
theorem Th26: :: ClicoComplChr:
for R being symmetric RelStr, C being Clique-partition of ComplRelStr R
  holds C is Coloring of R
proof
 let R be symmetric RelStr, C being Clique-partition of ComplRelStr 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 CR by DILWORTH:def 11;
      hence x is StableSet of R by Th20;
    end;
 hence C is Coloring of R by A1,DILWORTH:def 12;
end;
