Put quantifiers in pvs and wp definition in same order as wsat.

program_logic/adequacy.v

@@ -96,7 +96,7 @@ Proof.
   inversion Hwptp as [|?? r ?? rs Hwp _]; clear Hwptp; subst.
   move: Hwp. rewrite wp_eq. uPred.unseal=> /wp_value_inv Hwp.
   rewrite pvs_eq in Hwp.
-  destruct (Hwp (big_op rs) 2 ∅ σ2) as [r' []]; rewrite ?right_id_L; auto.
+  destruct (Hwp 2 ∅ σ2 (big_op rs)) as [r' []]; rewrite ?right_id_L; auto.
 Qed.
 
 Lemma ht_adequacy_result E φ e v t2 σ1 m σ2 :

program_logic/lifting.v

@@ -28,13 +28,13 @@ Lemma wp_lift_step E1 E2
 Proof.
   intros ? He Hsafe Hstep. rewrite pvs_eq wp_eq.
   uPred.unseal; split=> n r ? Hvs; constructor; auto.
-  intros rf k Ef σ1' ???; destruct (Hvs rf (S k) Ef σ1')
+  intros k Ef σ1' rf ???; destruct (Hvs (S k) Ef σ1' rf)
     as (r'&(r1&r2&?&?&Hwp)&Hws); auto; clear Hvs; cofe_subst r'.
   destruct (wsat_update_pst k (E2 ∪ Ef) σ1 σ1' r1 (r2 ⋅ rf)) as [-> Hws'].
   { 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)
+  destruct (λ H1 H2 H3, Hwp e2 σ2 ef k (update_pst σ2 r1) H1 H2 H3 k Ef σ2 rf)
     as (r'&(r1'&r2'&?&?&?)&?); auto; cofe_subst r'.
   { split. by eapply Hstep. apply ownP_spec; auto. }
   { rewrite (comm _ r2) -assoc; eauto using wsat_le. }
@@ -49,7 +49,7 @@ Lemma wp_lift_pure_step E (φ : expr Λ → option (expr Λ) → Prop) Φ e1 :
 Proof.
   intros He Hsafe Hstep; rewrite wp_eq; uPred.unseal.
   split=> n r ? Hwp; constructor; auto.
-  intros rf k Ef σ1 ???; split; [done|]. destruct n as [|n]; first lia.
+  intros k Ef σ1 rf ???; split; [done|]. destruct n as [|n]; first lia.
   intros e2 σ2 ef ?; destruct (Hstep σ1 e2 σ2 ef); auto; subst.
   destruct (Hwp e2 ef k r) as (r1&r2&Hr&?&?); auto.
   exists r1,r2; split_and?; try done.

program_logic/pviewshifts.v

@@ -11,14 +11,14 @@ Local Hint Extern 10 (✓{_} _) =>
   end; solve_validN.
 
 Program Definition pvs_def {Λ Σ} (E1 E2 : coPset) (P : iProp Λ Σ) : iProp Λ Σ :=
-  {| uPred_holds n r1 := ∀ rf k Ef σ,
+  {| uPred_holds n r1 := ∀ k Ef σ rf,
        0 < k ≤ n → E1 ∪ E2 ⊥ Ef →
        wsat k (E1 ∪ Ef) σ (r1 ⋅ rf) →
        ∃ r2, P k r2 ∧ wsat k (E2 ∪ Ef) σ (r2 ⋅ rf) |}.
 Next Obligation.
-  intros Λ Σ E1 E2 P n r1 r2 HP [r3 Hr2] rf k Ef σ ??.
+  intros Λ Σ E1 E2 P n r1 r2 HP [r3 Hr2] k Ef σ rf ??.
   rewrite (dist_le _ _ _ _ Hr2); last lia. intros Hws.
-  destruct (HP (r3 ⋅ rf) k Ef σ) as (r'&?&Hws'); rewrite ?(assoc op); auto.
+  destruct (HP k Ef σ (r3 ⋅ rf)) as (r'&?&Hws'); rewrite ?(assoc op); auto.
   exists (r' ⋅ r3); rewrite -assoc; split; last done.
   apply uPred_mono with r'; eauto using cmra_includedN_l.
 Qed.
@@ -63,8 +63,8 @@ Proof. intros ?????. exfalso. omega. Qed.
 Global Instance pvs_ne E1 E2 n : Proper (dist n ==> dist n) (@pvs Λ Σ E1 E2).
 Proof.
   rewrite pvs_eq.
-  intros P Q HPQ; split=> n' r1 ??; simpl; split; intros HP rf k Ef σ ???;
-    destruct (HP rf k Ef σ) as (r2&?&?); auto;
+  intros P Q HPQ; split=> n' r1 ??; simpl; split; intros HP k Ef σ rf ???;
+    destruct (HP k Ef σ rf) as (r2&?&?); auto;
     exists r2; split_and?; auto; apply HPQ; eauto.
 Qed.
 Global Instance pvs_proper E1 E2 : Proper ((≡) ==> (≡)) (@pvs Λ Σ E1 E2).
@@ -72,46 +72,46 @@ Proof. apply ne_proper, _. Qed.
 
