Commit 11eacd8b authored by Robbert Krebbers's avatar Robbert Krebbers

A stronger version of `cinv_open`.

This version allows one to either close or cancel the invariant after opening it.
parent b043f3a3
......@@ -70,6 +70,21 @@ Section proofs.
iIntros "!>". iExists P. iSplit; last done. iIntros "!# !>"; iSplit; auto.
Qed.
Lemma cinv_open_strong E N γ p P :
N E
cinv N γ P - cinv_own γ p ={E,E∖↑N}=
P cinv_own γ p ( P cinv_own γ 1 ={E∖↑N,E}= True).
Proof.
iIntros (?) "#Hinv Hγ". iDestruct "Hinv" as (P') "[#HP' Hinv]".
iInv N as "[HP | >Hγ']" "Hclose".
- iIntros "!> {$Hγ}". iSplitL "HP".
+ iNext. iApply "HP'". done.
+ iIntros "[HP|Hγ]".
* iApply "Hclose". iLeft. iNext. by iApply "HP'".
* iApply "Hclose". iRight. by iNext.
- iDestruct (cinv_own_1_l with "Hγ' Hγ") as %[].
Qed.
Lemma cinv_alloc E N P : P ={E}= γ, cinv N γ P cinv_own γ 1.
Proof.
iIntros "HP". iMod (cinv_alloc_strong E N) as (γ _) "[Hγ Halloc]".
......@@ -78,23 +93,18 @@ Section proofs.
Lemma cinv_cancel E N γ P : N E cinv N γ P - cinv_own γ 1 ={E}= P.
Proof.
iIntros (?) "#Hinv Hγ". iDestruct "Hinv" as (P') "[#HP' Hinv]".
iInv N as "[HP|>Hγ']" "Hclose".
- iMod ("Hclose" with "[Hγ]") as "_"; first by eauto. iModIntro. iNext.
iApply "HP'". done.
- iDestruct (cinv_own_1_l with "Hγ Hγ'") as %[].
iIntros (?) "#Hinv Hγ".
iMod (cinv_open_strong with "Hinv Hγ") as "($ & Hγ & H)"; first done.
iApply "H". by iRight.
Qed.
Lemma cinv_open E N γ p P :
N E
cinv N γ P - cinv_own γ p ={E,E∖↑N}= P cinv_own γ p ( P ={E∖↑N,E}= True).
Proof.
iIntros (?) "#Hinv Hγ". iDestruct "Hinv" as (P') "[#HP' Hinv]".
iInv N as "[HP | >Hγ']" "Hclose".
- iIntros "!> {$Hγ}". iSplitL "HP".
+ iNext. iApply "HP'". done.
+ iIntros "HP". iApply "Hclose". iLeft. iNext. by iApply "HP'".
- iDestruct (cinv_own_1_l with "Hγ' Hγ") as %[].
iIntros (?) "#Hinv Hγ".
iMod (cinv_open_strong with "Hinv Hγ") as "($ & $ & H)"; first done.
iIntros "!> HP". iApply "H"; auto.
Qed.
End proofs.
......
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