diff --git a/barrier/barrier.v b/barrier/barrier.v
index fd34e8f9b14bb3294637bad55eaa991bad59776a..65c0af7aa966a11a4e26501665ea5df95ab63953 100644
--- a/barrier/barrier.v
+++ b/barrier/barrier.v
@@ -210,7 +210,7 @@ Section proof.
     (* I think some evars here are better than repeating *everything* *)
     eapply (sts_fsaS _ (wp_fsa _)) with (N0:=N) (γ0:=γ); simpl;
       eauto with I ndisj.
-    rewrite [(_ ★ sts_ownS _ _ _)%I]comm -!assoc /wp_fsa. apply sep_mono_r.
+    rewrite [(_ ★ sts_ownS _ _ _)%I]comm -!assoc. apply sep_mono_r.
     apply forall_intro=>-[p I]. apply wand_intro_l. rewrite -!assoc.
     apply const_elim_sep_l=>Hs. destruct p; last done.
     rewrite {1}/barrier_inv =>/={Hs}. rewrite later_sep.
@@ -251,7 +251,7 @@ Section proof.
     (* I think some evars here are better than repeating *everything* *)
     eapply (sts_fsaS _ (wp_fsa _)) with (N0:=N) (γ0:=γ); simpl;
       eauto with I ndisj.
-    rewrite !assoc [(_ ★ sts_ownS _ _ _)%I]comm -!assoc /wp_fsa. apply sep_mono_r.
+    rewrite !assoc [(_ ★ sts_ownS _ _ _)%I]comm -!assoc. apply sep_mono_r.
     apply forall_intro=>-[p I]. apply wand_intro_l. rewrite -!assoc.
     apply const_elim_sep_l=>Hs.
     rewrite {1}/barrier_inv =>/=. rewrite later_sep.
diff --git a/heap_lang/heap.v b/heap_lang/heap.v
index 69596f9b642d3e81f5c2969f44b63f3eb5dede0e..9314bf11ff003900fe529a90b389dc2817d1f656 100644
--- a/heap_lang/heap.v
+++ b/heap_lang/heap.v
@@ -109,8 +109,7 @@ Section heap.
       with N heap_name ∅; simpl; eauto with I.
     rewrite -later_intro. apply sep_mono_r,forall_intro=> h; apply wand_intro_l.
     rewrite -assoc left_id; apply const_elim_sep_l=> ?.
-    rewrite {1}[(â–·ownP _)%I]pvs_timeless pvs_frame_r; apply wp_strip_pvs.
-    rewrite /wp_fsa -(wp_alloc_pst _ (of_heap h)) //.
+    rewrite -(wp_alloc_pst _ (of_heap h)) //.
     apply sep_mono_r; rewrite HP; apply later_mono.
     apply forall_mono=> l; apply wand_intro_l.
     rewrite always_and_sep_l -assoc; apply const_elim_sep_l=> ?.
@@ -134,7 +133,6 @@ Section heap.
       with N heap_name {[ l := Excl v ]}; simpl; eauto with I.
     rewrite HPΦ{HPΦ}; apply sep_mono_r, forall_intro=> h; apply wand_intro_l.
     rewrite -assoc; apply const_elim_sep_l=> ?.
-    rewrite {1}[(â–·ownP _)%I]pvs_timeless pvs_frame_r; apply wp_strip_pvs.
     rewrite -(wp_load_pst _ (<[l:=v]>(of_heap h))) ?lookup_insert //.
     rewrite const_equiv // left_id.
     rewrite -(map_insert_singleton_op h); last by eapply heap_singleton_inv_l.
@@ -153,7 +151,6 @@ Section heap.
       with N heap_name {[ l := Excl v' ]}; simpl; eauto with I.
     rewrite HPΦ{HPΦ}; apply sep_mono_r, forall_intro=> h; apply wand_intro_l.
     rewrite -assoc; apply const_elim_sep_l=> ?.
-    rewrite {1}[(â–·ownP _)%I]pvs_timeless pvs_frame_r; apply wp_strip_pvs.
     rewrite -(wp_store_pst _ (<[l:=v']>(of_heap h))) ?lookup_insert //.
     rewrite /heap_inv alter_singleton insert_insert.
     rewrite -!(map_insert_singleton_op h); try by eapply heap_singleton_inv_l.
@@ -174,7 +171,6 @@ Section heap.
       with N heap_name {[ l := Excl v' ]}; simpl; eauto 10 with I.
     rewrite HPΦ{HPΦ}; apply sep_mono_r, forall_intro=> h; apply wand_intro_l.
     rewrite -assoc; apply const_elim_sep_l=> ?.