 Lemma pvs_intro E P : P ={E}=> P.
 Proof.
-  rewrite pvs_eq. split=> n r ? HP rf k Ef σ ???; exists r; split; last done.
+  rewrite pvs_eq. split=> n r ? HP k Ef σ rf ???; exists r; split; last done.
   apply uPred_closed with n; eauto.
 Qed.
 Lemma pvs_mono E1 E2 P Q : (P ⊢ Q) → (|={E1,E2}=> P) ={E1,E2}=> Q.
 Proof.
-  rewrite pvs_eq. intros HPQ; split=> n r ? HP rf k Ef σ ???.
-  destruct (HP rf k Ef σ) as (r2&?&?); eauto.
+  rewrite pvs_eq. intros HPQ; split=> n r ? HP k Ef σ rf ???.
+  destruct (HP k Ef σ rf) as (r2&?&?); eauto.
   exists r2; eauto using uPred_in_entails.
 Qed.
 Lemma pvs_timeless E P : TimelessP P → ▷ P ={E}=> P.
 Proof.
   rewrite pvs_eq uPred.timelessP_spec=> HP.
-  uPred.unseal; split=>-[|n] r ? HP' rf k Ef σ ???; first lia.
+  uPred.unseal; split=>-[|n] r ? HP' k Ef σ rf ???; first lia.
   exists r; split; last done.
   apply HP, uPred_closed with n; eauto using cmra_validN_le.
 Qed.
 Lemma pvs_trans E1 E2 E3 P :
   E2 ⊆ E1 ∪ E3 → (|={E1,E2}=> |={E2,E3}=> P) ={E1,E3}=> P.
 Proof.
-  rewrite pvs_eq. intros ?; split=> n r1 ? HP1 rf k Ef σ ???.
-  destruct (HP1 rf k Ef σ) as (r2&HP2&?); auto.
+  rewrite pvs_eq. intros ?; split=> n r1 ? HP1 k Ef σ rf ???.
+  destruct (HP1 k Ef σ rf) as (r2&HP2&?); auto.
 Qed.
 Lemma pvs_mask_frame E1 E2 Ef P :
   Ef ⊥ E1 ∪ E2 → (|={E1,E2}=> P) ={E1 ∪ Ef,E2 ∪ Ef}=> P.
 Proof.
-  rewrite pvs_eq. intros ?; split=> n r ? HP rf k Ef' σ ???.
-  destruct (HP rf k (Ef∪Ef') σ) as (r'&?&?); rewrite ?(assoc_L _); eauto.
+  rewrite pvs_eq. intros ?; split=> n r ? HP k Ef' σ rf ???.
+  destruct (HP k (Ef∪Ef') σ rf) as (r'&?&?); rewrite ?(assoc_L _); eauto.
   by exists r'; rewrite -(assoc_L _).
 Qed.
 Lemma pvs_frame_r E1 E2 P Q : (|={E1,E2}=> P) ★ Q ={E1,E2}=> P ★ Q.
 Proof.
-  rewrite pvs_eq. uPred.unseal; split; intros n r ? (r1&r2&Hr&HP&?) rf k Ef σ ???.
-  destruct (HP (r2 ⋅ rf) k Ef σ) as (r'&?&?); eauto.
+  rewrite pvs_eq. uPred.unseal; split; intros n r ? (r1&r2&Hr&HP&?) k Ef σ rf ???.
