
theorem Th25: :: ChrClicoCompl:
for R being RelStr, C being Coloring of R
  holds C is Clique-partition of ComplRelStr R
proof
 let R be RelStr, C be Coloring of R;
A1: the carrier of R = the carrier of ComplRelStr R by NECKLACE:def 8;
    now
      let x be set;
      assume x in C;
        then x is StableSet of R by DILWORTH:def 12;
      hence x is Clique of ComplRelStr R by Th21;
    end;
 hence C is Clique-partition of ComplRelStr R by A1,DILWORTH:def 11;
end;
