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 Th18:
  for G2 being reverseEdgeDirections of G1, E
  for f1 being VColoring of G1, f2 being VColoring of G2
  st f1 = f2 holds f1 is proper iff f2 is proper
proof
  let G2 be reverseEdgeDirections of G1, E;
  let f1 be VColoring of G1, f2 be VColoring of G2;
  assume A1: f1 = f2;
  hence f1 is proper implies f2 is proper by Lm1;
  G1 is reverseEdgeDirections of G2, E by GLIB_007:3;
  hence thesis by A1, Lm1;
end;