+  destruct (HP k Ef σ (r2 ⋅ rf)) as (r'&?&?); eauto.
   { by rewrite assoc -(dist_le _ _ _ _ Hr); last lia. }
   exists (r' ⋅ r2); split; last by rewrite -assoc.
   exists r', r2; split_and?; auto. apply uPred_closed with n; auto.
 Qed.
 Lemma pvs_openI i P : ownI i P ={{[i]},∅}=> ▷ P.
 Proof.
-  rewrite pvs_eq. uPred.unseal; split=> -[|n] r ? Hinv rf [|k] Ef σ ???; try lia.
+  rewrite pvs_eq. uPred.unseal; split=> -[|n] r ? Hinv [|k] Ef σ rf ???; try lia.
   apply ownI_spec in Hinv; last auto.
   destruct (wsat_open k Ef σ (r ⋅ rf) i P) as (rP&?&?); auto.
   { rewrite lookup_wld_op_l ?Hinv; eauto; apply dist_le with (S n); eauto. }
@@ -121,7 +121,7 @@ Qed.
 Lemma pvs_closeI i P : ownI i P ∧ ▷ P ={∅,{[i]}}=> True.
 Proof.
   rewrite pvs_eq.
-  uPred.unseal; split=> -[|n] r ? [? HP] rf [|k] Ef σ ? HE ?; try lia.
+  uPred.unseal; split=> -[|n] r ? [? HP] [|k] Ef σ rf ? HE ?; try lia.
   exists ∅; split; [done|].
   rewrite left_id; apply wsat_close with P r.
   - apply ownI_spec, uPred_closed with (S n); auto.
@@ -133,7 +133,7 @@ Lemma pvs_ownG_updateP E m (P : iGst Λ Σ → Prop) :
   m ~~>: P → ownG m ={E}=> ∃ m', ■ P m' ∧ ownG m'.
 Proof.
   rewrite pvs_eq. intros Hup.
-  uPred.unseal; split=> -[|n] r ? /ownG_spec Hinv rf [|k] Ef σ ???; try lia.
+  uPred.unseal; split=> -[|n] r ? /ownG_spec Hinv [|k] Ef σ rf ???; try lia.
   destruct (wsat_update_gst k (E ∪ Ef) σ r rf m P) as (m'&?&?); eauto.
   { apply cmra_includedN_le with (S n); auto. }
   by exists (update_gst m' r); split; [exists m'; split; [|apply ownG_spec]|].
@@ -141,7 +141,7 @@ Qed.
 Lemma pvs_allocI E P : ¬set_finite E → ▷ P ={E}=> ∃ i, ■ (i ∈ E) ∧ ownI i P.
 Proof.
   rewrite pvs_eq. intros ?; rewrite /ownI; uPred.unseal.
-  split=> -[|n] r ? HP rf [|k] Ef σ ???; try lia.
+  split=> -[|n] r ? HP [|k] Ef σ rf ???; try lia.
   destruct (wsat_alloc k E Ef σ rf P r) as (i&?&?&?); auto.
   { apply uPred_closed with n; eauto. }
   exists (Res {[ i := to_agree (Next (iProp_unfold P)) ]} ∅ ∅).