-    rewrite {1}[(â–·ownP _)%I]pvs_timeless pvs_frame_r; apply wp_strip_pvs.
     rewrite -(wp_cas_fail_pst _ (<[l:=v']>(of_heap h))) ?lookup_insert //.
     rewrite const_equiv // left_id.
     rewrite -(map_insert_singleton_op h); last by eapply heap_singleton_inv_l.
@@ -194,7 +190,6 @@ Section heap.
       with N heap_name {[ l := Excl v1 ]}; simpl; eauto 10 with I.
     rewrite HPΦ{HPΦ}; apply sep_mono_r, forall_intro=> h; apply wand_intro_l.
     rewrite -assoc; apply const_elim_sep_l=> ?.
-    rewrite {1}[(â–·ownP _)%I]pvs_timeless pvs_frame_r; apply wp_strip_pvs.
     rewrite -(wp_cas_suc_pst _ (<[l:=v1]>(of_heap h))) ?lookup_insert //.
     rewrite /heap_inv alter_singleton insert_insert.
     rewrite -!(map_insert_singleton_op h); try by eapply heap_singleton_inv_l.
diff --git a/heap_lang/lifting.v b/heap_lang/lifting.v
index 5359b62ba1a0990e528c9c4e7e4a4836710291ae..276d910510cc886ad39227ac2d0789b41365a752 100644
--- a/heap_lang/lifting.v
+++ b/heap_lang/lifting.v
@@ -22,7 +22,7 @@ Proof. apply weakestpre.wp_bind. Qed.
 (** Base axioms for core primitives of the language: Stateful reductions. *)
 Lemma wp_alloc_pst E σ e v Φ :
   to_val e = Some v →
-  (ownP σ ★ ▷ (∀ l, σ !! l = None ∧ ownP (<[l:=v]>σ) -★ Φ (LocV l)))
+  (▷ ownP σ ★ ▷ (∀ l, σ !! l = None ∧ ownP (<[l:=v]>σ) -★ Φ (LocV l)))
   ⊑ || Alloc e @ E {{ Φ }}.
 Proof.
   (* TODO RJ: This works around ssreflect bug #22. *)
@@ -40,7 +40,7 @@ Qed.
 
 Lemma wp_load_pst E σ l v Φ :
   σ !! l = Some v →
-  (ownP σ ★ ▷ (ownP σ -★ Φ v)) ⊑ || Load (Loc l) @ E {{ Φ }}.
+  (▷ ownP σ ★ ▷ (ownP σ -★ Φ v)) ⊑ || Load (Loc l) @ E {{ Φ }}.
 Proof.
   intros. rewrite -(wp_lift_atomic_det_step σ v σ None) ?right_id //;
     last by intros; inv_step; eauto using to_of_val.
@@ -48,7 +48,7 @@ Qed.
 
 Lemma wp_store_pst E σ l e v v' Φ :
   to_val e = Some v → σ !! l = Some v' →
-  (ownP σ ★ ▷ (ownP (<[l:=v]>σ) -★ Φ (LitV LitUnit)))
+  (▷ ownP σ ★ ▷ (ownP (<[l:=v]>σ) -★ Φ (LitV LitUnit)))
   ⊑ || Store (Loc l) e @ E {{ Φ }}.
 Proof.
   intros. rewrite -(wp_lift_atomic_det_step σ (LitV LitUnit) (<[l:=v]>σ) None)
@@ -57,7 +57,7 @@ Qed.
 
 Lemma wp_cas_fail_pst E σ l e1 v1 e2 v2 v' Φ :
   to_val e1 = Some v1 → to_val e2 = Some v2 → σ !! l = Some v' → v' ≠ v1 →
-  (ownP σ ★ ▷ (ownP σ -★ Φ (LitV $ LitBool false)))
+  (▷ ownP σ ★ ▷ (ownP σ -★ Φ (LitV $ LitBool false)))
   ⊑ || Cas (Loc l) e1 e2 @ E {{ Φ }}.
 Proof.
   intros. rewrite -(wp_lift_atomic_det_step σ (LitV $ LitBool false) σ None)
@@ -66,7 +66,7 @@ Qed.
 
 Lemma wp_cas_suc_pst E σ l e1 v1 e2 v2 Φ :
   to_val e1 = Some v1 → to_val e2 = Some v2 → σ !! l = Some v1 →
-  (ownP σ ★ ▷ (ownP (<[l:=v2]>σ) -★ Φ (LitV $ LitBool true)))
+  (▷ ownP σ ★ ▷ (ownP (<[l:=v2]>σ) -★ Φ (LitV $ LitBool true)))
   ⊑ || Cas (Loc l) e1 e2 @ E {{ Φ }}.
