Commit 236891e9 authored by Ralf Jung's avatar Ralf Jung
Browse files

Add a rule to alloocate an invariant and open it

Fixes #59
Proof entirely by @janno
parent 65b9ce9f
......@@ -41,6 +41,33 @@ Proof.
- rewrite /uPred_except_0; eauto.
Lemma inv_alloc_open N E P :
N E True ={E, E∖↑N}= inv N P (P ={E∖↑N, E}= True).
rewrite inv_eq /inv_def fupd_eq /fupd_def.
iIntros (Sub) "[Hw HE]".
iMod (ownI_alloc_open ( N) P with "Hw") as (i) "(% & Hw & #Hi & HD)".
- intros Ef. exists (coPpick ( N coPset.of_gset Ef)).
rewrite -coPset.elem_of_of_gset comm -elem_of_difference.
apply coPpick_elem_of=> Hfin.
eapply nclose_infinite, (difference_finite_inv _ _), Hfin.
apply of_gset_finite.
- iAssert (ownE {[i]} ownE ( N {[i]}) ownE (E N))%I with "[HE]" as "(HEi & HEN\i & HE\N)".
{ rewrite -?ownE_op; [|set_solver|set_solver].
rewrite assoc_L. rewrite <-!union_difference_L; try done; set_solver. }
iModIntro. rewrite /uPred_except_0. iRight. iFrame.
iSplitL "Hw HEi".
+ by iApply "Hw".
+ iSplitL "Hi"; [eauto|].
iIntros "HP [Hw HE\N]".
iDestruct (ownI_close with "[$Hw $Hi $HP $HD]") as "[? HEi]".
iModIntro. iRight. iFrame. iSplitL; [|done].
iCombine "HEi" "HEN\i" as "HEN".
iCombine "HEN" "HE\N" as "HE".
rewrite -?ownE_op; [|set_solver|set_solver].
rewrite <-!union_difference_L; try done; set_solver.
Lemma inv_open E N P :
N E inv N P ={E,E∖↑N}= P ( P ={E∖↑N,E}= True).
......@@ -142,4 +142,28 @@ Proof.
iApply (big_sepM_insert _ I); first done.
iFrame "HI". iLeft. by rewrite /ownD; iFrame.
Lemma ownI_alloc_open φ P :
( E : gset positive, i, i E φ i)
wsat == i, ⌜φ i (ownE {[i]} - wsat) ownI i P ownD {[i]}.
iIntros (Hfresh) "Hw". iDestruct "Hw" as (I) "[? HI]".
iMod (own_empty (gset_disjUR positive) disabled_name) as "HD".
iMod (own_updateP with "HD") as "HD".
{ apply (gset_disj_alloc_empty_updateP_strong' (λ i, I !! i = None φ i)).
intros E. destruct (Hfresh (E dom _ I))
as (i & [? HIi%not_elem_of_dom]%not_elem_of_union & ?); eauto. }
iDestruct "HD" as (X) "[Hi HD]"; iDestruct "Hi" as %(i & -> & HIi & ?).
iMod (own_update with "Hw") as "[Hw HiP]".
{ eapply auth_update_alloc,
(alloc_singleton_local_update _ i (invariant_unfold P)); last done.
by rewrite /= lookup_fmap HIi. }
iModIntro; iExists i; iSplit; [done|]. rewrite /ownI; iFrame "HiP".
rewrite -/(ownD _). iFrame "HD".
iIntros "HE". iExists (<[i:=P]>I); iSplitL "Hw".
{ by rewrite fmap_insert insert_singleton_op ?lookup_fmap ?HIi. }
iApply (big_sepM_insert _ I); first done.
iFrame "HI". by iRight.
End wsat.
Supports Markdown
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment