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Commit efd340e5 authored by Ralf Jung's avatar Ralf Jung
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provide tactics to more easily apply wands

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algebra/upred.v
+ 15
− 0
View file @ efd340e5
...@@ -623,6 +623,21 @@ Lemma wand_elim_l' P Q R : P ⊑ (Q -★ R) → (P ★ Q) ⊑ R. ...@@ -623,6 +623,21 @@ Lemma wand_elim_l' P Q R : P ⊑ (Q -★ R) → (P ★ Q) ⊑ R.
Proof. intros ->; apply wand_elim_l. Qed. Proof. intros ->; apply wand_elim_l. Qed.
Lemma wand_elim_r' P Q R : Q ⊑ (P -★ R) → (P ★ Q) ⊑ R. Lemma wand_elim_r' P Q R : Q ⊑ (P -★ R) → (P ★ Q) ⊑ R.
Proof. intros ->; apply wand_elim_r. Qed. Proof. intros ->; apply wand_elim_r. Qed.
Lemma wand_apply_l P Q Q' R R' : P ⊑ (Q' -★ R') → R' ⊑ R → Q ⊑ Q' → (P ★ Q) ⊑ R.
Proof. intros -> -> <-; apply wand_elim_l. Qed.
Lemma wand_apply_r P Q Q' R R' : P ⊑ (Q' -★ R') → R' ⊑ R → Q ⊑ Q' → (Q ★ P) ⊑ R.
Proof. intros -> -> <-; apply wand_elim_r. Qed.
Lemma wand_apply_l' P Q Q' R : P ⊑ (Q' -★ R) → Q ⊑ Q' → (P ★ Q) ⊑ R.
Proof. intros -> <-; apply wand_elim_l. Qed.
Lemma wand_apply_r' P Q Q' R : P ⊑ (Q' -★ R) → Q ⊑ Q' → (Q ★ P) ⊑ R.
Proof. intros -> <-; apply wand_elim_r. Qed.
Lemma wand_frame_l P Q R : (Q -★ R) ⊑ (P ★ Q -★ P ★ R).
Proof. apply wand_intro_l. rewrite -assoc. apply sep_mono_r, wand_elim_r. Qed.
Lemma wand_frame_r P Q R : (Q -★ R) ⊑ (Q ★ P -★ R ★ P).
Proof.
apply wand_intro_l. rewrite ![(_ ★ P)%I]comm -assoc.
apply sep_mono_r, wand_elim_r.
Qed.
Lemma sep_and P Q : (P ★ Q) ⊑ (P ∧ Q). Lemma sep_and P Q : (P ★ Q) ⊑ (P ∧ Q).
Proof. auto. Qed. Proof. auto. Qed.
Lemma impl_wand P Q : (P → Q) ⊑ (P -★ Q). Lemma impl_wand P Q : (P → Q) ⊑ (P -★ Q).
......
program_logic/auth.v
+ 3
− 3
View file @ efd340e5
...@@ -116,9 +116,9 @@ Section auth. ...@@ -116,9 +116,9 @@ Section auth.
rewrite (auth_opened (E ∖ N)) !pvs_frame_r !sep_exist_r. rewrite (auth_opened (E ∖ N)) !pvs_frame_r !sep_exist_r.
apply (fsa_strip_pvs fsa). apply exist_elim=>a'. apply (fsa_strip_pvs fsa). apply exist_elim=>a'.
rewrite (forall_elim a'). rewrite [(▷_ ★ _)%I]comm. rewrite (forall_elim a'). rewrite [(▷_ ★ _)%I]comm.
(* Getting this wand eliminated is really annoying. *) eapply wand_apply_r; first (by eapply (wand_frame_l (own γ _))); last first.
rewrite [(■_ ★ _)%I]comm -!assoc [(▷φ _ ★ _ ★ _)%I]assoc [(▷φ _ ★ _)%I]comm. { rewrite assoc [(_ ★ own _ _)%I]comm -assoc. done. }
rewrite wand_elim_r fsa_frame_l. rewrite fsa_frame_l.
apply (fsa_mono_pvs fsa)=> x. apply (fsa_mono_pvs fsa)=> x.
rewrite sep_exist_l; apply exist_elim=> L. rewrite sep_exist_l; apply exist_elim=> L.
rewrite sep_exist_l; apply exist_elim=> Lv. rewrite sep_exist_l; apply exist_elim=> Lv.
......
program_logic/sts.v
+ 3
− 3
View file @ efd340e5
...@@ -133,9 +133,9 @@ Section sts. ...@@ -133,9 +133,9 @@ Section sts.
rewrite (sts_opened (E ∖ N)) !pvs_frame_r !sep_exist_r. rewrite (sts_opened (E ∖ N)) !pvs_frame_r !sep_exist_r.
apply (fsa_strip_pvs fsa). apply exist_elim=>s. apply (fsa_strip_pvs fsa). apply exist_elim=>s.
rewrite (forall_elim s). rewrite [(▷_ ★ _)%I]comm. rewrite (forall_elim s). rewrite [(▷_ ★ _)%I]comm.
(* Getting this wand eliminated is really annoying. *) eapply wand_apply_r; first (by eapply (wand_frame_l (own γ _))); last first.
rewrite [(■_ ★ _)%I]comm -!assoc [(▷φ _ ★ _ ★ _)%I]assoc [(▷φ _ ★ _)%I]comm. { rewrite assoc [(_ ★ own _ _)%I]comm -assoc. done. }
rewrite wand_elim_r fsa_frame_l. rewrite fsa_frame_l.
apply (fsa_mono_pvs fsa)=> x. apply (fsa_mono_pvs fsa)=> x.
rewrite sep_exist_l; apply exist_elim=> s'. rewrite sep_exist_l; apply exist_elim=> s'.
rewrite sep_exist_l; apply exist_elim=>T'. rewrite sep_exist_l; apply exist_elim=>T'.
......
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