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(* Specifications: *)
Lemma not_lt_le : forall n m : nat, ~ n < m -> m <= n.
Hint Immediate not_lt_le: arith.
Lemma lt_not_lt : forall n p : nat, n < p -> ~ p < S n.
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Lemma lt_a_a_plus_b : forall a b : nat, 0 < b -> a < a + b.
Hint Resolve lt_a_a_plus_b: arith.