reserve E,V for set, G,G1,G2 for _Graph, c,c1,c2 for Cardinal, n for Nat;
reserve f for VColoring of G;

theorem
  for f9 being one-to-one ManySortedSet of rng f
  holds f is proper implies f9*f is proper
proof
  let f9 be one-to-one ManySortedSet of rng f;
  rng f c= dom f9 by PARTFUN1:def 2;
  hence thesis by Th12;
end;
