generated V110( MajorityIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) gate`2=den Boolean MSAlgebra over MajorityIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)
1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')
1GateCircuit (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')
1GateCircuit ((g . (Sn + 1)),h,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(g . (Sn + 1)),h*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (Sn + 1)),h*>,'&')
1GateCircuit (<*(g . (Sn + 1)),h*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(g . (Sn + 1)),h*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (Sn + 1)),h*>,'&')
(1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),'&')) +* (1GateCircuit ((g . (Sn + 1)),h,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,'&'))
1GateCircuit (h,(f . (Sn + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*h,(f . (Sn + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*h,(f . (Sn + 1))*>,'&')
1GateCircuit (<*h,(f . (Sn + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*h,(f . (Sn + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*h,(f . (Sn + 1))*>,'&')
((1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),'&')) +* (1GateCircuit ((g . (Sn + 1)),h,'&'))) +* (1GateCircuit (h,(f . (Sn + 1)),'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,'&'))) +* (1GateCircStr (<*h,(f . (Sn + 1))*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) +* (1GateCircStr (<*(g . (Sn + 1)),h*>,'&'))) +* (1GateCircStr (<*h,(f . (Sn + 1))*>,'&'))
1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),h*>,'&'],[<*h,(f . (Sn + 1))*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),h*>,'&'],[<*h,(f . (Sn + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),h*>,'&'],[<*h,(f . (Sn + 1))*>,'&']*>,or3)
1GateCircuit (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),h*>,'&'],[<*h,(f . (Sn + 1))*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),h*>,'&'],[<*h,(f . (Sn + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),h*>,'&'],[<*h,(f . (Sn + 1))*>,'&']*>,or3)
(MajorityICirc ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),h*>,'&'],[<*h,(f . (Sn + 1))*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),h*>,'&'],[<*h,(f . (Sn + 1))*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),h*>,'&'],[<*h,(f . (Sn + 1))*>,'&']*>,or3))
(BitAdderCirc ((f . (Sn + 1)),(g . (Sn + 1)),h)) +* (MajorityCirc ((f . (Sn + 1)),(g . (Sn + 1)),h)) is strict non-empty finitely-generated V110((2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,'xor')) +* (MajorityStr ((f . (Sn + 1)),(g . (Sn + 1)),h))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),h,'xor')) +* (MajorityStr ((f . (Sn + 1)),(g . (Sn + 1)),h))
the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) is non empty set
the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))) is Relation-like non-empty the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) -defined Function-like total set
K235( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE)))) is non empty functional V52() V53() set
h is Relation-like the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) -defined Function-like the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))) -compatible total Element of K235( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))))
Following (h,1) is Relation-like the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) -defined Function-like the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))) -compatible total Element of K235( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))))
Following h is Relation-like the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) -defined Function-like the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))) -compatible total Element of K235( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))))
Following (h,H₄( 0 )) is Relation-like the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) -defined Function-like the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))) -compatible total Element of K235( the Sorts of (1GateCircuit ({},((0 -tuples_on BOOLEAN) --> FALSE))))
h is Relation-like NAT -defined Function-like total set
Sn is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
Sn + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . (Sn + 1) is non pair set
g . (Sn + 1) is non pair set
h . Sn is set
An is set
BitAdderWithOverflowStr ((f . (Sn + 1)),(g . (Sn + 1)),An) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(f . (Sn + 1)),(g . (Sn + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'},{<*(f . (Sn + 1)),(g . (Sn + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],An*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'xor'],An*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (Sn + 1)),(g . (Sn + 1)),An) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (Sn + 1)),(g . (Sn + 1)),An) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (Sn + 1)),An*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) +* (1GateCircStr (<*(g . (Sn + 1)),An*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*An,(f . (Sn + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*An,(f . (Sn + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) +* (1GateCircStr (<*(g . (Sn + 1)),An*>,'&'))) +* (1GateCircStr (<*An,(f . (Sn + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'] is non empty pair set
{<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'},{<*(f . (Sn + 1)),(g . (Sn + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (Sn + 1)),An*>,'&'] is non empty pair set
{<*(g . (Sn + 1)),An*>,'&'} is non empty functional V39() V54() set
