
theorem Th6:
  for ap,bp,cp,dp being non pair set for cin being set st cin <> [
<*dp,GFA0AdderOutput(ap,bp,cp)*>,and2] & not cin in InnerVertices BitGFA0Str(ap
  ,bp,cp) holds ap in InputVertices BitFTA0Str(ap,bp,cp,dp,cin) & bp in
InputVertices BitFTA0Str(ap,bp,cp,dp,cin) & cp in InputVertices BitFTA0Str(ap,
  bp,cp,dp,cin) & dp in InputVertices BitFTA0Str(ap,bp,cp,dp,cin) & cin in
  InputVertices BitFTA0Str(ap,bp,cp,dp,cin)
proof
  let ap,bp,cp,dp be non pair set;
  let cin be set;
  set S = BitFTA0Str(ap,bp,cp,dp,cin);
  set S1 = BitGFA0Str(ap,bp,cp);
  set A1 = GFA0AdderOutput(ap,bp,cp);
  set dpA1 = [<*dp,A1*>,and2];
  assume cin <> dpA1 & not cin in InnerVertices S1;
  then InputVertices S = {ap,bp,cp,dp,cin} by Th3;
  hence thesis by ENUMSET1:def 3;
end;
