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;
reserve t for TColoring of G;

theorem Th153:
  for G2 being reverseEdgeDirections of G1, E
  for t1 being TColoring of G1, t2 being TColoring of G2
  st t1 = t2 holds t1 is proper iff t2 is proper
proof
  let G2 be reverseEdgeDirections of G1, E;
  let t1 be TColoring of G1, t2 be TColoring of G2;
  assume A1: t1 = t2;
  hence t1 is proper implies t2 is proper by Lm16;
  G1 is reverseEdgeDirections of G2, E by GLIB_007:3;
  hence thesis by A1, Lm16;
end;
