
theorem Th26:
  for am,bp,cm,dp being non pair set for cin being set st cin <> [
<*dp,GFA2AdderOutput(am,bp,cm)*>,and2] & not cin in InnerVertices BitGFA2Str(am
  ,bp,cm) holds am in InputVertices BitFTA2Str(am,bp,cm,dp,cin) & bp in
InputVertices BitFTA2Str(am,bp,cm,dp,cin) & cm in InputVertices BitFTA2Str(am,
  bp,cm,dp,cin) & dp in InputVertices BitFTA2Str(am,bp,cm,dp,cin) & cin in
  InputVertices BitFTA2Str(am,bp,cm,dp,cin)
proof
  let am,bp,cm,dp be non pair set;
  let cin be set;
  set S = BitFTA2Str(am,bp,cm,dp,cin);
  set S1 = BitGFA2Str(am,bp,cm);
  set A1 = GFA2AdderOutput(am,bp,cm);
  set dpA1 = [<*dp,A1*>,and2];
  assume cin <> dpA1 & not cin in InnerVertices S1;
  then InputVertices S = {am,bp,cm,dp,cin} by Th23;
  hence thesis by ENUMSET1:def 3;
end;
