(********************************************************************)
 
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.

Lemma lt_prime : forall p : nat, prime p -> 1 < p.