
theorem Th14:
  for ap,bm,cp,dm,cin being set holds ap in the carrier of
BitFTA1Str(ap,bm,cp,dm,cin) & bm in the carrier of BitFTA1Str(ap,bm,cp,dm,cin)
  & cp in the carrier of BitFTA1Str(ap,bm,cp,dm,cin) & dm in the carrier of
BitFTA1Str(ap,bm,cp,dm,cin) & cin in the carrier of BitFTA1Str(ap,bm,cp,dm,cin)
  & [<*ap,bm*>,xor2c] in the carrier of BitFTA1Str(ap,bm,cp,dm,cin) &
GFA1AdderOutput(ap,bm,cp) in the carrier of BitFTA1Str(ap,bm,cp,dm,cin) & [<*ap
,bm*>,and2c] in the carrier of BitFTA1Str(ap,bm,cp,dm,cin) & [<*bm,cp*>,and2a]
  in the carrier of BitFTA1Str(ap,bm,cp,dm,cin) & [<*cp,ap*>,and2 ] in the
  carrier of BitFTA1Str(ap,bm,cp,dm,cin) & GFA1CarryOutput(ap,bm,cp) in the
  carrier of BitFTA1Str(ap,bm,cp,dm,cin) & [<*GFA1AdderOutput(ap,bm,cp),cin*>,
  xor2c] in the carrier of BitFTA1Str(ap,bm,cp,dm,cin) & GFA2AdderOutput(
GFA1AdderOutput(ap,bm,cp),cin,dm) in the carrier of BitFTA1Str(ap,bm,cp,dm,cin)
& [<*GFA1AdderOutput(ap,bm,cp),cin*>,and2a] in the carrier of BitFTA1Str(ap,bm,
cp,dm,cin) & [<*cin,dm*>,and2c] in the carrier of BitFTA1Str(ap,bm,cp,dm,cin) &
[<*dm,GFA1AdderOutput(ap,bm,cp)*>,nor2] in the carrier of BitFTA1Str(ap,bm,cp,
  dm,cin) & GFA2CarryOutput(GFA1AdderOutput(ap,bm,cp),cin,dm) in the carrier of
  BitFTA1Str(ap,bm,cp,dm,cin)
proof
  let ap,bm,cp,dm,cin be set;
  set S1 = BitGFA1Str(ap,bm,cp);
  set A1 = GFA1AdderOutput(ap,bm,cp);
  set C1 = GFA1CarryOutput(ap,bm,cp);
  set S2 = BitGFA2Str(A1,cin,dm);
  set A2 = GFA2AdderOutput(A1,cin,dm);
  set C2 = GFA2CarryOutput(A1,cin,dm);
  set apbm0 = [<*ap,bm*>, xor2c];
  set apbm = [<*ap,bm*>, and2c];
  set bmcp = [<*bm,cp*>, and2a];
  set cpap = [<*cp,ap*>, and2 ];
  set A1cin0 = [<*A1,cin*>,xor2c];
  set A1cin = [<*A1,cin*>,and2a];
  set cindm = [<*cin,dm*>,and2c];
  set dmA1 = [<*dm,A1*>, nor2];
A1: cp in the carrier of S1 & apbm0 in the carrier of S1 by GFACIRC1:68;
A2: apbm in the carrier of S1 & bmcp in the carrier of S1 by GFACIRC1:68;
A3: A1 in the carrier of S2 & cin in the carrier of S2 by GFACIRC1:100;
A4: cpap in the carrier of S1 & C1 in the carrier of S1 by GFACIRC1:68;
A5: C2 in the carrier of S2 by GFACIRC1:100;
A6: cindm in the carrier of S2 & dmA1 in the carrier of S2 by GFACIRC1:100;
A7: A2 in the carrier of S2 & A1cin in the carrier of S2 by GFACIRC1:100;
A8: dm in the carrier of S2 & A1cin0 in the carrier of S2 by GFACIRC1:100;
  ap in the carrier of S1 & bm in the carrier of S1 by GFACIRC1:68;
  hence thesis by A1,A2,A4,A3,A8,A7,A6,A5,FACIRC_1:20;
end;