{<*(g . (Sn + 1)),An*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (Sn + 1)),An*>,'&'},{<*(g . (Sn + 1)),An*>}} is non empty V39() V43() V54() set
[<*An,(f . (Sn + 1))*>,'&'] is non empty pair set
{<*An,(f . (Sn + 1))*>,'&'} is non empty functional V39() V54() set
{<*An,(f . (Sn + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*An,(f . (Sn + 1))*>,'&'},{<*An,(f . (Sn + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),An*>,'&'],[<*An,(f . (Sn + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),An*>,'&'],[<*An,(f . (Sn + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),An*>,'&'],[<*An,(f . (Sn + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),An,'xor')) +* (MajorityStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
BitAdderWithOverflowCirc ((f . (Sn + 1)),(g . (Sn + 1)),An) is strict non-empty finitely-generated V110( BitAdderWithOverflowStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) gate`2=den Boolean MSAlgebra over BitAdderWithOverflowStr ((f . (Sn + 1)),(g . (Sn + 1)),An)
BitAdderCirc ((f . (Sn + 1)),(g . (Sn + 1)),An) is strict non-empty finitely-generated V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110((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'))
MajorityCirc ((f . (Sn + 1)),(g . (Sn + 1)),An) is strict non-empty finitely-generated V110( MajorityStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) gate`2=den Boolean MSAlgebra over MajorityStr ((f . (Sn + 1)),(g . (Sn + 1)),An)
MajorityICirc ((f . (Sn + 1)),(g . (Sn + 1)),An) is strict non-empty finitely-generated V110( MajorityIStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) gate`2=den Boolean MSAlgebra over MajorityIStr ((f . (Sn + 1)),(g . (Sn + 1)),An)
1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')
1GateCircuit (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')
1GateCircuit ((g . (Sn + 1)),An,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(g . (Sn + 1)),An*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (Sn + 1)),An*>,'&')
1GateCircuit (<*(g . (Sn + 1)),An*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(g . (Sn + 1)),An*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (Sn + 1)),An*>,'&')
(1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),'&')) +* (1GateCircuit ((g . (Sn + 1)),An,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) +* (1GateCircStr (<*(g . (Sn + 1)),An*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) +* (1GateCircStr (<*(g . (Sn + 1)),An*>,'&'))
1GateCircuit (An,(f . (Sn + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*An,(f . (Sn + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*An,(f . (Sn + 1))*>,'&')
1GateCircuit (<*An,(f . (Sn + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*An,(f . (Sn + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*An,(f . (Sn + 1))*>,'&')
((1GateCircuit ((f . (Sn + 1)),(g . (Sn + 1)),'&')) +* (1GateCircuit ((g . (Sn + 1)),An,'&'))) +* (1GateCircuit (An,(f . (Sn + 1)),'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) +* (1GateCircStr (<*(g . (Sn + 1)),An*>,'&'))) +* (1GateCircStr (<*An,(f . (Sn + 1))*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&')) +* (1GateCircStr (<*(g . (Sn + 1)),An*>,'&'))) +* (1GateCircStr (<*An,(f . (Sn + 1))*>,'&'))
1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),An*>,'&'],[<*An,(f . (Sn + 1))*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),An*>,'&'],[<*An,(f . (Sn + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),An*>,'&'],[<*An,(f . (Sn + 1))*>,'&']*>,or3)
1GateCircuit (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),An*>,'&'],[<*An,(f . (Sn + 1))*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),An*>,'&'],[<*An,(f . (Sn + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),An*>,'&'],[<*An,(f . (Sn + 1))*>,'&']*>,or3)
(MajorityICirc ((f . (Sn + 1)),(g . (Sn + 1)),An)) +* (1GateCircuit ([<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),An*>,'&'],[<*An,(f . (Sn + 1))*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),An*>,'&'],[<*An,(f . (Sn + 1))*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) +* (1GateCircStr (<*[<*(f . (Sn + 1)),(g . (Sn + 1))*>,'&'],[<*(g . (Sn + 1)),An*>,'&'],[<*An,(f . (Sn + 1))*>,'&']*>,or3))
(BitAdderCirc ((f . (Sn + 1)),(g . (Sn + 1)),An)) +* (MajorityCirc ((f . (Sn + 1)),(g . (Sn + 1)),An)) is strict non-empty finitely-generated V110((2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),An,'xor')) +* (MajorityStr ((f . (Sn + 1)),(g . (Sn + 1)),An))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((f . (Sn + 1)),(g . (Sn + 1)),An,'xor')) +* (MajorityStr ((f . (Sn + 1)),(g . (Sn + 1)),An))
the carrier of H<sub>1</sub>(An,Sn) is non empty set
o0 is non-empty finitely-generated V110(H<sub>1</sub>(An,Sn)) MSAlgebra over H<sub>1</sub>(An,Sn)
the Sorts of o0 is Relation-like non-empty the carrier of H<sub>1</sub>(An,Sn) -defined Function-like total set
K235( the Sorts of o0) is non empty functional V52() V53() set
(Sn,f,g) is Element of InnerVertices (Sn,f,g)
(Sn,f,g) is non empty non void V74() 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 K23( the carrier of (Sn,f,g))
K23( the carrier of (Sn,f,g)) is non empty set
the ResultSort of (Sn,f,g) is Relation-like the carrier' of (Sn,f,g) -defined the carrier of (Sn,f,g) -valued Function-like V30( the carrier' of (Sn,f,g), the carrier of (Sn,f,g)) Element of K23(K24( the carrier' of (Sn,f,g), the carrier of (Sn,f,g)))
the carrier' of (Sn,f,g) is non empty set
K24( the carrier' of (Sn,f,g), the carrier of (Sn,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (Sn,f,g), the carrier of (Sn,f,g))) is non empty set
K497( the carrier of (Sn,f,g), the ResultSort of (Sn,f,g)) is Element of K23( the carrier of (Sn,f,g))
