
theorem :: staRcliCR:
for R being with_finite_stability# symmetric RelStr
  holds stability# R = clique# ComplRelStr R
proof
 let R be with_finite_stability# symmetric RelStr;
   set CR = ComplRelStr R;   set k = clique# CR;
   consider A being finite Clique of CR such that
A1: card A = k by DILWORTH:def 4;
   A is StableSet of R by Th20;
   then
A2: ex C being finite StableSet of R st card C = k by A1;
   now let T be finite StableSet of R;
     T is Clique of CR by Th21;
    hence card T <= k by DILWORTH:def 4;
   end;
 hence stability# R = clique# ComplRelStr R by A2,DILWORTH:def 6;
end;
