
theorem Th36:
  for am,bm,cm,dm being non pair set for cin being set st cin <> [
<*dm,GFA3AdderOutput(am,bm,cm)*>,nor2] & not cin in InnerVertices BitGFA3Str(
  am,bm,cm) holds am in InputVertices BitFTA3Str(am,bm,cm,dm,cin) & bm in
InputVertices BitFTA3Str(am,bm,cm,dm,cin) & cm in InputVertices BitFTA3Str(am,
  bm,cm,dm,cin) & dm in InputVertices BitFTA3Str(am,bm,cm,dm,cin) & cin in
  InputVertices BitFTA3Str(am,bm,cm,dm,cin)
proof
  let am,bm,cm,dm be non pair set;
  let cin be set;
  set S = BitFTA3Str(am,bm,cm,dm,cin);
  set S1 = BitGFA3Str(am,bm,cm);
  set A1 = GFA3AdderOutput(am,bm,cm);
  set dmA1 = [<*dm,A1*>,nor2];
  assume cin <> dmA1 & not cin in InnerVertices S1;
  then InputVertices S = {am,bm,cm,dm,cin} by Th33;
  hence thesis by ENUMSET1:def 3;
end;
