
theorem Th20: :: CliComplSta:
for R being symmetric RelStr, C being Clique of ComplRelStr R
  holds C is StableSet of R
proof
 let R be symmetric RelStr, C be Clique of ComplRelStr R;
    now
      let x, y be Element of R such that
    A1: x in C and
    A2: y in C and
    A3: x <> y;
        reconsider a = x, b = y as Element of ComplRelStr R by NECKLACE:def 8;
        a <= b or b <= a by A1,A2,A3,DILWORTH:6;
        then a <= b & b <= a by Th6;
      hence not x <= y & not y <= x by Th17;
    end;
   hence C is StableSet of R by DILWORTH:def 2,NECKLACE:def 8;
end;
