Implicit Types m n x y : nat.Definition zerop n : {n = 0} + {0 < n}.Definition lt_eq_lt_dec n m : {n < m} + {n = m} + {m < n}.Definition gt_eq_gt_dec n m : {m > n} + {n = m} + {n > m}.Definition le_lt_dec n m : {n <= m} + {m < n}.Definition le_le_S_dec n m : {n <= m} + {S m <= n}.Definition le_ge_dec n m : {n <= m} + {n >= m}.Definition le_gt_dec n m : {n <= m} + {n > m}.Definition le_lt_eq_dec n m : n <= m -> {n < m} + {n = m}.

Theorem not_eq n m : n <> m -> n < m \/ m < n.