(* step 6 *)
(* The set of Pythagorean triples *)

(* Relative primality and fractions *)
Lemma relp_frac : forall a b c d : Z,
(b <> 0) -> (d <> 0) -> (frac a b) = (frac c d) -> (rel_prime c d) ->
exists m : Z, m <> 0 /\ b = m * d.