proposition: Theorem div_by_prime : forall n:nat, 1 < n -> (exists p:nat, 1 < p < n /\ (exists q : nat, n=p*q)) -> (exists p:nat, 1 < p < n /\ (prime p) /\ (exists q:nat, n=p*q)).
proof: Proof. intros n; apply (div_by_prime_aux n n). auto with arith. Qed.
imports: List Arith