Commit 97ba3264 authored by Robbert Krebbers's avatar Robbert Krebbers

Remove unused lemmas wp_impl_{l,r}.

And introduce more useful variants with a wand.
parent d0276a67
...@@ -186,14 +186,14 @@ Proof. ...@@ -186,14 +186,14 @@ Proof.
split; [done|intros e2 σ2 ef ?]. split; [done|intros e2 σ2 ef ?].
destruct (Hstep e2 σ2 ef) as (r2&r2'&?&?&?); auto. destruct (Hstep e2 σ2 ef) as (r2&r2'&?&?&?); auto.
exists (r2 rR), r2'; split_and?; auto. exists (r2 rR), r2'; split_and?; auto.
- by rewrite -(assoc _ r2) - by rewrite -(assoc _ r2) (comm _ rR) !assoc -(assoc _ _ rR).
(comm _ rR) !assoc -(assoc _ _ rR).
- apply IH; eauto using uPred_weaken. - apply IH; eauto using uPred_weaken.
Qed. Qed.
Lemma wp_frame_step_r E e Φ R : Lemma wp_frame_step_r E e Φ R :
to_val e = None (WP e @ E {{ Φ }} R) WP e @ E {{ λ v, Φ v R }}. to_val e = None (WP e @ E {{ Φ }} R) WP e @ E {{ λ v, Φ v R }}.
Proof. Proof.
rewrite wp_eq. intros He; uPred.unseal; split; intros n r' Hvalid (r&rR&Hr&Hwp&?). rewrite wp_eq.
intros He; uPred.unseal; split; intros n r' Hvalid (r&rR&Hr&Hwp&?).
revert Hvalid; rewrite Hr; clear Hr. revert Hvalid; rewrite Hr; clear Hr.
destruct Hwp as [|n r e ? Hgo]; [by rewrite to_of_val in He|]. destruct Hwp as [|n r e ? Hgo]; [by rewrite to_of_val in He|].
constructor; [done|]=>rf k Ef σ1 ???; destruct n as [|n]; first omega. constructor; [done|]=>rf k Ef σ1 ???; destruct n as [|n]; first omega.
...@@ -253,15 +253,15 @@ Proof. by setoid_rewrite (always_and_sep_l _ _); rewrite wp_frame_l. Qed. ...@@ -253,15 +253,15 @@ Proof. by setoid_rewrite (always_and_sep_l _ _); rewrite wp_frame_l. Qed.
Lemma wp_always_r E e Φ R `{!PersistentP R} : Lemma wp_always_r E e Φ R `{!PersistentP R} :
(WP e @ E {{ Φ }} R) WP e @ E {{ λ v, Φ v R }}. (WP e @ E {{ Φ }} R) WP e @ E {{ λ v, Φ v R }}.
Proof. by setoid_rewrite (always_and_sep_r _ _); rewrite wp_frame_r. Qed. Proof. by setoid_rewrite (always_and_sep_r _ _); rewrite wp_frame_r. Qed.
Lemma wp_impl_l E e Φ Ψ : Lemma wp_wand_l E e Φ Ψ :
(( v, Φ v Ψ v) WP e @ E {{ Φ }}) WP e @ E {{ Ψ }}. (( v, Φ v - Ψ v) WP e @ E {{ Φ }}) WP e @ E {{ Ψ }}.
Proof. Proof.
rewrite wp_always_l. apply wp_mono=> // v. rewrite wp_frame_l. apply wp_mono=> v. by rewrite (forall_elim v) wand_elim_l.
by rewrite always_elim (forall_elim v) impl_elim_l.
Qed. Qed.
Lemma wp_impl_r E e Φ Ψ : Lemma wp_wand_r E e Φ Ψ :
(WP e @ E {{ Φ }} ( v, Φ v Ψ v)) WP e @ E {{ Ψ }}. (WP e @ E {{ Φ }} ( v, Φ v - Ψ v)) WP e @ E {{ Ψ }}.
Proof. by rewrite comm wp_impl_l. Qed. Proof. by rewrite comm wp_wand_l. Qed.
Lemma wp_mask_weaken E1 E2 e Φ : Lemma wp_mask_weaken E1 E2 e Φ :
E1 E2 WP e @ E1 {{ Φ }} WP e @ E2 {{ Φ }}. E1 E2 WP e @ E1 {{ Φ }} WP e @ E2 {{ Φ }}.
Proof. auto using wp_mask_frame_mono. Qed. Proof. auto using wp_mask_frame_mono. Qed.
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