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From iris.algebra Require Import auth.
From iris.proofmode Require Import proofmode.
From semantics.pl.program_logic Require Export sequential_wp adequacy.
From iris.heap_lang Require Import notation.
From semantics.pl.heap_lang Require Export proofmode.
From iris.prelude Require Import options.
Class heapGpreS Σ := HeapGpreS {
heapGpreS_iris : invGpreS Σ;
heapGpreS_heap : gen_heapGpreS loc (option val) Σ;
}.
#[export] Existing Instance heapGpreS_iris.
#[export] Existing Instance heapGpreS_heap.
Definition heapΣ : gFunctors :=
#[invΣ; gen_heapΣ loc (option val)].
Global Instance subG_heapGpreS {Σ} : subG heapΣ Σ heapGpreS Σ.
Proof. solve_inG. Qed.
Definition heap_adequacy Σ `{!heapGpreS Σ} s e σ φ :
( `{!heapGS Σ}, WP e @ s; {{ v, φ v }})
adequate s e σ (λ v _, φ v).
Proof.
intros Hwp; eapply (wp_adequacy _ _); iIntros (?).
iMod (gen_heap_init σ.(heap)) as (?) "[Hh _]".
iModIntro. iExists
(λ σ, (gen_heap_interp σ.(heap))%I).
iFrame. iApply (Hwp (HeapGS _ _ _)).
Qed.