(********************************************************************)
 
Inductive prime : nat -> Prop :=
    primeDef :
      forall a : nat,
      a <> 1 -> (forall b : nat, divides b a -> b <> 1 -> a = b) -> prime a.(********************************************************************)
 
Inductive prime : nat -> Prop :=
    primeDef :
      forall a : nat,
      a <> 1 -> (forall b : nat, divides b a -> b <> 1 -> a = b) -> prime a.

(* Specifications: *)
Lemma not_prime_O : ~ prime 0.
Lemma not_prime_1 : ~ prime 1.
Lemma lt_prime : forall p : nat, prime p -> 1 < p.