
theorem :: covRchrCR:
for R being with_finite_cliquecover# symmetric RelStr
  holds cliquecover# R = chromatic# ComplRelStr R
proof
 let R be with_finite_cliquecover# symmetric RelStr;
 set CR = ComplRelStr R;      set k = chromatic# CR;
    consider C being finite Coloring of CR such that
 A1: card C = k by Def3;
    C is Clique-partition of R by Th28;
    then
 A2: ex C being finite Clique-partition of R st card C = k by A1;
   now
     let C be finite Clique-partition of R;
     assume A3: k > card C;
     C is Coloring of CR by Th27;
     hence contradiction by A3,Def3;
   end;
 hence cliquecover# R = chromatic# CR by A2,Def5;
end;