f1 is Relation-like the carrier of H₁(An,Sn) -defined Function-like the Sorts of o0 -compatible total Element of K235( the Sorts of o0)
Following (f1,(N . 1)) is Relation-like the carrier of (BitAdderWithOverflowStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) -defined Function-like the Sorts of o0 -compatible total Element of K235( the Sorts of o0)
the carrier of (BitAdderWithOverflowStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) is non empty set
the Sorts of o0 is Relation-like non-empty the carrier of (BitAdderWithOverflowStr ((f . (Sn + 1)),(g . (Sn + 1)),An)) -defined Function-like total set
K235( the Sorts of o0) is non empty functional V52() V53() set
(0,f,g) is non empty pair Element of InnerVertices (0,f,g)
(0,f,g) is non empty non void V74() 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 K23( the carrier of (0,f,g))
K23( the carrier of (0,f,g)) is non empty set
the ResultSort of (0,f,g) is Relation-like the carrier' of (0,f,g) -defined the carrier of (0,f,g) -valued Function-like V30( the carrier' of (0,f,g), the carrier of (0,f,g)) Element of K23(K24( the carrier' of (0,f,g), the carrier of (0,f,g)))
the carrier' of (0,f,g) is non empty set
K24( the carrier' of (0,f,g), the carrier of (0,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (0,f,g), the carrier of (0,f,g))) is non empty set
K497( the carrier of (0,f,g), the ResultSort of (0,f,g)) is Element of K23( the carrier of (0,f,g))
f1 is Relation-like NAT -defined Function-like total set
f1 . n is set
g1 is Relation-like NAT -defined Function-like total set
g1 . n is set
f1 . 0 is set
g1 . 0 is set
h1 is Relation-like NAT -defined Function-like total set
h1 . 0 is set
n is set
h1 . n is set
x is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
(x,f,g) is non empty pair Element of InnerVertices (x,f,g)
(x,f,g) is non empty non void V74() 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 K23( the carrier of (x,f,g))
K23( the carrier of (x,f,g)) is non empty set
the ResultSort of (x,f,g) is Relation-like the carrier' of (x,f,g) -defined the carrier of (x,f,g) -valued Function-like V30( the carrier' of (x,f,g), the carrier of (x,f,g)) Element of K23(K24( the carrier' of (x,f,g), the carrier of (x,f,g)))
the carrier' of (x,f,g) is non empty set
K24( the carrier' of (x,f,g), the carrier of (x,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (x,f,g), the carrier of (x,f,g))) is non empty set
K497( the carrier of (x,f,g), the ResultSort of (x,f,g)) is Element of K23( 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 V74() ManySortedSign
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . (n + 1) is non pair set
g . (n + 1) is non pair set
xy is set
BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),xy) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(f . (n + 1)),(g . (n + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'xor'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],xy*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],xy*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (n + 1)),(g . (n + 1)),xy) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (n + 1)),(g . (n + 1)),xy) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (n + 1)),xy*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),xy*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*xy,(f . (n + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*xy,(f . (n + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),xy*>,'&'))) +* (1GateCircStr (<*xy,(f . (n + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,'&'] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'&'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (n + 1)),xy*>,'&'] is non empty pair set
{<*(g . (n + 1)),xy*>,'&'} is non empty functional V39() V54() set
{<*(g . (n + 1)),xy*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (n + 1)),xy*>,'&'},{<*(g . (n + 1)),xy*>}} is non empty V39() V43() V54() set
[<*xy,(f . (n + 1))*>,'&'] is non empty pair set
{<*xy,(f . (n + 1))*>,'&'} is non empty functional V39() V54() set
{<*xy,(f . (n + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*xy,(f . (n + 1))*>,'&'},{<*xy,(f . (n + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (n + 1)),(g . (n + 1)),xy)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (n + 1)),(g . (n + 1)),xy,'xor')) +* (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)) is non empty non void V74() 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 BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),xy)
BitAdderWithOverflowCirc ((f . (n + 1)),(g . (n + 1)),xy) is strict non-empty finitely-generated V110( BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),xy)) gate`2=den Boolean MSAlgebra over BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),xy)
BitAdderCirc ((f . (n + 1)),(g . (n + 1)),xy) is strict non-empty finitely-generated V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110( 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 V110((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'))
MajorityCirc ((f . (n + 1)),(g . (n + 1)),xy) is strict non-empty finitely-generated V110( MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)) gate`2=den Boolean MSAlgebra over MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)
MajorityICirc ((f . (n + 1)),(g . (n + 1)),xy) is strict non-empty finitely-generated V110( MajorityIStr ((f . (n + 1)),(g . (n + 1)),xy)) gate`2=den Boolean MSAlgebra over MajorityIStr ((f . (n + 1)),(g . (n + 1)),xy)
1GateCircuit ((f . (n + 1)),(g . (n + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')
1GateCircuit (<*(f . (n + 1)),(g . (n + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')
