Factor out lemma for initializing `gen_heap`.

theories/base_logic/lib/gen_heap.v

@@ -72,6 +72,14 @@ Section to_gen_heap.
   Proof. by rewrite /to_gen_heap fmap_delete. Qed.
 End to_gen_heap.
 
+Lemma gen_heap_init `{gen_heapPreG L V Σ} σ :
+  (|==> ∃ _ : gen_heapG L V Σ, gen_heap_ctx σ)%I.
+Proof.
+  iMod (own_alloc (● to_gen_heap σ)) as (γ) "Hh".
+  { apply: auth_auth_valid. exact: to_gen_heap_valid. }
+  iModIntro. by iExists (GenHeapG L V Σ _ _ _ γ).
+Qed.
+
 Section gen_heap.
   Context `{gen_heapG L V Σ}.
   Implicit Types P Q : iProp Σ.

theories/heap_lang/adequacy.v

@@ -19,9 +19,7 @@ Definition heap_adequacy Σ `{heapPreG Σ} e σ φ :
   adequate e σ φ.
 Proof.
   intros Hwp; eapply (wp_adequacy _ _); iIntros (?) "".
-  iMod (own_alloc (● to_gen_heap σ)) as (γ) "Hh".
-  { apply: auth_auth_valid. exact: to_gen_heap_valid. }
-  iModIntro. iExists (λ σ, own γ (● to_gen_heap σ)); iFrame.
-  set (Hheap := GenHeapG loc val Σ _ _ _ γ).
+  iMod (gen_heap_init σ) as (?) "Hh".
+  iModIntro. iExists gen_heap_ctx. iFrame "Hh".
   iApply (Hwp (HeapG _ _ _)).
 Qed.