reserve A, B for non empty preBoolean set,
  x, y for Element of [:A,B:];
reserve X for set,
  a,b,c for Element of [:A,B:];
reserve a for Element of [:Fin X, Fin X:];
reserve A for set;

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;
