one gen_heap_init lemma is enough

CHANGELOG.md

@@ -128,6 +128,8 @@ With this release, we dropped support for Coq 8.9.
   by `gen_heap`.
 * Strengthen `mapsto_valid_2` conclusion from `✓ (q1 + q2)%Qp` to
   `⌜✓ (q1 + q2)%Qp ∧ v1 = v2⌝`.
+* Change `gen_heap_init` to also return ownership of the points-to facts for the
+  initial heap.
 
 **Changes in `program_logic`:**
 

theories/base_logic/lib/gen_heap.v

@@ -290,24 +290,18 @@ Section gen_heap.
   Qed.
 End gen_heap.
 
-(** This lemma drops ownership of the initial [σ] on the floor; see
-[gen_heap_init_big] for a version of the lemma that preserves this ownership. *)
 Lemma gen_heap_init `{Countable L, !gen_heapPreG L V Σ} σ :
-  ⊢ |==> ∃ _ : gen_heapG L V Σ, gen_heap_interp σ.
+  ⊢ |==> ∃ _ : gen_heapG L V Σ,
+    gen_heap_interp σ ∗ ([∗ map] l ↦ v ∈ σ, l ↦ v) ∗ ([∗ map] l ↦ _ ∈ σ, meta_token l ⊤).
 Proof.
-  iMod (own_alloc (gmap_view_auth 1 (σ : gmap L (leibnizO V)))) as (γh) "Hh".
+  iMod (own_alloc (gmap_view_auth 1 (∅ : gmap L (leibnizO V)))) as (γh) "Hh".
   { exact: gmap_view_auth_valid. }
   iMod (own_alloc (gmap_view_auth 1 (∅ : gmap L gnameO))) as (γm) "Hm".
   { exact: gmap_view_auth_valid. }
-  iModIntro. iExists (GenHeapG L V Σ _ _ _ _ _ γh γm).
-  iExists ∅; simpl. iFrame "Hh Hm". by rewrite dom_empty_L.
-Qed.
-
-Lemma gen_heap_init_big `{Countable L, !gen_heapPreG L V Σ} σ :
-  ⊢ |==> ∃ _ : gen_heapG L V Σ,
-    gen_heap_interp σ ∗ ([∗ map] l ↦ v ∈ σ, l ↦ v) ∗ ([∗ map] l ↦ _ ∈ σ, meta_token l ⊤).
-Proof.
-  iMod (gen_heap_init ∅) as (gen_heap) "Hinterp". iExists gen_heap.
+  pose (gen_heap := GenHeapG L V Σ _ _ _ _ _ γh γm).
+  iExists gen_heap.
+  iAssert (gen_heap_interp ∅) with "[Hh Hm]" as "Hinterp".
+  { iExists ∅; simpl. iFrame "Hh Hm". by rewrite dom_empty_L. }
   iMod (gen_heap_alloc_big with "Hinterp") as "(Hinterp & $ & $)".
   { apply map_disjoint_empty_r. }
   rewrite right_id_L. done.

theories/heap_lang/adequacy.v

@@ -21,7 +21,7 @@ Definition heap_adequacy Σ `{!heapPreG Σ} s e σ φ :
   adequate s e σ (λ v _, φ v).
 Proof.
   intros Hwp; eapply (wp_adequacy _ _); iIntros (??) "".
-  iMod (gen_heap_init σ.(heap)) as (?) "Hh".
+  iMod (gen_heap_init σ.(heap)) as (?) "[Hh _]".
   iMod (inv_heap_init loc (option val)) as (?) ">Hi".
   iMod (proph_map_init κs σ.(used_proph_id)) as (?) "Hp".
   iModIntro. iExists