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 Th114:
  for G1 being addVertices of G2, V
  holds G1 is finite-ecolorable iff G2 is finite-ecolorable
proof
  let G1 be addVertices of G2, V;
  hereby
    assume G1 is finite-ecolorable;
    then consider n such that
      A1: G1 is n-ecolorable;
    G2 is n-ecolorable by A1, Th105;
    hence G2 is finite-ecolorable;
  end;
  assume G2 is finite-ecolorable;
  then consider n such that
    A2: G2 is n-ecolorable;
  thus thesis by A2;
end;
