Definition prime' p := 1<p /\ (forall n, 1<n<p -> ~ (n|p)).

(* Specifications: *)
Lemma Z_0_1_more x : 0<=x -> x=0 \/ x=1 \/ 1<x.
Theorem prime_alt p : prime' p <-> prime p.
Theorem square_not_prime: forall a, ~ prime (a * a).
Theorem prime_div_prime: forall p q, prime p -> prime q -> (p | q) -> p = q.