diff options
Diffstat (limited to 'theories/Structures/OrderedType.v')
| -rw-r--r-- | theories/Structures/OrderedType.v | 28 |
1 files changed, 15 insertions, 13 deletions
diff --git a/theories/Structures/OrderedType.v b/theories/Structures/OrderedType.v index f84cdf32..75578195 100644 --- a/theories/Structures/OrderedType.v +++ b/theories/Structures/OrderedType.v @@ -108,19 +108,21 @@ Module OrderedTypeFacts (Import O: OrderedType). Lemma lt_total : forall x y, lt x y \/ eq x y \/ lt y x. Proof. intros; destruct (compare x y); auto. Qed. - Module OrderElts <: Orders.TotalOrder. - Definition t := t. - Definition eq := eq. - Definition lt := lt. - Definition le x y := lt x y \/ eq x y. - Definition eq_equiv := eq_equiv. - Definition lt_strorder := lt_strorder. - Definition lt_compat := lt_compat. - Definition lt_total := lt_total. - Lemma le_lteq : forall x y, le x y <-> lt x y \/ eq x y. - Proof. unfold le; intuition. Qed. - End OrderElts. - Module OrderTac := !MakeOrderTac OrderElts. + Module TO. + Definition t := t. + Definition eq := eq. + Definition lt := lt. + Definition le x y := lt x y \/ eq x y. + End TO. + Module IsTO. + Definition eq_equiv := eq_equiv. + Definition lt_strorder := lt_strorder. + Definition lt_compat := lt_compat. + Definition lt_total := lt_total. + Lemma le_lteq x y : TO.le x y <-> lt x y \/ eq x y. + Proof. reflexivity. Qed. + End IsTO. + Module OrderTac := !MakeOrderTac TO IsTO. Ltac order := OrderTac.order. Lemma le_eq x y z : ~lt x y -> eq y z -> ~lt x z. Proof. order. Qed. |