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 Th103:
  G1 == G2 & G1 is c-ecolorable implies G2 is c-ecolorable
proof
  assume A1: G1 == G2 & G1 is c-ecolorable;
  then consider g1 being proper EColoring of G1 such that
    A2: card rng g1 c= c;
  the_Edges_of G1 = the_Edges_of G2 by A1, GLIB_000:def 34;
  then reconsider g2 = g1 as EColoring of G2;
  g2 is proper by A1, Th90;
  hence thesis by A2;
end;
