:: deftheorem Def9 defines -BitFTA1Circ FTACELL2:def 9 :
for n being Nat
for ap, bm, cp, dm being FinSequence
for b₆ being strict gate`2=den Boolean Circuit of n -BitFTA1Str (ap,bm,cp,dm) holds
( b₆ = n -BitFTA1Circ (ap,bm,cp,dm) iff ex f, g, h being ManySortedSet of NAT st
( n -BitFTA1Str (ap,bm,cp,dm) = f . n & b₆ = g . n & f . 0 = 1GateCircStr (<*>,((0 -tuples_on BOOLEAN) --> FALSE)) & g . 0 = 1GateCircuit (<*>,((0 -tuples_on BOOLEAN) --> FALSE)) & h . 0 = [<*>,((0 -tuples_on BOOLEAN) --> FALSE)] & ( for n being Nat
for S being non empty ManySortedSign
for A being non-empty MSAlgebra over S
for z being set st S = f . n & A = g . n & z = h . n holds
( f . (n + 1) = S +* (BitFTA1Str ((ap . (n + 1)),(bm . (n + 1)),(cp . (n + 1)),(dm . (n + 1)),z)) & g . (n + 1) = A +* (BitFTA1Circ ((ap . (n + 1)),(bm . (n + 1)),(cp . (n + 1)),(dm . (n + 1)),z)) & h . (n + 1) = BitFTA1CarryOutput ((ap . (n + 1)),(bm . (n + 1)),(cp . (n + 1)),(dm . (n + 1)),z) ) ) ) );