:: deftheorem Def2 defines -BitFTA0Circ FTACELL2:def 2 :
for n being Nat
for ap, bp, cp, dp being FinSequence
for b₆ being strict gate`2=den Boolean Circuit of n -BitFTA0Str (ap,bp,cp,dp) holds
( b₆ = n -BitFTA0Circ (ap,bp,cp,dp) iff ex f, g, h being ManySortedSet of NAT st
( n -BitFTA0Str (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 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 +* (BitFTA0Str ((ap . (n + 1)),(bp . (n + 1)),(cp . (n + 1)),(dp . (n + 1)),z)) & g . (n + 1) = A +* (BitFTA0Circ ((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) ) ) ) );