
theorem Th16:
  for ap,bm,cp,dm being non pair set for cin being set st cin <> [
<*dm,GFA1AdderOutput(ap,bm,cp)*>,nor2] & not cin in InnerVertices BitGFA1Str(
  ap,bm,cp) holds ap in InputVertices BitFTA1Str(ap,bm,cp,dm,cin) & bm in
InputVertices BitFTA1Str(ap,bm,cp,dm,cin) & cp in InputVertices BitFTA1Str(ap,
  bm,cp,dm,cin) & dm in InputVertices BitFTA1Str(ap,bm,cp,dm,cin) & cin in
  InputVertices BitFTA1Str(ap,bm,cp,dm,cin)
proof
  let ap,bm,cp,dm be non pair set;
  let cin be set;
  set S = BitFTA1Str(ap,bm,cp,dm,cin);
  set S1 = BitGFA1Str(ap,bm,cp);
  set A1 = GFA1AdderOutput(ap,bm,cp);
  set dmA1 = [<*dm,A1*>,nor2];
  assume cin <> dmA1 & not cin in InnerVertices S1;
  then InputVertices S = {ap,bm,cp,dm,cin} by Th13;
  hence thesis by ENUMSET1:def 3;
end;