1GateCircuit ((g . (n + 1)),xy,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(g . (n + 1)),xy*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (n + 1)),xy*>,'&')
1GateCircuit (<*(g . (n + 1)),xy*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*(g . (n + 1)),xy*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*(g . (n + 1)),xy*>,'&')
(1GateCircuit ((f . (n + 1)),(g . (n + 1)),'&')) +* (1GateCircuit ((g . (n + 1)),xy,'&')) is strict non-empty finitely-generated V110((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),xy*>,'&'))) gate`2=den Boolean MSAlgebra over (1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),xy*>,'&'))
1GateCircuit (xy,(f . (n + 1)),'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*xy,(f . (n + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*xy,(f . (n + 1))*>,'&')
1GateCircuit (<*xy,(f . (n + 1))*>,'&') is strict non-empty finitely-generated V110( 1GateCircStr (<*xy,(f . (n + 1))*>,'&')) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*xy,(f . (n + 1))*>,'&')
((1GateCircuit ((f . (n + 1)),(g . (n + 1)),'&')) +* (1GateCircuit ((g . (n + 1)),xy,'&'))) +* (1GateCircuit (xy,(f . (n + 1)),'&')) is strict non-empty finitely-generated V110(((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),xy*>,'&'))) +* (1GateCircStr (<*xy,(f . (n + 1))*>,'&'))) gate`2=den Boolean MSAlgebra over ((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),xy*>,'&'))) +* (1GateCircStr (<*xy,(f . (n + 1))*>,'&'))
1GateCircuit ([<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&'],or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&']*>,or3)
1GateCircuit (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&']*>,or3) is strict non-empty finitely-generated V110( 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&']*>,or3)) gate`2=den Boolean MSAlgebra over 1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&']*>,or3)
(MajorityICirc ((f . (n + 1)),(g . (n + 1)),xy)) +* (1GateCircuit ([<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&'],or3)) is strict non-empty finitely-generated V110((MajorityIStr ((f . (n + 1)),(g . (n + 1)),xy)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&']*>,or3))) gate`2=den Boolean MSAlgebra over (MajorityIStr ((f . (n + 1)),(g . (n + 1)),xy)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&']*>,or3))
(BitAdderCirc ((f . (n + 1)),(g . (n + 1)),xy)) +* (MajorityCirc ((f . (n + 1)),(g . (n + 1)),xy)) is strict non-empty finitely-generated V110((2GatesCircStr ((f . (n + 1)),(g . (n + 1)),xy,'xor')) +* (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy))) gate`2=den Boolean MSAlgebra over (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),xy,'xor')) +* (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy))
f1 . (n + 1) is set
x +* (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),xy)) is non empty non void V74() strict ManySortedSign
g1 . (n + 1) is set
xx +* c<sub>18</sub> is strict non-empty MSAlgebra over x +* (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),xy))
h . (n + 1) is set
MajorityOutput ((f . (n + 1)),(g . (n + 1)),xy) is Element of InnerVertices (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy))
the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)) is non empty set
InnerVertices (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)) is non empty Element of K23( the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)))
K23( the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy))) is non empty set
the ResultSort of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)) is Relation-like the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)) -defined the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)) -valued Function-like V30( the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)), the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy))) Element of K23(K24( the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)), the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy))))
the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)) is non empty set
K24( the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)), the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)), the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)))) is non empty set
K497( the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)), the ResultSort of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy))) is Element of K23( the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),xy)))
[<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&']*>,or3] is non empty pair set
{<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&']*>,or3},{<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),xy*>,'&'],[<*xy,(f . (n + 1))*>,'&']*>}} is non empty V39() V43() V54() set
InnerVertices (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) is non empty Element of K23( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))))
K23( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)))) is non empty set
the ResultSort of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) is Relation-like the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) -defined the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) -valued Function-like V30( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)))) Element of K23(K24( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)))))
the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) is non empty set
K24( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)))) is non empty Relation-like set
K23(K24( the carrier' of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))), the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))))) is non empty set
