theorem Th23:
  for y being Element of [:Fin X, Fin X:] holds y in
  DISJOINT_PAIRS X iff y`1 misses y`2
proof
  let y be Element of [:Fin X, Fin X:];
  y in DISJOINT_PAIRS X iff ex a st y = a & a`1 misses a`2;
  hence thesis;
end;
