
theorem Th06:
  for P,Q being Element of TOP-REAL 2 st P <> Q holds
  P.1 <> Q.1 or P.2 <> Q.2
  proof
    let P,Q be Element of TOP-REAL 2;
    assume
A1: P <> Q;
    assume P.1 = Q.1 & P.2 = Q.2;
    then P`1 = Q`1 & P`2 = Q`2;
    then P = |[Q`1,Q`2]| by EUCLID:53
          .= Q by EUCLID:53;
    hence contradiction by A1;
  end;