program_logic/weakestpre.v

@@ -10,7 +10,7 @@ Local Hint Extern 10 (✓{_} _) =>
   end; solve_validN.
 
 Record wp_go {Λ Σ} (E : coPset) (Φ Φfork : expr Λ → nat → iRes Λ Σ → Prop)
-    (k : nat) (rf : iRes Λ Σ) (e1 : expr Λ) (σ1 : state Λ) := {
+    (k : nat) (σ1 : state Λ) (rf : iRes Λ Σ) (e1 : expr Λ) := {
   wf_safe : reducible e1 σ1;
   wp_step e2 σ2 ef :
     prim_step e1 σ1 e2 σ2 ef →
@@ -24,11 +24,11 @@ CoInductive wp_pre {Λ Σ} (E : coPset)
   | wp_pre_value n r v : (|={E}=> Φ v)%I n r → wp_pre E Φ (of_val v) n r
   | wp_pre_step n r1 e1 :
      to_val e1 = None →
-     (∀ rf k Ef σ1,
+     (∀ k Ef σ1 rf,
        0 < k < n → E ⊥ Ef →
        wsat (S k) (E ∪ Ef) σ1 (r1 ⋅ rf) →
        wp_go (E ∪ Ef) (wp_pre E Φ)
-                      (wp_pre ⊤ (λ _, True%I)) k rf e1 σ1) →
+                      (wp_pre ⊤ (λ _, True%I)) k σ1 rf e1) →
      wp_pre E Φ e1 n r1.
 Program Definition wp_def {Λ Σ} (E : coPset) (e : expr Λ)
   (Φ : val Λ → iProp Λ Σ) : iProp Λ Σ := {| uPred_holds := wp_pre E Φ e |}.
@@ -37,8 +37,8 @@ Next Obligation.
   induction n as [n IH] using lt_wf_ind; intros Φ E e r1 r1'.
   destruct 1 as [|n r1 e1 ? Hgo].
   - constructor; eauto using uPred_mono.
-  - intros [rf' Hr]; constructor; [done|intros rf k Ef σ1 ???].
-    destruct (Hgo (rf' ⋅ rf) k Ef σ1) as [Hsafe Hstep];
+  - intros [rf' Hr]; constructor; [done|intros k Ef σ1 rf ???].
+    destruct (Hgo k Ef σ1 (rf' ⋅ rf)) as [Hsafe Hstep];
       rewrite ?assoc -?(dist_le _ _ _ _ Hr); auto; constructor; [done|].
     intros e2 σ2 ef ?; destruct (Hstep e2 σ2 ef) as (r2&r2'&?&?&?); auto.
     exists r2, (r2' ⋅ rf'); split_and?; eauto 10 using (IH k), cmra_includedN_l.
@@ -85,8 +85,8 @@ Proof.
   induction n' as [n' IH] using lt_wf_ind=> e r.
   destruct 3 as [n' r v HpvsQ|n' r e1 ? Hgo].
   { constructor. by eapply pvs_ne, HpvsQ; eauto. }
-  constructor; [done|]=> rf k Ef σ1 ???.
-  destruct (Hgo rf k Ef σ1) as [Hsafe Hstep]; auto.
+  constructor; [done|]=> k Ef σ1 rf ???.
+  destruct (Hgo k Ef σ1 rf) as [Hsafe Hstep]; auto.
   split; [done|intros e2 σ2 ef ?].
   destruct (Hstep e2 σ2 ef) as (r2&r2'&?&?&?); auto.
   exists r2, r2'; split_and?; [|eapply IH|]; eauto.
@@ -104,10 +104,10 @@ Proof.
   revert e r; induction n as [n IH] using lt_wf_ind=> e r.
   destruct 2 as [n' r v HpvsQ|n' r e1 ? Hgo].
   { constructor; eapply pvs_mask_frame_mono, HpvsQ; eauto. }
-  constructor; [done|]=> rf k Ef σ1 ???.
+  constructor; [done|]=> k Ef σ1 rf ???.
   assert (E2 ∪ Ef = E1 ∪ (E2 ∖ E1 ∪ Ef)) as HE'.
   { by rewrite assoc_L -union_difference_L. }
-  destruct (Hgo rf k ((E2 ∖ E1) ∪ Ef) σ1) as [Hsafe Hstep]; rewrite -?HE'; auto.
