
theorem Th130:
  for x,y,z being non pair set holds InputVertices BitGFA3Str(x,y ,z) = {x,y,z}
proof
  let x,y,z be non pair set;
  set S = BitGFA3Str(x,y,z);
  set S1 = GFA3AdderStr(x,y,z);
  set S2 = GFA3CarryStr(x,y,z);
A1: InputVertices S1 = {x,y,z} & InputVertices S2 = {x,y,z} by Th114,
FACIRC_1:57;
  InnerVertices S1 is Relation & InnerVertices S2 is Relation by Th107,
FACIRC_1:58;
  hence InputVertices S = {x,y,z} \/ {x,y,z} by A1,FACIRC_1:7
    .= {x,y,z};
end;
