diff options
-rw-r--r-- | backend/Kildall.v | 31 |
1 files changed, 1 insertions, 30 deletions
diff --git a/backend/Kildall.v b/backend/Kildall.v index 2a4b4bda..4379b00f 100644 --- a/backend/Kildall.v +++ b/backend/Kildall.v @@ -1101,36 +1101,7 @@ End BBlock_solver. Require Import FSets. Require Import FSetAVL. - -Module OrderedPositive <: OrderedType with Definition t := positive. - Definition t := positive. - Definition eq (x y: t) := x = y. - Definition lt := Plt. - - Lemma eq_refl : forall x : t, eq x x. - Proof. unfold eq; auto. Qed. - - Lemma eq_sym : forall x y : t, eq x y -> eq y x. - Proof. unfold eq; auto. Qed. - - Lemma eq_trans : forall x y z : t, eq x y -> eq y z -> eq x z. - Proof. unfold eq; intros. transitivity y; auto. Qed. - - Lemma lt_trans : forall x y z : t, lt x y -> lt y z -> lt x z. - Proof Plt_trans. - - Lemma lt_not_eq : forall x y : t, lt x y -> ~ eq x y. - Proof Plt_ne. - - Lemma compare : forall x y : t, Compare lt eq x y. - Proof. - intros. - caseEq (Zcompare (Zpos x) (Zpos y)); intros. - apply EQ. unfold eq. generalize (Zcompare_Eq_eq _ _ H). congruence. - apply LT. exact H. - apply GT. rewrite Zcompare_Gt_Lt_antisym in H. exact H. - Qed. -End OrderedPositive. +Require Import Ordered. Module PositiveSet := FSetAVL.Make(OrderedPositive). Module PositiveSetFacts := FSetFacts.Facts(PositiveSet). |