+  destruct (Hgo k ((E2 ∖ E1) ∪ Ef) σ1 rf) as [Hsafe Hstep]; rewrite -?HE'; auto.
   split; [done|intros e2 σ2 ef ?].
   destruct (Hstep e2 σ2 ef) as (r2&r2'&?&?&?); auto.
   exists r2, r2'; split_and?; [rewrite HE'|eapply IH|]; eauto.
@@ -127,7 +127,7 @@ Qed.
 Lemma wp_step_inv E Ef Φ e k n σ r rf :
   to_val e = None → 0 < k < n → E ⊥ Ef →
   wp_def E e Φ n r → wsat (S k) (E ∪ Ef) σ (r ⋅ rf) →
-  wp_go (E ∪ Ef) (λ e, wp_def E e Φ) (λ e, wp_def ⊤ e (λ _, True%I)) k rf e σ.
+  wp_go (E ∪ Ef) (λ e, wp_def E e Φ) (λ e, wp_def ⊤ e (λ _, True%I)) k σ rf e.
 Proof.
   intros He; destruct 3; [by rewrite ?to_of_val in He|eauto].
 Qed.
@@ -140,8 +140,8 @@ Proof.
   destruct (to_val e) as [v|] eqn:He; [apply of_to_val in He; subst|].
   { constructor; eapply pvs_trans', pvs_mono, Hvs; eauto.
     split=> ???; apply wp_value_inv. }
-  constructor; [done|]=> rf k Ef σ1 ???.
-  rewrite pvs_eq in Hvs. destruct (Hvs rf (S k) Ef σ1) as (r'&Hwp&?); auto.
+  constructor; [done|]=> k Ef σ1 rf ???.
+  rewrite pvs_eq in Hvs. destruct (Hvs (S k) Ef σ1 rf) as (r'&Hwp&?); auto.
   eapply wp_step_inv with (S k) r'; eauto.
 Qed.
 Lemma wp_pvs E e Φ : WP e @ E {{ v, |={E}=> Φ v }} ⊢ WP e @ E {{ Φ }}.
@@ -150,7 +150,7 @@ Proof.
     induction n as [n IH] using lt_wf_ind=> e r Hr HΦ.
   destruct (to_val e) as [v|] eqn:He; [apply of_to_val in He; subst|].
   { constructor; apply pvs_trans', (wp_value_inv _ (pvs E E ∘ Φ)); auto. }
-  constructor; [done|]=> rf k Ef σ1 ???.
+  constructor; [done|]=> k Ef σ1 rf ???.
   destruct (wp_step_inv E Ef (pvs E E ∘ Φ) e k n σ1 r rf) as [? Hstep]; auto.
   split; [done|intros e2 σ2 ef ?].
   destruct (Hstep e2 σ2 ef) as (r2&r2'&?&Hwp'&?); auto.
@@ -161,8 +161,8 @@ Lemma wp_atomic E1 E2 e Φ :
   (|={E1,E2}=> WP e @ E2 {{ v, |={E2,E1}=> Φ v }}) ⊢ WP e @ E1 {{ Φ }}.
 Proof.
   rewrite wp_eq pvs_eq. intros ? He; split=> n r ? Hvs; constructor.
-  eauto using atomic_not_val. intros rf k Ef σ1 ???.
-  destruct (Hvs rf (S k) Ef σ1) as (r'&Hwp&?); auto.
+  eauto using atomic_not_val. intros k Ef σ1 rf ???.
+  destruct (Hvs (S k) Ef σ1 rf) as (r'&Hwp&?); auto.
   destruct (wp_step_inv E2 Ef (pvs_def E2 E1 ∘ Φ) e k (S k) σ1 r' rf)
     as [Hsafe Hstep]; auto using atomic_not_val; [].
   split; [done|]=> e2 σ2 ef ?.
@@ -170,7 +170,7 @@ Proof.
   destruct Hwp' as [k r2 v Hvs'|k r2 e2 Hgo];
     [|destruct (atomic_step e σ1 e2 σ2 ef); naive_solver].
   rewrite -pvs_eq in Hvs'. apply pvs_trans in Hvs';auto. rewrite pvs_eq in Hvs'.
-  destruct (Hvs' (r2' ⋅ rf) k Ef σ2) as (r3&[]); rewrite ?assoc; auto.
+  destruct (Hvs' k Ef σ2 (r2' ⋅ rf)) as (r3&[]); rewrite ?assoc; auto.