K497( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))), the ResultSort of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)))) is Element of K23( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))))
InputVertices (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) is Element of K23( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))))
the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))) \ K497( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))), the ResultSort of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE)))) is Element of K23( the carrier of (1GateCircStr ({},((0 -tuples_on BOOLEAN) --> FALSE))))
{[{},((0 -tuples_on BOOLEAN) --> FALSE)]} is non empty V5() Relation-like Function-like constant V39() 1 -element V54() set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . (n + 1) is non pair set
g . (n + 1) is non pair set
x is set
BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(f . (n + 1)),(g . (n + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'xor'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (n + 1)),x*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),x*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*x,(f . (n + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*x,(f . (n + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),x*>,'&'))) +* (1GateCircStr (<*x,(f . (n + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,'&'] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'&'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (n + 1)),x*>,'&'] is non empty pair set
{<*(g . (n + 1)),x*>,'&'} is non empty functional V39() V54() set
{<*(g . (n + 1)),x*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (n + 1)),x*>,'&'},{<*(g . (n + 1)),x*>}} is non empty V39() V43() V54() set
[<*x,(f . (n + 1))*>,'&'] is non empty pair set
{<*x,(f . (n + 1))*>,'&'} is non empty functional V39() V54() set
{<*x,(f . (n + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*x,(f . (n + 1))*>,'&'},{<*x,(f . (n + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (n + 1)),(g . (n + 1)),x)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')) +* (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InnerVertices (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty Element of K23( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)))
the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
K23( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))) is non empty set
the ResultSort of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) is Relation-like the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) -defined the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))))
the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the ResultSort of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)))
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
h . n is set
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f . (n + 1) is non pair set
g . (n + 1) is non pair set
x is set
BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V74() 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 V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'xor') is non empty non void V74() 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 V39() V54() set
{<*(f . (n + 1)),(g . (n + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'xor'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (n + 1)),x*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),x*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*x,(f . (n + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*x,(f . (n + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),x*>,'&'))) +* (1GateCircStr (<*x,(f . (n + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,'&'] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,'&'} is non empty functional V39() V54() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'&'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (n + 1)),x*>,'&'] is non empty pair set
{<*(g . (n + 1)),x*>,'&'} is non empty functional V39() V54() set
{<*(g . (n + 1)),x*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (n + 1)),x*>,'&'},{<*(g . (n + 1)),x*>}} is non empty V39() V43() V54() set
[<*x,(f . (n + 1))*>,'&'] is non empty pair set
{<*x,(f . (n + 1))*>,'&'} is non empty functional V39() V54() set
{<*x,(f . (n + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*x,(f . (n + 1))*>,'&'},{<*x,(f . (n + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (n + 1)),(g . (n + 1)),x)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')) +* (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty non void V74() 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 K23( the carrier of H<sub>1</sub>(x,n))
K23( the carrier of H<sub>1</sub>(x,n)) is non empty set
the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
the ResultSort of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) is Relation-like the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) -defined the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))))
the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the ResultSort of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)))
K23( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))) is non empty set
the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) \ K497( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the ResultSort of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)))
{x} is non empty V5() V39() 1 -element V54() set
