rel_apply_l/r tactics

F_mu_ref_conc/examples/counter.v

@@ -50,15 +50,15 @@ Section CG_Counter.
   Proof.
     iIntros (?) "Hx Hl Hlog".
     unfold CG_increment. unlock. simpl_subst/=.
-    rel_rec_r.    
-    rel_bind_r (acquire #l).
-    iApply (bin_log_related_acquire_r with "Hl"); eauto. iIntros "Hl". simpl.
+    rel_rec_r.
+    rel_apply_r (bin_log_related_acquire_r with "Hl"); eauto.
+    iIntros "Hl".
     rel_rec_r.
     rel_load_r.
     rel_op_r.
     rel_store_r. simpl.
     rel_rec_r.
-    iApply (bin_log_related_release_r with "Hl"); eauto.
+    rel_apply_r (bin_log_related_release_r with "Hl"); eauto.
     by iApply "Hlog".
   Qed.
  
@@ -150,8 +150,7 @@ Section CG_Counter.
     iLöb as "IH".
     rel_rec_l.
     iPoseProof "H" as "H2". (* lolwhat *)
-    rel_bind_l (Load #x).
-    iApply (bin_log_related_load_l).
+    rel_load_l_atomic.
     iMod "H" as (n) "[Hx [HR Hrev]]".  iModIntro.
     iExists (#nv n). iFrame. iNext. iIntros "Hx".
     iDestruct "Hrev" as "[Hrev _]".
@@ -160,8 +159,7 @@ Section CG_Counter.
     { iExists _. iFrame. } iModIntro. simpl.
     rel_rec_l.
     rel_op_l.
-    rel_bind_l (CAS _ _ _).
-    iApply (bin_log_related_cas_l); auto.
+    rel_cas_l_atomic.
     iMod "H2" as (n') "[Hx [HR HQ]]". iModIntro. simpl.
     destruct (decide (n = n')); subst.
     - iExists (#nv n'). iFrame.
@@ -169,12 +167,12 @@ Section CG_Counter.
       iIntros "_ !> Hx". simpl.
       iDestruct "HQ" as "[_ HQ]".
       iSpecialize ("HQ" $! n' with "[Hx HR]"). { iFrame. }
-      iApply bin_log_related_if_true_masked_l; auto.
+      rel_if_true_l. done.
     - iExists (#nv n'). iFrame. 
       iSplitL; eauto; last first.
       { iDestruct 1 as %Hfoo. exfalso. simplify_eq. }
       iIntros "_ !> Hx". simpl.
-      iApply bin_log_related_if_false_masked_l; auto.
+      rel_if_false_l.
       iDestruct "HQ" as "[HQ _]".
       iMod ("HQ" with "[Hx HR]").
       { iExists _; iFrame. }
@@ -192,7 +190,7 @@ Section CG_Counter.
     iIntros "#H".
     unfold counter_read. unlock. simpl.
     rel_rec_l.
-    iApply bin_log_related_load_l.
+    rel_load_l_atomic.
     iMod "H" as (n) "[Hx [HR Hfin]]". iModIntro.
     iExists _; iFrame "Hx". iNext.
     iIntros "Hx".
@@ -267,8 +265,7 @@ Section CG_Counter.
     iApply bin_log_related_arrow; try by (unlock; eauto).
     iAlways. iIntros ([? ?]) "/= [% %]"; simplify_eq/=.
     unlock. rel_rec_l. rel_rec_r.
-    rel_bind_r (newlock ())%E.
-    iApply (bin_log_related_newlock_r); auto; simpl.
+    rel_apply_r bin_log_related_newlock_r; auto.
     iIntros (l) "Hl".
     rel_rec_r.
     rel_alloc_r as cnt' "Hcnt'".

