
theorem Th29: :: chrRcovCR:
for R being with_finite_chromatic# symmetric RelStr
  holds chromatic# R = cliquecover# ComplRelStr R
proof
 let R be with_finite_chromatic# symmetric RelStr;
 set CR = ComplRelStr R;      set k = cliquecover# CR;
    consider C being finite Clique-partition of CR such that
 A1: card C = k by Def5;
    C is Coloring of R by Th26;
    then
 A2: ex C being finite Coloring of R st card C = k by A1;
   now
     let C be finite Coloring of R;
     assume A3: k > card C;
     C is Clique-partition of CR by Th25;
     hence contradiction by A3,Def5;
   end;
 hence chromatic# R = cliquecover# CR by A2,Def3;
end;
