
theorem Th14: :: AChain36b:
for R being non empty RelStr, a1, a2 being Element of R
 st not (a1 <= a2 or a2 <= a1) holds {a1,a2} is StableSet of R
proof
 let R be non empty RelStr, a1,a2 be Element of R;
  assume
A1: not (a1 <= a2 or a2 <= a1);
    set S = {a1,a2};
   S is stable proof
    let x, y be Element of R such that
   A2: x in S & y in S & x <> y;
      (x = a1 or x = a2) & (y = a1 or y = a2) by A2,TARSKI:def 2;
      hence thesis by A1,A2;
   end;
   hence thesis;
end;
