Commit f72563c7 authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Simplify pure_elim primitive of uPred.

parent d04287bc
......@@ -35,7 +35,7 @@ Notation "P ⊣⊢ Q" := (equiv (A:=uPred M) P%I Q%I). (* Force implicit argumen
(* Derived logical stuff *)
Lemma False_elim P : False P.
Proof. by apply (pure_elim False). Qed.
Proof. by apply (pure_elim' False). Qed.
Lemma True_intro P : P True.
Proof. by apply pure_intro. Qed.
......@@ -212,6 +212,11 @@ Proof.
- apply or_elim; apply exist_elim=> a; rewrite -(exist_intro a); auto.
Lemma pure_elim φ Q R : (Q φ) (φ Q R) Q R.
intros HQ HQR. rewrite -(idemp uPred_and Q) {1}HQ.
apply impl_elim_l', pure_elim'=> ?. by apply entails_impl, HQR.
Lemma pure_mono φ1 φ2 : (φ1 φ2) φ1 φ2.
Proof. intros; apply pure_elim with φ1; eauto. Qed.
Global Instance pure_mono' : Proper (impl ==> ()) (@uPred_pure M).
......@@ -319,10 +319,8 @@ Global Instance bupd_proper : Proper ((≡) ==> (≡)) (@uPred_bupd M) := ne_pro
(** Introduction and elimination rules *)
Lemma pure_intro φ P : φ P φ.
Proof. by intros ?; unseal; split. Qed.
Lemma pure_elim φ Q R : (Q φ) (φ Q R) Q R.
unseal; intros HQP HQR; split=> n x ??; apply HQR; first eapply HQP; eauto.
Lemma pure_elim' φ P : (φ True P) φ P.
Proof. unseal; intros HP; split=> n x ??. by apply HP. Qed.
Lemma pure_forall_2 {A} (φ : A Prop) : ( x : A, φ x) ( x : A, φ x).
Proof. by unseal. Qed.
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