F_mu_ref_conc/examples/lateearlychoice.v

@@ -50,8 +50,7 @@ Section Refinement.
     iIntros (?) "#Hs Hlog".
     unfold rand. unlock. simpl.
     rel_rec_l.
-    rel_bind_l (Alloc _).
-    iApply bin_log_related_alloc_l'; first eauto. iNext. iIntros (y) "Hy". simpl.
+    rel_alloc_l as y "Hy". simpl.
     rel_rec_l.
     iMod (inv_alloc choiceN _ (∃ b, y ↦ᵢ (#♭v b))%I with "[Hy]") as "#Hinv".
     { iNext. eauto. }
@@ -65,10 +64,10 @@ Section Refinement.
       done.
     - simpl.
       rel_rec_l.
-      rel_load_l under choiceN as "Hy" "Hcl".
-        iDestruct "Hy" as (b) "Hy".
-        iExists (#♭v b). iFrame.
-        iModIntro. iNext. iIntros "Hy".
+      rel_load_l_atomic.
+      iInv choiceN as (b) "Hy" "Hcl".
+      iExists (#♭v b). iFrame.
+      iModIntro. iNext. iIntros "Hy".
       iMod ("Hcl" with "[Hy]").
       { iNext. iExists b. iFrame. }
       done. 
@@ -104,8 +103,7 @@ Section Refinement.
     rel_rec_l.
     rel_store_l. simpl.
     rel_rec_l.
-    rel_bind_l (rand ())%E.
-    iApply (rand_l with "Hs"); eauto. simpl.
+    rel_apply_l (rand_l with "Hs"); eauto.
     by iApply "Hlog".
   Qed.
    
@@ -119,12 +117,11 @@ Section Refinement.
     unfold earlyChoice. unlock.
     rel_rec_r.
 
-    rel_bind_r (rand ())%E.
-    iApply (rand_r b with "Hspec"); eauto. simpl.
+    rel_apply_r (rand_r b with "Hspec"); eauto.
     rel_rec_r.
     rel_store_r. simpl.
     rel_rec_r.
-    rel_vals; simpl; eauto.
+    rel_vals; eauto.
   Qed.
 
   Lemma prerefinement2 Δ Γ x x' n ρ :
@@ -134,20 +131,19 @@ Section Refinement.
     iIntros "#Hspec Hx Hx'".
     unfold earlyChoice. unlock.
     rel_rec_l.
-    rel_bind_l (rand ())%E.
-    iApply (rand_l with "Hspec"); eauto. simpl. iIntros (b).
+    rel_apply_l (rand_l with "Hspec"); eauto.
+    iIntros (b).
     rel_rec_l.
 
     unfold lateChoice. unlock.
     rel_rec_r.
     rel_store_r. simpl.
     rel_rec_r.
-    rel_bind_r (rand ())%E.
-    iApply (rand_r b with "Hspec"); eauto. simpl.
+    rel_apply_r (rand_r b with "Hspec"); eauto.
 
     rel_store_l. simpl.
     rel_rec_l.
-    rel_vals; simpl; eauto.
+    rel_vals; eauto.
   Qed.
 
 End Refinement.

F_mu_ref_conc/fundamental_binary.v

@@ -671,8 +671,8 @@ Section masked.
   Qed.
 End masked.
 
-Theorem binary_fundamental Γ e τ :
-  Γ ⊢ₜ e : τ → (Γ ⊨ e ≤log≤ e : τ)%I.
+Theorem binary_fundamental Δ Γ e τ :
+  Γ ⊢ₜ e : τ → ({⊤,⊤;Δ;Γ} ⊨ e ≤log≤ e : τ)%I.
 Proof. by eapply binary_fundamental_masked. Qed.
 
 End fundamental.

F_mu_ref_conc/proofmode/rel_tactics.v

@@ -7,6 +7,7 @@ From iris_logrel.F_mu_ref_conc.proofmode Require Export tactics classes.
 Set Default Proof Using "Type".
 Import lang.
 
