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 Th137:
  G is edgeless implies [f, {}] is TColoring of G
proof
  assume A1: G is edgeless;
  reconsider g = id the_Edges_of G as EColoring of G;
  g = {} by A1;
  hence thesis by Def9;
end;