   exists r3, r2'; split_and?; last done.
   - by rewrite -assoc.
   - constructor; apply pvs_intro; auto.
@@ -183,8 +183,8 @@ Proof.
   destruct 1 as [|n r e ? Hgo]=>?.
   { constructor. rewrite -uPred_sep_eq; apply pvs_frame_r; auto.
     uPred.unseal; exists r, rR; eauto. }
-  constructor; [done|]=> rf k Ef σ1 ???.
-  destruct (Hgo (rR⋅rf) k Ef σ1) as [Hsafe Hstep]; auto.
+  constructor; [done|]=> k Ef σ1 rf ???.
+  destruct (Hgo k Ef σ1 (rR⋅rf)) as [Hsafe Hstep]; auto.
   { by rewrite assoc. }
   split; [done|intros e2 σ2 ef ?].
   destruct (Hstep e2 σ2 ef) as (r2&r2'&?&?&?); auto.
@@ -199,27 +199,27 @@ Lemma wp_frame_step_r E E1 E2 e Φ R :
 Proof.
   rewrite wp_eq pvs_eq=> He ??.
   uPred.unseal; split; intros n r' Hvalid (r&rR&Hr&Hwp&HR); cofe_subst.
-  constructor; [done|]=>rf k Ef σ1 ?? Hws1.
+  constructor; [done|]=> k Ef σ1 rf ?? Hws1.
   destruct Hwp as [|n r e ? Hgo]; [by rewrite to_of_val in He|].
   (* "execute" HR *)
-  destruct (HR (r ⋅ rf) (S k) (E ∪ Ef) σ1) as (s&Hvs&Hws2); auto.
+  destruct (HR (S k) (E ∪ Ef) σ1 (r ⋅ rf)) as (s&Hvs&Hws2); auto.
   { eapply wsat_proper, Hws1; first by set_solver+.
     by rewrite assoc [rR ⋅ _]comm. }
   clear Hws1 HR.
   (* Take a step *)
-  destruct (Hgo (s⋅rf) k (E2 ∪ Ef) σ1) as [Hsafe Hstep]; auto.
+  destruct (Hgo k (E2 ∪ Ef) σ1 (s ⋅ rf)) as [Hsafe Hstep]; auto.
   { eapply wsat_proper, Hws2; first by set_solver+.
     by rewrite !assoc [s ⋅ _]comm. }
   clear Hgo.
   split; [done|intros e2 σ2 ef ?].
   destruct (Hstep e2 σ2 ef) as (r2&r2'&Hws3&?&?); auto. clear Hws2.
   (* Execute 2nd part of the view shift *)
-  destruct (Hvs (r2 ⋅ r2' ⋅ rf) k (E ∪ Ef) σ2) as (t&HR&Hws4); auto.
+  destruct (Hvs k (E ∪ Ef) σ2 (r2 ⋅ r2' ⋅ rf)) as (t&HR&Hws4); auto.
   { eapply wsat_proper, Hws3; first by set_solver+.
     by rewrite !assoc [_ ⋅ s]comm !assoc. }
   clear Hvs Hws3.
   (* Execute the rest of e *)
-  exists (r2 ⋅ t), r2'. split_and?; auto.
+  exists (r2 ⋅ t), r2'; split_and?; auto.
   - eapply wsat_proper, Hws4; first by set_solver+.
     by rewrite !assoc [_ ⋅ t]comm.
   - rewrite -uPred_sep_eq. move: wp_frame_r. rewrite wp_eq=>Hframe.
@@ -234,8 +234,8 @@ Proof.
     induction n as [n IH] using lt_wf_ind=> e r ?.
   destruct 1 as [|n r e ? Hgo].
   { rewrite -wp_eq. apply pvs_wp; rewrite ?wp_eq; done. }
-  constructor; auto using fill_not_val=> rf k Ef σ1 ???.
-  destruct (Hgo rf k Ef σ1) as [Hsafe Hstep]; auto.
+  constructor; auto using fill_not_val=> k Ef σ1 rf ???.
+  destruct (Hgo k Ef σ1 rf) as [Hsafe Hstep]; auto.
   split.
   { destruct Hsafe as (e2&σ2&ef&?).
     by exists (K e2), σ2, ef; apply fill_step. }

