fix nits

theories/heap_lang/lib/coin_flip.v

@@ -76,7 +76,7 @@ Section coinflip.
   Proof using N.
     iApply wp_atomic_intro. iIntros (Φ) "AU". wp_lam.
     wp_apply wp_new_proph; first done.
-    iIntros (p) "Hp". iDestruct "Hp" as (v) "Hp".
+    iIntros (v p) "Hp".
     wp_let.
     wp_bind (_ <- _)%E.
     iMod "AU" as "[Hl [_ Hclose]]".

theories/heap_lang/lifting.v

@@ -289,7 +289,7 @@ Qed.
 
 (** Lifting lemmas for creating and resolving prophecy variables *)
 Lemma wp_new_proph :
-  {{{ True }}} NewProph {{{ (p : proph), RET (LitV (LitProphecy p)); p ⥱ - }}}.
+  {{{ True }}} NewProph {{{ v (p : proph), RET (LitV (LitProphecy p)); p ⥱ v }}}.
 Proof.
   iIntros (Φ) "_ HΦ". iApply wp_lift_atomic_head_step_no_fork; auto.
   iIntros (σ1 κs) "[Hσ HR] !>". iDestruct "HR" as (R [Hfr Hdom]) "HR". iSplit.
@@ -304,7 +304,7 @@ Proof.
     iPureIntro. split.
     + apply first_resolve_insert; auto.
     + rewrite dom_insert_L. by apply union_mono_l.
-  - iApply "HΦ". by iExists _.
+  - iApply "HΦ". done.
 Qed.
 
 Lemma wp_resolve_proph e1 e2 p v w:
@@ -320,7 +320,7 @@ Proof.
   unfold cons_obs. simpl.
   iNext; iIntros (κ κs' v2 σ2 efs [Hstep ->]); inv_head_step. iApply fupd_frame_l.
   iSplit=> //. iFrame.
-  iMod ((@proph_map_remove _ _ _ _ _ _ _ p0) with "HR Hp") as "Hp". iModIntro.
+  iMod (@proph_map_remove with "HR Hp") as "Hp". iModIntro.
   iSplitR "HΦ".
   - iExists _. iFrame. iPureIntro. split; first by eapply first_resolve_delete.
     rewrite dom_delete. rewrite <- difference_empty_L. by eapply difference_mono.

theories/heap_lang/proph_map.v

@@ -20,7 +20,7 @@ Section first_resolve.
     (map_of_list pvs : gmap P V) !! p.
 
   Definition first_resolve_in_list R pvs :=
-    forall p v, p ∈ dom (gset _) R →
+    ∀ p v, p ∈ dom (gset _) R →
            first_resolve pvs p = Some v →
            R !! p = Some (Some v).
 
@@ -156,13 +156,11 @@ Section proph_map.
     p ∉ dom (gset _) R →
     proph_map_auth R ==∗ proph_map_auth (<[p := v]> R) ∗ p ⥱ v.
   Proof.
-    iIntros (?) "HR". rewrite /proph_map_ctx p_mapsto_eq /p_mapsto_def.
+    iIntros (Hp) "HR". rewrite /proph_map_ctx p_mapsto_eq /p_mapsto_def.
     iMod (own_update with "HR") as "[HR Hl]".
-    {
-      eapply auth_update_alloc,
+    { eapply auth_update_alloc,
         (alloc_singleton_local_update _ _ (Excl $ (v : option (leibnizC _))))=> //.
-      apply lookup_to_proph_map_None. apply (iffLR (not_elem_of_dom _ _) H1).
-    }
+      apply lookup_to_proph_map_None. apply (iffLR (not_elem_of_dom _ _) Hp). }
     iModIntro. rewrite /proph_map_auth to_proph_map_insert. iFrame.
   Qed.
 

theories/program_logic/language.v

@@ -103,6 +103,7 @@ Section language.
        ρ2 = (t1 ++ e2 :: t2 ++ efs, σ2) →
        prim_step e1 σ1 κ e2 σ2 efs →
        step ρ1 κ ρ2.
+  Hint Constructors step.
 
   (* TODO (MR) introduce notation ::? for cons_obs and suggest for inclusion to stdpp? *)
   Definition cons_obs {A} (x : option A) (xs : list A) :=
@@ -115,10 +116,9 @@ Section language.
       step ρ1 κ ρ2 →
       nsteps n ρ2 κs ρ3 →
       nsteps (S n) ρ1 (cons_obs κ κs) ρ3.
+  Hint Constructors nsteps.
 
-  Definition erased_step (ρ1 ρ2 : cfg Λ) := exists κ, step ρ1 κ ρ2.
-
-  Hint Constructors step nsteps.
+  Definition erased_step (ρ1 ρ2 : cfg Λ) := ∃ κ, step ρ1 κ ρ2.
 
   Lemma erased_steps_nsteps ρ1 ρ2 :
     rtc erased_step ρ1 ρ2 →

theories/program_logic/ownp.v

@@ -134,8 +134,8 @@ Section lifting.
       iDestruct "Hσκs" as "[Hσ Hκs]".
       rewrite /ownP_state /ownP_obs.
       iMod (own_update_2 with "Hσ Hσf") as "[Hσ Hσf]".
-       { apply auth_update. apply: option_local_update.
-         by apply: (exclusive_local_update _ (Excl σ2)). }
+      { apply auth_update. apply: option_local_update.
+        by apply: (exclusive_local_update _ (Excl σ2)). }
       iMod (own_update_2 with "Hκs Hκsf") as "[Hκs Hκsf]".
       { apply auth_update. apply: option_local_update.
         by apply: (exclusive_local_update _ (Excl (κs'':leibnizC _))). }

theories/program_logic/weakestpre.v

@@ -58,7 +58,7 @@ Proof.
   (* FIXME: reflexivity, as being called many times by f_equiv and f_contractive
   is very slow here *)
   do 24 (f_contractive || f_equiv). apply IH; first lia.
-  intros v. eapply dist_le; eauto with omega.
+  intros v. eapply dist_le; eauto with lia.
 Qed.
 Global Instance wp_proper s E e :
   Proper (pointwise_relation _ (≡) ==> (≡)) (wp (PROP:=iProp Σ) s E e).