diff options
Diffstat (limited to 'theories/Arith/Lt.v')
-rw-r--r-- | theories/Arith/Lt.v | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/theories/Arith/Lt.v b/theories/Arith/Lt.v index 1f7e6e018..940448202 100644 --- a/theories/Arith/Lt.v +++ b/theories/Arith/Lt.v @@ -51,7 +51,7 @@ Qed. Theorem lt_not_le : forall n m, n < m -> ~ m <= n. Proof. - red in |- *; intros n m Lt Le; exact (le_not_lt m n Le Lt). + red; intros n m Lt Le; exact (le_not_lt m n Le Lt). Qed. Hint Immediate le_not_lt lt_not_le: arith v62. @@ -107,12 +107,12 @@ Qed. Lemma lt_pred : forall n m, S n < m -> n < pred m. Proof. -induction 1; simpl in |- *; auto with arith. +induction 1; simpl; auto with arith. Qed. Hint Immediate lt_pred: arith v62. Lemma lt_pred_n_n : forall n, 0 < n -> pred n < n. -destruct 1; simpl in |- *; auto with arith. +destruct 1; simpl; auto with arith. Qed. Hint Resolve lt_pred_n_n: arith v62. @@ -159,7 +159,7 @@ Hint Immediate lt_le_weak: arith v62. Theorem le_or_lt : forall n m, n <= m \/ m < n. Proof. - intros n m; pattern n, m in |- *; apply nat_double_ind; auto with arith. + intros n m; pattern n, m; apply nat_double_ind; auto with arith. induction 1; auto with arith. Qed. |