program_logic/weakestpre_fix.v

@@ -18,7 +18,7 @@ Local Notation coPsetC := (leibnizC (coPset)).
 Program Definition wp_pre
     (wp : coPsetC -n> exprC Λ -n> (valC Λ -n> iProp) -n> iProp)
     (E : coPset) (e1 : expr Λ) (Φ : valC Λ -n> iProp) :  iProp :=
-  {| uPred_holds n r1 := ∀ rf k Ef σ1,
+  {| uPred_holds n r1 := ∀ k Ef σ1 rf,
        0 ≤ k < n → E ⊥ Ef →
        wsat (S k) (E ∪ Ef) σ1 (r1 ⋅ rf) →
        (∀ v, to_val e1 = Some v →
@@ -31,9 +31,9 @@ Program Definition wp_pre
              wp E e2 Φ k r2 ∧
              default True ef (λ ef, wp ⊤ ef (cconst True%I) k r2'))) |}.
 Next Obligation.
-  intros wp E e1 Φ n r1 r2 Hwp [r3 Hr2] rf k Ef σ1 ??.
+  intros wp E e1 Φ n r1 r2 Hwp [r3 Hr2] k Ef σ1 rf ??.
   rewrite (dist_le _ _ _ _ Hr2); last lia. intros Hws.
-  destruct (Hwp (r3 ⋅ rf) k Ef σ1) as [Hval Hstep]; rewrite ?assoc; auto.
+  destruct (Hwp k Ef σ1 (r3 ⋅ rf)) as [Hval Hstep]; rewrite ?assoc; auto.
   split.
   - intros v Hv. destruct (Hval v Hv) as [r4 [??]].
     exists (r4 ⋅ r3). rewrite -assoc. eauto using uPred_mono, cmra_includedN_l.
@@ -51,8 +51,8 @@ Lemma wp_pre_contractive' n E e Φ1 Φ2 r
   (∀ i : nat, i < n → wp1 ≡{i}≡ wp2) → Φ1 ≡{n}≡ Φ2 →
   wp_pre wp1 E e Φ1 n r → wp_pre wp2 E e Φ2 n r.
 Proof.
-  intros HI HΦ Hwp rf k Ef σ1 ???.
-  destruct (Hwp rf k Ef σ1) as [Hval Hstep]; auto.
+  intros HI HΦ Hwp k Ef σ1 rf ???.
+  destruct (Hwp k Ef σ1 rf) as [Hval Hstep]; auto.
   split.
   { intros v ?. destruct (Hval v) as (r2&?&?); auto.
     exists r2. split; [apply HΦ|]; auto. }
@@ -95,25 +95,25 @@ Proof.
   - induction n as [n IH] using lt_wf_ind=> r1 E e Φ ? Hwp.
     case EQ: (to_val e)=>[v|].
     + rewrite -(of_to_val _ _ EQ) {IH}. constructor. rewrite pvs_eq.
-      intros rf [|k] Ef σ ???; first omega.
+      intros [|k] Ef σ rf ???; first omega.
       apply wp_fix_unfold in Hwp; last done.
-      destruct (Hwp rf k Ef σ); auto.
-    + constructor; [done|]=> rf k Ef σ1 ???.
+      destruct (Hwp k Ef σ rf); auto.
+    + constructor; [done|]=> k Ef σ1 rf ???.
       apply wp_fix_unfold in Hwp; last done.
-      destruct (Hwp rf k Ef σ1) as [Hval [Hred Hpstep]]; auto.
+      destruct (Hwp k Ef σ1 rf) as [Hval [Hred Hpstep]]; auto.
       split; [done|]=> e2 σ2 ef ?.
       destruct (Hpstep e2 σ2 ef) as (r2&r2'&?&?&?); [done..|].
       exists r2, r2'; split_and?; auto.
       intros ? ->. change (weakestpre.wp_pre ⊤ (cconst True%I) e' k r2'); eauto.
   - induction n as [n IH] using lt_wf_ind=> r1 E e Φ ? Hwp.
-    apply wp_fix_unfold; [done|]=> rf k Ef σ1 ???. split.
+    apply wp_fix_unfold; [done|]=> k Ef σ1 rf ???. split.
     + intros v Hval.
       destruct Hwp as [??? Hpvs|]; rewrite ?to_of_val in Hval; simplify_eq/=.
       rewrite pvs_eq in Hpvs.
-      destruct (Hpvs rf (S k) Ef σ1) as (r2&?&?); eauto.
+      destruct (Hpvs (S k) Ef σ1 rf) as (r2&?&?); eauto.
     + intros Hval ?.
       destruct Hwp as [|???? Hwp]; rewrite ?to_of_val in Hval; simplify_eq/=.
-      edestruct (Hwp rf k Ef σ1) as [? Hpstep]; auto.
+      edestruct (Hwp k Ef σ1 rf) as [? Hpstep]; auto.
       split; [done|]=> e2 σ2 ef ?.
       destruct (Hpstep e2 σ2 ef) as (r2&r2'&?&?&?); auto.
       exists r2, r2'. destruct ef; simpl; auto.