
theorem Th78:
for G being SimpleGraph, C being Clique-partition of Complement G
  holds C is Coloring of G
proof
 let G be SimpleGraph, C be Clique-partition of Complement G;
   set CG = Complement G;
    now
      let x be set;
      assume A1: x in C;
  then A2: (Complement G) SubgraphInducedBy x is Clique of CG by Def16;
       union ((Complement G) SubgraphInducedBy x) = x by A1,Lm9;
      hence x is StableSet of G by A2,Th73;
    end;
 hence C is Coloring of G by Lm4,Def20;
end;