 Proof.
   intros. rewrite -(wp_lift_atomic_det_step σ (LitV $ LitBool true)
diff --git a/program_logic/hoare_lifting.v b/program_logic/hoare_lifting.v
index cda1417822f8691af3df00fb0d59526dc2faa6c5..b5c38de20820c96d92a7b03e5585e84ad8347e7e 100644
--- a/program_logic/hoare_lifting.v
+++ b/program_logic/hoare_lifting.v
@@ -22,7 +22,7 @@ Lemma ht_lift_step E1 E2
   E1 ⊆ E2 → to_val e1 = None →
   reducible e1 σ1 →
   (∀ e2 σ2 ef, prim_step e1 σ1 e2 σ2 ef → φ e2 σ2 ef) →
-  ((P ={E2,E1}=> ownP σ1 ★ ▷ P') ∧ ∀ e2 σ2 ef,
+  ((P ={E2,E1}=> ▷ ownP σ1 ★ ▷ P') ∧ ∀ e2 σ2 ef,
     (■ φ e2 σ2 ef ★ ownP σ2 ★ P' ={E1,E2}=> Φ1 e2 σ2 ef ★ Φ2 e2 σ2 ef) ∧
     {{ Φ1 e2 σ2 ef }} e2 @ E2 {{ Ψ }} ∧
     {{ Φ2 e2 σ2 ef }} ef ?@ ⊤ {{ λ _, True }})
@@ -54,7 +54,7 @@ Lemma ht_lift_atomic_step
   reducible e1 σ1 →
   (∀ e2 σ2 ef, prim_step e1 σ1 e2 σ2 ef → φ e2 σ2 ef) →
   (∀ e2 σ2 ef, {{ ■ φ e2 σ2 ef ★ P }} ef ?@ ⊤ {{ λ _, True }}) ⊑
-  {{ ownP σ1 ★ ▷ P }} e1 @ E {{ λ v, ∃ σ2 ef, ownP σ2 ★ ■ φ (of_val v) σ2 ef }}.
+  {{ ▷ ownP σ1 ★ ▷ P }} e1 @ E {{ λ v, ∃ σ2 ef, ownP σ2 ★ ■ φ (of_val v) σ2 ef }}.
 Proof.
   intros ? Hsafe Hstep; set (φ' e σ ef := is_Some (to_val e) ∧ φ e σ ef).
   rewrite -(ht_lift_step E E φ'  _ P
diff --git a/program_logic/lifting.v b/program_logic/lifting.v
index 77cd393d0259e98ada8f51bfeec4be4fc6e0648d..ada372ac10f4b2b28a9094d33fd143cb915e9763 100644
--- a/program_logic/lifting.v
+++ b/program_logic/lifting.v
@@ -23,7 +23,7 @@ Lemma wp_lift_step E1 E2
   E1 ⊆ E2 → to_val e1 = None →
   reducible e1 σ1 →
   (∀ e2 σ2 ef, prim_step e1 σ1 e2 σ2 ef → φ e2 σ2 ef) →
-  (|={E2,E1}=> ownP σ1 ★ ▷ ∀ e2 σ2 ef,
+  (|={E2,E1}=> ▷ ownP σ1 ★ ▷ ∀ e2 σ2 ef,
     (■ φ e2 σ2 ef ∧ ownP σ2) -★ |={E1,E2}=> || e2 @ E2 {{ Φ }} ★ wp_fork ef)
   ⊑ || e1 @ E2 {{ Φ }}.
 Proof.
@@ -31,7 +31,7 @@ Proof.
   intros rf k Ef σ1' ???; destruct (Hvs rf (S k) Ef σ1')
     as (r'&(r1&r2&?&?&Hwp)&Hws); auto; clear Hvs; cofe_subst r'.
   destruct (wsat_update_pst k (E1 ∪ Ef) σ1 σ1' r1 (r2 ⋅ rf)) as [-> Hws'].
