
theorem Th8: :: Clique36b:
for R being non empty RelStr, a1,a2 being Element of R
 st a1 <= a2 or a2 <= a1 holds {a1,a2} is Clique of R
proof
let R be non empty RelStr, a1,a2 be Element of R;
  assume A1: a1 <= a2 or a2 <= a1;
  now
    let x,y be Element of R;
    assume x in {a1,a2} & y in {a1,a2};
     then A2: (x = a1 or x = a2) & (y = a1 or y = a2) by TARSKI:def 2;
    assume x <> y;
    hence x <= y or y <= x by A1,A2;
  end;
  hence thesis by Th6;
end;
