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(* Specifications: *)
Lemma mult_p_lt_pq : forall p q : nat, 0 < p -> one < q -> p < p * q.
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Lemma mult_p_le_pq : forall p q : nat, 0 < q -> p <= p * q.
Hint Resolve mult_p_lt_pq mult_p_le_pq: arith.
Lemma enum4 :
forall n : nat,
n < S four -> n = 0 \/ n = one \/ n = two \/ n = three \/ n = four.