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
  G1 == G2 & G1 is finite-ecolorable implies G2 is finite-ecolorable
proof
  assume A1: G1 == G2 & G1 is finite-ecolorable;
  then consider n such that
    A2: G1 is n-ecolorable;
  G2 is n-ecolorable by A1, A2, Th103;
  hence thesis;
end;
