diff options
Diffstat (limited to 'theories/Arith')
| -rw-r--r-- | theories/Arith/Compare_dec.v | 16 |
1 files changed, 8 insertions, 8 deletions
diff --git a/theories/Arith/Compare_dec.v b/theories/Arith/Compare_dec.v index deb6f229b..d696360fd 100644 --- a/theories/Arith/Compare_dec.v +++ b/theories/Arith/Compare_dec.v @@ -22,17 +22,17 @@ Definition zerop n : {n = 0} + {0 < n}. Defined. Definition lt_eq_lt_dec n m : {n < m} + {n = m} + {m < n}. - induction n; simple destruct m; auto with arith. - intros m0; elim (IHn m0); auto with arith. - induction 1; auto with arith. + intros; induction n in m |- *; destruct m; auto with arith. + destruct (IHn m) as [H|H]; auto with arith. + destruct H; auto with arith. Defined. Definition gt_eq_gt_dec n m : {m > n} + {n = m} + {n > m}. - exact lt_eq_lt_dec. + intros; apply lt_eq_lt_dec; assumption. Defined. Definition le_lt_dec n m : {n <= m} + {m < n}. - induction n. + intros; induction n in m |- *. auto with arith. destruct m. auto with arith. @@ -40,7 +40,7 @@ Definition le_lt_dec n m : {n <= m} + {m < n}. Defined. Definition le_le_S_dec n m : {n <= m} + {S m <= n}. - exact le_lt_dec. + intros; exact (le_lt_dec n m). Defined. Definition le_ge_dec n m : {n <= m} + {n >= m}. @@ -48,11 +48,11 @@ Definition le_ge_dec n m : {n <= m} + {n >= m}. Defined. Definition le_gt_dec n m : {n <= m} + {n > m}. - exact le_lt_dec. + intros; exact (le_lt_dec n m). Defined. Definition le_lt_eq_dec n m : n <= m -> {n < m} + {n = m}. - intros; elim (lt_eq_lt_dec n m); auto with arith. + intros; destruct (lt_eq_lt_dec n m); auto with arith. intros; absurd (m < n); auto with arith. Defined. |