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 Th53:
  for F being PGraphMapping of G1, G2 st F is isomorphism
  holds G1 is finite-vcolorable iff G2 is finite-vcolorable
proof
  let F be PGraphMapping of G1, G2;
  assume A1: F is isomorphism;
  then reconsider F0 = F as one-to-one PGraphMapping of G1, G2;
  F0" is isomorphism by A1, GLIB_010:75;
  hence G1 is finite-vcolorable implies G2 is finite-vcolorable by Th52;
  thus G2 is finite-vcolorable implies G1 is finite-vcolorable by A1, Th52;
end;
