:: deftheorem Def5 defines -BitGFA1Str GFACIRC2:def 5 :
for n being Nat
for x, y being FinSequence
for b₄ being non empty non void strict unsplit gate`1=arity gate`2isBoolean ManySortedSign holds
( b₄ = n -BitGFA1Str (x,y) iff ex f, h being ManySortedSet of NAT st
( b₄ = f . n & f . 0 = 1GateCircStr (<*>,((0 -tuples_on BOOLEAN) --> TRUE)) & h . 0 = [<*>,((0 -tuples_on BOOLEAN) --> TRUE)] & ( 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 +* (BitGFA1Str ((x . (n + 1)),(y . (n + 1)),z)) & h . (n + 1) = GFA1CarryOutput ((x . (n + 1)),(y . (n + 1)),z) ) ) ) );