
theorem Th80:
for G being SimpleGraph, C being Coloring of G
  holds C is Clique-partition of Complement G
proof
 let G be SimpleGraph, C be Coloring of G;
   set CG = Complement G;
    now
      let x be set;
      assume x in C;
       then x is StableSet of G by Def20;
      hence CG SubgraphInducedBy x is Clique of CG by Th74;
    end;
 hence C is Clique-partition of CG by Lm4,Def16;
end;
