proposition: Theorem prime_divide_prime_eq: forall p1 p2, prime p1 -> prime p2 -> Z.divide p1 p2 -> p1 = p2.
proof: Proof. intros p1 p2 Hp1 Hp2 Hp3. assert (Ha: 1 < p1). inversion Hp1; auto. assert (Ha1: 1 < p2). inversion Hp2; auto. case (Zle_lt_or_eq p1 p2); auto with zarith. apply Zdivide_le; auto with zarith. intros Hp4. case (prime_div_prime p1 p2); auto with zarith. Qed.
imports: ArithRing ZArith Zpow_facts Znumtheory Tactic