Verified Commit 56f311a9 authored by Ralf Jung's avatar Ralf Jung Committed by Rodolphe Lepigre
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parent b16b9f33
......@@ -4,7 +4,7 @@ From iris.proofmode Require Import tactics.
Set Default Proof Using "Type".
Import uPred.
Definition proph_map (P V : Type) `{Countable P} := gmap P (list V).
Local Notation proph_map P V := (gmap P (list V)).
Definition proph_val_list (P V : Type) := list (P * V).
Definition proph_mapUR (P V : Type) `{Countable P} : ucmraT :=
......@@ -137,14 +137,13 @@ Section proph_map.
rewrite proph_eq /proph_def.
iMod (own_update with "H●") as "[H● H◯]". {
eapply auth_update_alloc, (alloc_singleton_local_update _ p (Excl _))=> //.
apply lookup_to_proph_map_None.
assert (p dom (gset P) R). { set_solver. }
apply (iffLR (not_elem_of_dom _ _) H3).
apply lookup_to_proph_map_None.
apply (not_elem_of_dom (D:=gset P)). set_solver.
iModIntro. iFrame.
iExists (<[p := list_resolves pvs p]> R). iSplitR "H●".
- iPureIntro. split.
+ apply resolves_insert. exact H1. set_solver.
+ apply resolves_insert; first done. set_solver.
+ rewrite dom_insert. set_solver.
- unfold to_proph_map. by rewrite fmap_insert.
......@@ -153,29 +152,27 @@ Section proph_map.
proph_map_ctx ((p,v) :: pvs) ps proph p vs ==
vs', vs = v::vs' proph_map_ctx pvs ps proph p vs'.
iIntros "[HR Hp]". iDestruct "HR" as (R) "[[% %] H●]".
iIntros "[HR Hp]". iDestruct "HR" as (R) "[HP H●]". iDestruct "HP" as %[Hres Hdom].
rewrite /proph_map_ctx proph_eq /proph_def.
iDestruct (own_valid_2 with "H● Hp") as %[HR%proph_map_singleton_included _]%auth_valid_discrete_2.
assert (vs = v :: list_resolves pvs p). {
rewrite (H1 p vs HR). simpl. rewrite decide_True; done.
assert (vs = v :: list_resolves pvs p) as ->. {
rewrite (Hres p vs HR). simpl. rewrite decide_True; done.
SearchAbout "own_update".
iMod (own_update_2 with "H● Hp") as "[H● H◯]". {
apply auth_update.
apply (singleton_local_update (to_proph_map R) p (Excl (vs : list (leibnizC V))) _ (Excl (list_resolves pvs p)) (Excl (list_resolves pvs p))).
eapply auth_update. apply: singleton_local_update.
- unfold to_proph_map. rewrite lookup_fmap. rewrite HR. done.
- apply exclusive_local_update. done.
- apply (exclusive_local_update _ (Excl (list_resolves pvs p : list (leibnizC V)))). done.
unfold to_proph_map. rewrite <- fmap_insert.
unfold to_proph_map. rewrite -fmap_insert.
iModIntro. iExists (list_resolves pvs p). iFrame. iSplitR.
- iPureIntro. exact H3.
- iPureIntro. done.
- iExists _. iFrame. iPureIntro. split.
+ intros q ws HEq. destruct (decide (p = q)) as [<-|NEq].
* rewrite lookup_insert in HEq. by inversion HEq.
* rewrite lookup_insert_ne in HEq; last done.
pose (HHH := H1 q ws HEq). rewrite HHH.
simpl. rewrite decide_False; last done. reflexivity.
+ assert (p dom (gset P) R). { by apply: elem_of_dom_2. }
rewrite (Hres q ws HEq).
simpl. rewrite decide_False; done.
+ assert (p dom (gset P) R) by exact: elem_of_dom_2.
rewrite dom_insert. set_solver.
End proph_map.
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