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

theorem Th91:
  for G2 being reverseEdgeDirections of G1, E
  for g1 being EColoring of G1, g2 being EColoring of G2
  st g1 = g2 holds g1 is proper iff g2 is proper
proof
  let G2 be reverseEdgeDirections of G1, E;
  let g1 be EColoring of G1, g2 be EColoring of G2;
  assume A1: g1 = g2;
  hence g1 is proper implies g2 is proper by Lm7;
  G1 is reverseEdgeDirections of G2, E by GLIB_007:3;
  hence thesis by A1, Lm7;
end;