(InputVertices H<sub>1</sub>(x,n)) \ {x} is Element of K23( 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 V74() 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 K23( the carrier of (n,f,g))
K23( the carrier of (n,f,g)) is non empty set
the ResultSort of (n,f,g) is Relation-like the carrier' of (n,f,g) -defined the carrier of (n,f,g) -valued Function-like V30( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K24( the carrier' of (n,f,g), the carrier of (n,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g))) is non empty set
K497( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K23( the carrier of (n,f,g))
{(f . (n + 1)),(g . (n + 1)),x} is non empty V39() V54() set
xx is non empty pair set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() set
h . n is set
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() 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
MajorityOutput ((f . (n + 1)),(g . (n + 1)),x) is Element of InnerVertices (MajorityStr ((f . (n + 1)),(g . (n + 1)),x))
MajorityStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
MajorityIStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&') is non empty non void V74() 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 V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*(g . (n + 1)),x*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),x*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
<*x,(f . (n + 1))*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*x,(f . (n + 1))*>,'&') is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
((1GateCircStr (<*(f . (n + 1)),(g . (n + 1))*>,'&')) +* (1GateCircStr (<*(g . (n + 1)),x*>,'&'))) +* (1GateCircStr (<*x,(f . (n + 1))*>,'&')) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
[<*(f . (n + 1)),(g . (n + 1))*>,'&'] is non empty pair set
{<*(f . (n + 1)),(g . (n + 1))*>,'&'} is non empty functional V39() V54() set
{<*(f . (n + 1)),(g . (n + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'&'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V39() V43() V54() set
[<*(g . (n + 1)),x*>,'&'] is non empty pair set
{<*(g . (n + 1)),x*>,'&'} is non empty functional V39() V54() set
{<*(g . (n + 1)),x*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*(g . (n + 1)),x*>,'&'},{<*(g . (n + 1)),x*>}} is non empty V39() V43() V54() set
[<*x,(f . (n + 1))*>,'&'] is non empty pair set
{<*x,(f . (n + 1))*>,'&'} is non empty functional V39() V54() set
{<*x,(f . (n + 1))*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*x,(f . (n + 1))*>,'&'},{<*x,(f . (n + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']*> is non empty Relation-like NAT -defined Function-like V39() 3 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']*>,or3) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(MajorityIStr ((f . (n + 1)),(g . (n + 1)),x)) +* (1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']*>,or3)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
InnerVertices (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty Element of K23( the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)))
K23( the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x))) is non empty set
the ResultSort of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)) is Relation-like the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)) -defined the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)) -valued Function-like V30( the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x))) Element of K23(K24( the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x))))
the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
K24( the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x))) is non empty Relation-like set
K23(K24( the carrier' of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)))) is non empty set
K497( the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)), the ResultSort of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x))) is Element of K23( the carrier of (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)))
[<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']*>,or3] is non empty pair set
{<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']*>,or3} is non empty functional V39() V54() set
{<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']*>,or3},{<*[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']*>}} is non empty V39() V43() V54() set
BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x) is non empty non void V74() 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 V74() 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 V74() 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 V39() V54() set
{{<*(f . (n + 1)),(g . (n + 1))*>,'xor'},{<*(f . (n + 1)),(g . (n + 1))*>}} is non empty V39() V43() V54() set
<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*> is non empty Relation-like NAT -defined Function-like V39() 2 -element FinSequence-like FinSubsequence-like V54() set
1GateCircStr (<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>,'xor') is non empty non void V74() 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 V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
(2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')) +* (MajorityStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty non void V74() strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ManySortedSign
InputVertices H<sub>1</sub>(x,n) is Element of K23( the carrier of H<sub>1</sub>(x,n))
the carrier of H<sub>1</sub>(x,n) is non empty set
K23( the carrier of H<sub>1</sub>(x,n)) is non empty set
the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
