Commit a64118a2 authored by Ralf Jung's avatar Ralf Jung

prove pvs_alloc, modulo the closure under suffixes being infinite

parent 680ce446
......@@ -44,7 +44,7 @@ Local Hint Resolve nclose_subseteq ndot_nclose.
(** Derived forms and lemmas about them. *)
Definition inv {Λ Σ} (N : namespace) (P : iProp Λ Σ) : iProp Λ Σ :=
( i : positive, ownI (encode $ ndot N i) P)%I.
( i : positive, (i nclose N) ownI i P)%I.
Section inv.
Context {Λ : language} {Σ : iFunctor}.
......@@ -55,6 +55,7 @@ Implicit Types P Q R : iProp Λ Σ.
Global Instance inv_contractive N : Contractive (@inv Λ Σ N).
Proof.
intros n ? ? EQ. apply exists_ne=>i.
apply and_ne; first done.
by apply ownI_contractive.
Qed.
......@@ -75,17 +76,18 @@ Lemma pvs_open_close E N P Q R :
Proof.
move=>HN -> {P}.
rewrite /inv and_exist_r. apply exist_elim=>i.
rewrite -associative. apply const_elim_l=>HiN.
(* Add this to the local context, so that solve_elem_of finds it. *)
assert ({[encode (ndot N i)]} nclose N) by eauto.
assert ({[encode i]} nclose N) by eauto.
rewrite always_and_sep_l' (always_sep_dup' (ownI _ _)).
rewrite {1}pvs_openI !pvs_frame_r.
(* TODO is there a common pattern here in the way we combine pvs_trans
and pvs_mask_frame_mono? *)
rewrite -(pvs_trans E (E {[ (encode (ndot N i)) ]}));
rewrite -(pvs_trans E (E {[ encode i ]}));
last by solve_elem_of. (* FIXME: Shouldn't eauto work, since I added a Hint Extern? *)
apply pvs_mask_frame_mono; [solve_elem_of..|].
rewrite (commutative _ (R)%I) -associative wand_elim_r pvs_frame_l.
rewrite -(pvs_trans _ (E {[ (encode (ndot N i)) ]}) E); last by solve_elem_of.
rewrite -(pvs_trans _ (E {[ encode i ]}) E); last by solve_elem_of.
apply pvs_mask_frame_mono; [solve_elem_of..|].
rewrite associative -always_and_sep_l' pvs_closeI pvs_frame_r left_id.
apply pvs_mask_frame'; solve_elem_of.
......@@ -93,8 +95,8 @@ Qed.
Lemma pvs_alloc N P : P pvs N N (inv N P).
Proof.
(* FIXME: Can we have the E that contains exactly all (encode $ ndot N i) for all i?
If not, then we have to change the def. of inv. *)
rewrite /inv (pvs_allocI N); first done.
(* FIXME use coPset_suffixes_infinite. *)
Abort.
End inv.
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