let ap, bp, cp, dp be FinSequence; :: thesis: 0 -BitFTA0Layer2Str (ap,bp,cp,dp) = 1GateCircStr (<*>,((0 -tuples_on BOOLEAN) --> FALSE))
set S0 = 1GateCircStr (<*>,((0 -tuples_on BOOLEAN) --> FALSE));
consider g, h being ManySortedSet of NAT such that
A1: 0 -BitFTA0Layer2Str (ap,bp,cp,dp) = g . 0 and
A2: g . 0 = 1GateCircStr (<*>,((0 -tuples_on BOOLEAN) --> FALSE)) and
h . 0 = [<*>,((0 -tuples_on BOOLEAN) --> FALSE)] and
for k being Nat
for S being non empty ManySortedSign
for z being set st S = g . k & z = h . k holds
( g . (k + 1) = S +* (BitGFA0Str ((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))) ) by Def6;
thus 0 -BitFTA0Layer2Str (ap,bp,cp,dp) = 1GateCircStr (<*>,((0 -tuples_on BOOLEAN) --> FALSE)) by A1, A2; :: thesis: verum