
theorem Th57:
  for x,y,z being set holds [<*x,y*>,xor2c] in InnerVertices
GFA1AdderStr(x,y,z) & GFA1AdderOutput(x,y,z) in InnerVertices GFA1AdderStr(x,y,
  z)
proof
  let x,y,z be set;
  set f = xor2c;
  set S = GFA1AdderStr(x,y,z);
  InnerVertices S = {[<*x,y*>,f]} \/ {GFA1AdderOutput(x,y,z)} by Th55
    .= {[<*x,y*>,f],GFA1AdderOutput(x,y,z)} by ENUMSET1:1;
  hence thesis by TARSKI:def 2;
end;
