
theorem Th34:
  for am,bm,cm,dm,cin being set holds am in the carrier of
BitFTA3Str(am,bm,cm,dm,cin) & bm in the carrier of BitFTA3Str(am,bm,cm,dm,cin)
  & cm in the carrier of BitFTA3Str(am,bm,cm,dm,cin) & dm in the carrier of
BitFTA3Str(am,bm,cm,dm,cin) & cin in the carrier of BitFTA3Str(am,bm,cm,dm,cin)
  & [<*am,bm*>,xor2] in the carrier of BitFTA3Str(am,bm,cm,dm,cin) &
GFA3AdderOutput(am,bm,cm) in the carrier of BitFTA3Str(am,bm,cm,dm,cin) & [<*am
,bm*>,nor2] in the carrier of BitFTA3Str(am,bm,cm,dm,cin) & [<*bm,cm*>,nor2]
  in the carrier of BitFTA3Str(am,bm,cm,dm,cin) & [<*cm,am*>,nor2] in the
  carrier of BitFTA3Str(am,bm,cm,dm,cin) & GFA3CarryOutput(am,bm,cm) in the
  carrier of BitFTA3Str(am,bm,cm,dm,cin) & [<*GFA3AdderOutput(am,bm,cm),cin*>,
  xor2] in the carrier of BitFTA3Str(am,bm,cm,dm,cin) & GFA3AdderOutput(
GFA3AdderOutput(am,bm,cm),cin,dm) in the carrier of BitFTA3Str(am,bm,cm,dm,cin)
& [<*GFA3AdderOutput(am,bm,cm),cin*>,nor2] in the carrier of BitFTA3Str(am,bm,
cm,dm,cin) & [<*cin,dm*>,nor2] in the carrier of BitFTA3Str(am,bm,cm,dm,cin) &
[<*dm,GFA3AdderOutput(am,bm,cm)*>,nor2] in the carrier of BitFTA3Str(am,bm,cm,
  dm,cin) & GFA3CarryOutput(GFA3AdderOutput(am,bm,cm),cin,dm) in the carrier of
  BitFTA3Str(am,bm,cm,dm,cin)
proof
  let am,bm,cm,dm,cin be set;
  set S1 = BitGFA3Str(am,bm,cm);
  set A1 = GFA3AdderOutput(am,bm,cm);
  set C1 = GFA3CarryOutput(am,bm,cm);
  set S2 = BitGFA3Str(A1,cin,dm);
  set A2 = GFA3AdderOutput(A1,cin,dm);
  set C2 = GFA3CarryOutput(A1,cin,dm);
  set ambm0 = [<*am,bm*>, xor2 ];
  set ambm = [<*am,bm*>, nor2];
  set bmcm = [<*bm,cm*>, nor2];
  set cmam = [<*cm,am*>, nor2];
  set A1cin0 = [<*A1,cin*>,xor2 ];
  set A1cin = [<*A1,cin*>,nor2];
  set cindm = [<*cin,dm*>,nor2];
  set dmA1 = [<*dm,A1*>, nor2];
A1: cm in the carrier of S1 & ambm0 in the carrier of S1 by GFACIRC1:132;
A2: ambm in the carrier of S1 & bmcm in the carrier of S1 by GFACIRC1:132;
A3: A1 in the carrier of S2 & cin in the carrier of S2 by GFACIRC1:132;
A4: cmam in the carrier of S1 & C1 in the carrier of S1 by GFACIRC1:132;
A5: C2 in the carrier of S2 by GFACIRC1:132;
A6: cindm in the carrier of S2 & dmA1 in the carrier of S2 by GFACIRC1:132;
A7: A2 in the carrier of S2 & A1cin in the carrier of S2 by GFACIRC1:132;
A8: dm in the carrier of S2 & A1cin0 in the carrier of S2 by GFACIRC1:132;
  am in the carrier of S1 & bm in the carrier of S1 by GFACIRC1:132;
  hence thesis by A1,A2,A4,A3,A8,A7,A6,A5,FACIRC_1:20;
end;