the ResultSort of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) is Relation-like the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) -defined the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) -valued Function-like V30( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))) Element of K23(K24( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))))
the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) is non empty set
K24( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))) is non empty Relation-like set
K23(K24( the carrier' of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)))) is non empty set
K497( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the ResultSort of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)))
K23( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))) is non empty set
the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)) \ K497( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)), the ResultSort of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x))) is Element of K23( the carrier of (BitAdderWithOverflowStr ((f . (n + 1)),(g . (n + 1)),x)))
InnerVertices H<sub>1</sub>(x,n) is non empty Element of K23( 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 V74() 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 K23( the carrier of (n,f,g))
K23( the carrier of (n,f,g)) is non empty set
the ResultSort of (n,f,g) is Relation-like the carrier' of (n,f,g) -defined the carrier of (n,f,g) -valued Function-like V30( the carrier' of (n,f,g), the carrier of (n,f,g)) Element of K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g)))
the carrier' of (n,f,g) is non empty set
K24( the carrier' of (n,f,g), the carrier of (n,f,g)) is non empty Relation-like set
K23(K24( the carrier' of (n,f,g), the carrier of (n,f,g))) is non empty set
K497( the carrier of (n,f,g), the ResultSort of (n,f,g)) is Element of K23( 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 V74() 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 K23( the carrier of ((n + 1),f,g))
K23( the carrier of ((n + 1),f,g)) is non empty set
the ResultSort of ((n + 1),f,g) is Relation-like the carrier' of ((n + 1),f,g) -defined the carrier of ((n + 1),f,g) -valued Function-like V30( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) Element of K23(K24( 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
K24( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g)) is non empty Relation-like set
K23(K24( the carrier' of ((n + 1),f,g), the carrier of ((n + 1),f,g))) is non empty set
K497( the carrier of ((n + 1),f,g), the ResultSort of ((n + 1),f,g)) is Element of K23( the carrier of ((n + 1),f,g))
{(f . (n + 1)),(g . (n + 1)),x} is non empty V39() V54() set
{H₃(x,n)} is non empty V5() V39() 1 -element V54() 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 K23( the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')))
K23( the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor'))) is non empty set
the ResultSort of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')) is Relation-like the carrier' of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')) -defined the carrier of (2GatesCircStr ((f . (n + 1)),(g . (n + 1)),x,'xor')) -valued Function-like V30( 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 K23(K24( 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
K24( 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 Relation-like set
K23(K24( 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
K497( 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 K23( 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 V39() V54() set
{<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>} is non empty V5() functional V39() V43() 1 -element V52() V54() set
{{<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>,'xor'},{<*[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],x*>}} is non empty V39() V43() V54() set
{[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(2GatesCircOutput ((f . (n + 1)),(g . (n + 1)),x,'xor'))} is non empty Relation-like V39() V54() set
{[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']} is non empty Relation-like V39() V54() set
{[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(2GatesCircOutput ((f . (n + 1)),(g . (n + 1)),x,'xor'))} \/ {[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']} is non empty Relation-like V39() V54() set
{(MajorityOutput ((f . (n + 1)),(g . (n + 1)),x))} is non empty V5() V39() 1 -element V54() set
({[<*(f . (n + 1)),(g . (n + 1))*>,'xor'],(2GatesCircOutput ((f . (n + 1)),(g . (n + 1)),x,'xor'))} \/ {[<*(f . (n + 1)),(g . (n + 1))*>,'&'],[<*(g . (n + 1)),x*>,'&'],[<*x,(f . (n + 1))*>,'&']}) \/ {(MajorityOutput ((f . (n + 1)),(g . (n + 1)),x))} is non empty V39() V54() set
H₄(2) * H₄(1) is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
H₄( 0 ) + (H₄(2) * H₄(1)) is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n is Relation-like the carrier of (n,f,g) -defined Function-like the Sorts of (n,f,g) -compatible total Element of K235( the Sorts of (n,f,g))
Following (n,(1 + (2 * n))) is Relation-like the carrier of (n,f,g) -defined Function-like the Sorts of (n,f,g) -compatible total Element of K235( the Sorts of (n,f,g))
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f is Relation-like NAT -defined Function-like V39() n + 1 -element FinSequence-like FinSubsequence-like V54() set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
n + 1 is ext-real positive non negative non empty V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT
f is Relation-like NAT -defined Function-like V39() n + 1 -element FinSequence-like FinSubsequence-like V54() nonpair-yielding set
n is ext-real non negative V12() V13() V14() V18() non pair V33() V34() V39() cardinal V54() Element of NAT