+(** General tactics *)
 Lemma tac_rel_bind_l `{logrelG Σ} e' K Δ E1 E2 Γ e t Δ' τ :
   e = fill K e' →
   (Δ ⊢ bin_log_related E1 E2 Δ' Γ (fill K e') t τ) →
@@ -57,18 +58,42 @@ Tactic Notation "rel_bind_l" open_constr(efoc) :=
   | (* new goal *) 
   ].
 
+Ltac rel_bind_ctx_l K :=
+  eapply (tac_rel_bind_l _ K);
+  [reflexivity || tac_bind_helper
+  |].
+
 Tactic Notation "rel_bind_r" open_constr(efoc) :=
   iStartProof;
   eapply (tac_rel_bind_r efoc);
-  [ tac_bind_helper
+  [tac_bind_helper
   | (* new goal *) 
   ].
 
+Ltac rel_bind_ctx_r K :=
+  eapply (tac_rel_bind_r _ K);
+  [reflexivity || tac_bind_helper
+  |].
+
 Tactic Notation "rel_vals" :=
   iStartProof;
-  iApply bin_log_related_val; [ try solve_to_val | try solve_to_val | ].
+  iApply bin_log_related_val; [ try solve_to_val | try solve_to_val | simpl ].
+
+
+Tactic Notation "rel_apply_l" open_constr(lem) :=
+  iStartProof;
+  rel_reshape_cont_l ltac:(fun K e =>
+    rel_bind_ctx_l K; iApply lem; tac_rel_done; try iNext; simpl_subst/=)
+  || fail "rel_apply_l: Cannot apply " lem.
+
+Tactic Notation "rel_apply_r" open_constr(lem) :=
+  iStartProof;
+  rel_reshape_cont_r ltac:(fun K e =>
+    rel_bind_ctx_r K; iApply lem; tac_rel_done; try iNext; simpl_subst/=)
+  || fail "rel_apply_r: Cannot apply " lem.
 
 (** Pure reductions *)
+
 Lemma tac_rel_pure_l `{logrelG Σ} K e1 Δ' E1 E2 Δ Γ e e2 ϕ t τ (b : bool) :
   e = fill K e1 →
   PureExec ϕ e1 e2 →
@@ -193,56 +218,7 @@ Tactic Notation "rel_fork_l" :=
     |solve_closed
     |simpl (* new goal *) ].
 
