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
  for G being loopless non edgeless _Graph holds 2 c= G.vChromaticNum()
proof
  let G be loopless non edgeless _Graph;
  assume not 2 c= G.vChromaticNum();
  then G.vChromaticNum() in 2 by ORDINAL1:16;
  then G.vChromaticNum() = 1 by CARD_1:50, TARSKI:def 2;
  hence contradiction by Th60;
end;
