:: deftheorem Def1 defines -BitFTA0Str FTACELL2:def 1 :
for n being Nat
for ap, bp, cp, dp being FinSequence
for b₆ being non empty non void strict unsplit gate`1=arity gate`2isBoolean ManySortedSign holds
( b₆ = n -BitFTA0Str (ap,bp,cp,dp) iff ex f, h being ManySortedSet of NAT st
( b₆ = f . n & f . 0 = 1GateCircStr (<*>,((0 -tuples_on BOOLEAN) --> FALSE)) & h . 0 = [<*>,((0 -tuples_on BOOLEAN) --> FALSE)] & ( for n being Nat
for S being non empty ManySortedSign
for z being set st S = f . n & z = h . n holds
( f . (n + 1) = S +* (BitFTA0Str ((ap . (n + 1)),(bp . (n + 1)),(cp . (n + 1)),(dp . (n + 1)),z)) & h . (n + 1) = BitFTA0CarryOutput ((ap . (n + 1)),(bp . (n + 1)),(cp . (n + 1)),(dp . (n + 1)),z) ) ) ) );