proposition: Lemma inj_mul (n m : nat) : n<>0 -> m<>0 -> Pos.of_nat (n*m) = (Pos.of_nat n * Pos.of_nat m)%positive.
proof: Proof. intros Hn Hm. apply Pos2Nat.inj. rewrite Pos2Nat.inj_mul, !id; trivial. intros H. apply Nat.mul_eq_0 in H. destruct H. - now elim Hn. - now elim Hm. Qed.
imports: BinPos PeanoNat