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 Th59:
  for G being loopless _Graph holds 1 c= G.vChromaticNum()
proof
  let G be loopless _Graph;
  assume not 1 c= G.vChromaticNum();
  then G.vChromaticNum() in 1 by ORDINAL1:16;
  hence contradiction by CARD_1:49, TARSKI:def 1;
end;
