
theorem Th27: :: ClicoChrCompl:
for R being symmetric RelStr, C being Clique-partition of R
  holds C is Coloring of ComplRelStr R
proof
 let R be symmetric RelStr, C being Clique-partition of R;
  set CR = ComplRelStr R;
A1: the carrier of R = the carrier of CR by NECKLACE:def 8;
    now
      let x be set;
      assume x in C;
        then x is Clique of R by DILWORTH:def 11;
      hence x is StableSet of CR by Th19;
    end;
 hence C is Coloring of ComplRelStr R by A1,DILWORTH:def 12;
end;
