
theorem Th24:
  for am,bp,cm,dp,cin being set holds am in the carrier of
BitFTA2Str(am,bp,cm,dp,cin) & bp in the carrier of BitFTA2Str(am,bp,cm,dp,cin)
  & cm in the carrier of BitFTA2Str(am,bp,cm,dp,cin) & dp in the carrier of
BitFTA2Str(am,bp,cm,dp,cin) & cin in the carrier of BitFTA2Str(am,bp,cm,dp,cin)
  & [<*am,bp*>,xor2c] in the carrier of BitFTA2Str(am,bp,cm,dp,cin) &
GFA2AdderOutput(am,bp,cm) in the carrier of BitFTA2Str(am,bp,cm,dp,cin) & [<*am
,bp*>,and2a] in the carrier of BitFTA2Str(am,bp,cm,dp,cin) & [<*bp,cm*>,and2c]
  in the carrier of BitFTA2Str(am,bp,cm,dp,cin) & [<*cm,am*>,nor2] in the
  carrier of BitFTA2Str(am,bp,cm,dp,cin) & GFA2CarryOutput(am,bp,cm) in the
  carrier of BitFTA2Str(am,bp,cm,dp,cin) & [<*GFA2AdderOutput(am,bp,cm),cin*>,
  xor2c] in the carrier of BitFTA2Str(am,bp,cm,dp,cin) & GFA1AdderOutput(
GFA2AdderOutput(am,bp,cm),cin,dp) in the carrier of BitFTA2Str(am,bp,cm,dp,cin)
& [<*GFA2AdderOutput(am,bp,cm),cin*>,and2c] in the carrier of BitFTA2Str(am,bp,
cm,dp,cin) & [<*cin,dp*>,and2a] in the carrier of BitFTA2Str(am,bp,cm,dp,cin) &
[<*dp,GFA2AdderOutput(am,bp,cm)*>,and2] in the carrier of BitFTA2Str(am,bp,cm,
  dp,cin) & GFA1CarryOutput(GFA2AdderOutput(am,bp,cm),cin,dp) in the carrier of
  BitFTA2Str(am,bp,cm,dp,cin)
proof
  let am,bp,cm,dp,cin be set;
  set S1 = BitGFA2Str(am,bp,cm);
  set A1 = GFA2AdderOutput(am,bp,cm);
  set C1 = GFA2CarryOutput(am,bp,cm);
  set S2 = BitGFA1Str(A1,cin,dp);
  set A2 = GFA1AdderOutput(A1,cin,dp);
  set C2 = GFA1CarryOutput(A1,cin,dp);
  set ambp0 = [<*am,bp*>, xor2c];
  set ambp = [<*am,bp*>, and2a];
  set bpcm = [<*bp,cm*>, and2c];
  set cmam = [<*cm,am*>, nor2];
  set A1cin0 = [<*A1,cin*>,xor2c];
  set A1cin = [<*A1,cin*>,and2c];
  set cindp = [<*cin,dp*>,and2a];
  set dpA1 = [<*dp,A1*>, and2 ];
A1: cm in the carrier of S1 & ambp0 in the carrier of S1 by GFACIRC1:100;
A2: ambp in the carrier of S1 & bpcm in the carrier of S1 by GFACIRC1:100;
A3: A1 in the carrier of S2 & cin in the carrier of S2 by GFACIRC1:68;
A4: cmam in the carrier of S1 & C1 in the carrier of S1 by GFACIRC1:100;
A5: C2 in the carrier of S2 by GFACIRC1:68;
A6: cindp in the carrier of S2 & dpA1 in the carrier of S2 by GFACIRC1:68;
A7: A2 in the carrier of S2 & A1cin in the carrier of S2 by GFACIRC1:68;
A8: dp in the carrier of S2 & A1cin0 in the carrier of S2 by GFACIRC1:68;
  am in the carrier of S1 & bp in the carrier of S1 by GFACIRC1:100;
  hence thesis by A1,A2,A4,A3,A8,A7,A6,A5,FACIRC_1:20;
end;
