:: deftheorem Def7 defines -BitFTA0Layer2Circ FTACELL2:def 7 :
for n being Nat
for ap, bp, cp, dp being FinSequence
for b₆ being strict gate`2=den Boolean Circuit of n -BitFTA0Layer2Str (ap,bp,cp,dp) holds
( b₆ = n -BitFTA0Layer2Circ (ap,bp,cp,dp) iff ex f, g, h being ManySortedSet of NAT st
( n -BitFTA0Layer2Str (ap,bp,cp,dp) = 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 k being Nat
for S being non empty ManySortedSign
for A being non-empty MSAlgebra over S
for z being set st S = f . k & A = g . k & z = h . k holds
( f . (k + 1) = S +* (BitGFA0Str ((GFA0AdderOutput ((ap . (k + 1)),(bp . (k + 1)),(cp . (k + 1)))),z,(dp . (k + 1)))) & g . (k + 1) = A +* (BitGFA0Circ ((GFA0AdderOutput ((ap . (k + 1)),(bp . (k + 1)),(cp . (k + 1)))),z,(dp . (k + 1)))) & h . (k + 1) = GFA0CarryOutput ((ap . (k + 1)),(bp . (k + 1)),(cp . (k + 1))) ) ) ) );