diff options
Diffstat (limited to 'theories/Structures/OrderedTypeEx.v')
| -rw-r--r-- | theories/Structures/OrderedTypeEx.v | 24 |
1 files changed, 7 insertions, 17 deletions
diff --git a/theories/Structures/OrderedTypeEx.v b/theories/Structures/OrderedTypeEx.v index 128cd576..adeba9e4 100644 --- a/theories/Structures/OrderedTypeEx.v +++ b/theories/Structures/OrderedTypeEx.v @@ -6,8 +6,6 @@ (* * GNU Lesser General Public License Version 2.1 *) (***********************************************************************) -(* $Id: OrderedTypeEx.v 13297 2010-07-19 23:32:42Z letouzey $ *) - Require Import OrderedType. Require Import ZArith. Require Import Omega. @@ -111,26 +109,18 @@ Module Positive_as_OT <: UsualOrderedType. Definition eq_sym := @sym_eq t. Definition eq_trans := @trans_eq t. - Definition lt p q:= (p ?= q) Eq = Lt. + Definition lt := Plt. - Lemma lt_trans : forall x y z : t, lt x y -> lt y z -> lt x z. - Proof. - unfold lt; intros x y z. - change ((Zpos x < Zpos y)%Z -> (Zpos y < Zpos z)%Z -> (Zpos x < Zpos z)%Z). - omega. - Qed. + Definition lt_trans := Plt_trans. Lemma lt_not_eq : forall x y : t, lt x y -> ~ eq x y. Proof. - intros; intro. - rewrite H0 in H. - unfold lt in H. - rewrite Pcompare_refl in H; discriminate. + intros x y H. contradict H. rewrite H. apply Plt_irrefl. Qed. Definition compare : forall x y : t, Compare lt eq x y. Proof. - intros x y. destruct ((x ?= y) Eq) as [ | | ]_eqn. + intros x y. destruct (x ?= y) as [ | | ]_eqn. apply EQ; apply Pcompare_Eq_eq; assumption. apply LT; assumption. apply GT; apply ZC1; assumption. @@ -324,10 +314,10 @@ Module PositiveOrderedTypeBits <: UsualOrderedType. Lemma eq_dec (x y: positive): {x = y} + {x <> y}. Proof. - intros. case_eq ((x ?= y) Eq); intros. + intros. case_eq (x ?= y); intros. left. apply Pcompare_Eq_eq; auto. - right. red. intro. subst y. rewrite (Pcompare_refl x) in H. discriminate. - right. red. intro. subst y. rewrite (Pcompare_refl x) in H. discriminate. + right. red. intro. subst y. rewrite (Pos.compare_refl x) in H. discriminate. + right. red. intro. subst y. rewrite (Pos.compare_refl x) in H. discriminate. Qed. End PositiveOrderedTypeBits. |