-  { by apply ownP_spec; auto. }
+  { apply equiv_dist. rewrite -(ownP_spec k); auto. }
   { by rewrite assoc. }
   constructor; [done|intros e2 σ2 ef ?; specialize (Hws' σ2)].
   destruct (λ H1 H2 H3, Hwp e2 σ2 ef k (update_pst σ2 r1) H1 H2 H3 rf k Ef σ2)
@@ -64,7 +64,7 @@ Lemma wp_lift_atomic_step {E Φ} e1
   reducible e1 σ1 →
   (∀ e2 σ2 ef,
     prim_step e1 σ1 e2 σ2 ef → ∃ v2, to_val e2 = Some v2 ∧ φ v2 σ2 ef) →
-  (ownP σ1 ★ ▷ ∀ v2 σ2 ef, ■ φ v2 σ2 ef ∧ ownP σ2 -★ Φ v2 ★ wp_fork ef)
+  (▷ ownP σ1 ★ ▷ ∀ v2 σ2 ef, ■ φ v2 σ2 ef ∧ ownP σ2 -★ Φ v2 ★ wp_fork ef)
   ⊑ || e1 @ E {{ Φ }}.
 Proof.
   intros. rewrite -(wp_lift_step E E (λ e2 σ2 ef, ∃ v2,
@@ -84,7 +84,7 @@ Lemma wp_lift_atomic_det_step {E Φ e1} σ1 v2 σ2 ef :
   reducible e1 σ1 →
   (∀ e2' σ2' ef', prim_step e1 σ1 e2' σ2' ef' →
     σ2 = σ2' ∧ to_val e2' = Some v2 ∧ ef = ef') →
-  (ownP σ1 ★ ▷ (ownP σ2 -★ Φ v2 ★ wp_fork ef)) ⊑ || e1 @ E {{ Φ }}.
+  (▷ ownP σ1 ★ ▷ (ownP σ2 -★ Φ v2 ★ wp_fork ef)) ⊑ || e1 @ E {{ Φ }}.
 Proof.
   intros. rewrite -(wp_lift_atomic_step _ (λ v2' σ2' ef',
     σ2 = σ2' ∧ v2 = v2' ∧ ef = ef') σ1) //; last naive_solver.
diff --git a/program_logic/ownership.v b/program_logic/ownership.v
index 2cbb11caef8aceb0b98da3358866c469c8920777..ce69c6dff8e94af692e1c21995f8934c8fc566de 100644
--- a/program_logic/ownership.v
+++ b/program_logic/ownership.v
@@ -71,7 +71,7 @@ Global Instance ownG_unit_always_stable m : AlwaysStable (ownG (unit m)).
 Proof. by rewrite /AlwaysStable always_ownG_unit. Qed.
 
 (* inversion lemmas *)
-Lemma ownI_spec r n i P :
+Lemma ownI_spec n r i P :
   ✓{n} r →
   (ownI i P) n r ↔ wld r !! i ≡{n}≡ Some (to_agree (Next (iProp_unfold P))).
 Proof.
@@ -81,12 +81,12 @@ Proof.
       (cmra_included_includedN _ P'),HP; apply map_lookup_validN with (wld r) i.
   - intros ?; split_and?; try apply cmra_empty_leastN; eauto.
 Qed.
-Lemma ownP_spec r n σ : ✓{n} r → (ownP σ) n r ↔ pst r ≡{n}≡ Excl σ.
+Lemma ownP_spec n r σ : ✓{n} r → (ownP σ) n r ↔ pst r ≡ Excl σ.
 Proof.
   intros (?&?&?); rewrite /uPred_holds /= res_includedN /= Excl_includedN //.
-  naive_solver (apply cmra_empty_leastN).
+  rewrite (timeless_iff n). naive_solver (apply cmra_empty_leastN).
 Qed.
-Lemma ownG_spec r n m : (ownG m) n r ↔ Some m ≼{n} gst r.
+Lemma ownG_spec n r m : (ownG m) n r ↔ Some m ≼{n} gst r.
 Proof.
   rewrite /uPred_holds /= res_includedN; naive_solver (apply cmra_empty_leastN).
 Qed.
diff --git a/program_logic/weakestpre.v b/program_logic/weakestpre.v
index 28f4f2ac7352672af8f34d624c4656a7c7069536..4ff71923da3025016bd98fc5b60e3cc8673b3a87 100644
--- a/program_logic/weakestpre.v
+++ b/program_logic/weakestpre.v
@@ -247,6 +247,7 @@ Proof. auto using wp_mask_frame_mono. Qed.
 
 (** * Weakest-pre is a FSA. *)
 Definition wp_fsa (e : expr Λ) : FSA Λ Σ (val Λ) := λ E, wp E e.
+Global Arguments wp_fsa _ _ / _.
 Global Instance wp_fsa_prf : FrameShiftAssertion (atomic e) (wp_fsa e).
 Proof.
   rewrite /wp_fsa; split; auto using wp_mask_frame_mono, wp_atomic, wp_frame_r.