lib/spawn: make proofs more readable / steppable

heap_lang/lib/spawn.v

@@ -56,23 +56,23 @@ Lemma spawn_spec (Ψ : val → iProp) e (f : val) (Φ : val → iProp) :
   heap_ctx heapN ★ WP f #() {{ Ψ }} ★ (∀ l, join_handle l Ψ -★ Φ #l)
   ⊢ WP spawn e {{ Φ }}.
 Proof.
-  iIntros {<-%of_to_val ?} "(#Hh&Hf&HΦ)". rewrite /spawn.
+  iIntros {<-%of_to_val ?} "(#Hh & Hf & HΦ)". rewrite /spawn.
   wp_let. wp_alloc l as "Hl". wp_let.
   iPvs (own_alloc (Excl ())) as {γ} "Hγ"; first done.
   iPvs (inv_alloc N _ (spawn_inv γ l Ψ) with "[Hl]") as "#?"; first done.
   { iNext. iExists (InjLV #0). iFrame; eauto. }
   wp_apply wp_fork. iSplitR "Hf".
-  - iPvsIntro. wp_seq. iPvsIntro. iApply "HΦ"; rewrite /join_handle. eauto.
-  - wp_focus (f _). iApply wp_wand_l; iFrame "Hf"; iIntros {v} "Hv".
+  - iPvsIntro. wp_seq. iPvsIntro. iApply "HΦ". rewrite /join_handle. eauto.
+  - wp_focus (f _). iApply wp_wand_l. iFrame "Hf"; iIntros {v} "Hv".
     iInv N as {v'} "[Hl _]"; first wp_done.
-    wp_store. iPvsIntro; iSplit; [iNext|done].
-    iExists (InjRV v); iFrame; eauto.
+    wp_store. iPvsIntro. iSplit; [iNext|done].
+    iExists (InjRV v). iFrame. eauto.
 Qed.
 
 Lemma join_spec (Ψ : val → iProp) l (Φ : val → iProp) :
   join_handle l Ψ ★ (∀ v, Ψ v -★ Φ v) ⊢ WP join #l {{ Φ }}.
 Proof.
-  rewrite /join_handle; iIntros "[[% H] Hv]"; iDestruct "H" as {γ} "(#?&Hγ&#?)".
+  rewrite /join_handle; iIntros "[[% H] Hv]". iDestruct "H" as {γ} "(#?&Hγ&#?)".
   iLöb as "IH". wp_rec. wp_focus (! _)%E. iInv N as {v} "[Hl Hinv]".
   wp_load. iDestruct "Hinv" as "[%|Hinv]"; subst.
   - iPvsIntro; iSplitL "Hl"; [iNext; iExists _; iFrame; eauto|].