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 Th41:
  for G2 being removeDParallelEdges of G1
  holds G1 is c-vcolorable iff G2 is c-vcolorable
proof
  let G2 be removeDParallelEdges of G1;
  thus G1 is c-vcolorable implies G2 is c-vcolorable by Th31;
  assume A1: G2 is c-vcolorable;
  set G3 = the removeParallelEdges of G2;
  G3 is c-vcolorable & G3 is removeParallelEdges of G1
    by A1, Th31, GLIB_009:95;
  hence thesis by Th40;
end;