-Lemma tac_rel_alloc_l `{logrelG Σ} nam nam_cl Δ1 Δ2 E1 E2 p i1 N P e' v' K' Γ e t Δ' τ :
-  nclose N ⊆ E1 →
-  envs_lookup i1 Δ1 = Some (p, inv N P) →
-  E2 = E1 ∖ ↑N →
-  e = fill K' (Alloc e') →
-  to_val e' = Some v' →
-  envs_lookup nam Δ1 = None →
-  envs_lookup nam_cl Δ1 = None →
-  nam_cl ≠ nam →
-  Δ2 = envs_snoc (envs_snoc Δ1 false nam (▷ P)%I) false nam_cl (▷ P ={E1 ∖ ↑N,E1}=∗ True)%I →
-  (Δ2 ⊢ |={E2}=> ▷ ∀ l,
-     (l ↦ᵢ v' -∗ bin_log_related E2 E1 Δ' Γ (fill K' (Loc l)) t τ)) →
-  (Δ1 ⊢ bin_log_related E1 E1 Δ' Γ e t τ).
-Proof.
-  intros ??????????.
-  rewrite -(idemp uPred_and Δ1).
-  rewrite {1}envs_lookup_sound'. 2: eassumption.
-  rewrite uPred.sep_elim_l uPred.always_and_sep_l.
-  rewrite inv_open. 2: eassumption.
-  subst e.
-  rewrite -(bin_log_related_alloc_l Δ' Γ E1 E2). 2: eassumption.
-  rewrite fupd_frame_r.
-  rewrite -(fupd_trans E1 E2 E2).
-  subst E2.
-  apply fupd_mono.  
-  rewrite -H9.
-  subst Δ2.
-  rewrite (envs_snoc_sound Δ1 false nam (▷P)) /=. 2: eassumption.
-  rewrite comm.
-  rewrite assoc.
-  rewrite uPred.wand_elim_l.
-  rewrite (envs_snoc_sound (envs_snoc Δ1 false nam (▷ P)) false nam_cl (▷ P ={E1 ∖ ↑N,E1}=∗ True)) //;
-          last first.
-  { rewrite (envs_lookup_snoc_ne Δ1); eassumption. }
-  apply uPred.wand_elim_l.
-Qed.
-
-Tactic Notation "rel_alloc_l" "under" constr(N) "as" constr(nam) constr(nam_cl) :=
-  iStartProof;
-  eapply (tac_rel_alloc_l nam nam_cl);
-    [solve_ndisj || fail "rel_alloc_l: cannot prove 'nclose " N " ⊆ ?'"
-    |iAssumptionCore || fail "rel_alloc_l: cannot find inv " N " ?" 
-    |try fast_done (* E2 = E1 \ ↑N *)
-    |tac_bind_helper (* e = fill K' (Store (Loc l) e') *)
-    |solve_to_val (* to_val e' = Some v *)
-    |try fast_done (* nam fresh *)
-    |try fast_done (* nam_cl fresh *)
-    |eauto (* nam =/= nam_cl *)
-    |env_cbv; reflexivity || fail "rel_alloc_l: this should not happen"
-    |(* new goal *)].
+Tactic Notation "rel_alloc_l_atomic" := rel_apply_l bin_log_related_alloc_l.
 
 Lemma tac_rel_alloc_l_simp `{logrelG Σ} Δ1 Δ2 E1 e' v' K' Γ e t Δ' τ :
   e = fill K' (Alloc e') →
@@ -261,61 +237,13 @@ Qed.
 
 Tactic Notation "rel_alloc_l" "as" ident(l) constr(H) :=
   iStartProof;
-  eapply (tac_rel_alloc_l_simp);
-    [tac_bind_helper (* e = fill K' .. *)
-    |apply _ (* IntoLaterNEnvs _ _ _ *)
-    |solve_to_val (* to_val e' = Some v *)
-    |iIntros (l) H (* new goal *)].
+  eapply tac_rel_alloc_l_simp;
+    [tac_bind_helper       (* e = fill K' .. *)
+    |apply _               (* IntoLaterNEnvs _ _ _ *)
+    |solve_to_val          (* to_val e' = Some v *)
+    |iIntros (l) H         (* new goal *)].
 
-Lemma tac_rel_load_l `{logrelG Σ} nam nam_cl Δ1 Δ2 E1 E2 p i1 N P l K' Γ e t Δ' τ :
-  nclose N ⊆ E1 →
-  envs_lookup i1 Δ1 = Some (p, inv N P) →
-  E2 = E1 ∖ ↑N →
-  e = fill K' (Load (Loc l)) →
-  envs_lookup nam Δ1 = None →
-  envs_lookup nam_cl Δ1 = None →
-  nam_cl ≠ nam →
-  Δ2 = envs_snoc (envs_snoc Δ1 false nam (▷ P)%I) false nam_cl (▷ P ={E1 ∖ ↑N,E1}=∗ True)%I →
-  (Δ2 ⊢ |={E2}=> ∃ v, ▷ (l ↦ᵢ v) ∗
-     ▷ (l ↦ᵢ v -∗ bin_log_related E2 E1 Δ' Γ (fill K' (of_val v)) t τ)) →
-  (Δ1 ⊢ bin_log_related E1 E1 Δ' Γ e t τ).
-Proof.
-  intros ?????????.
-  rewrite -(idemp uPred_and Δ1).
-  rewrite {1}envs_lookup_sound'. 2: eassumption.
-  rewrite uPred.sep_elim_l uPred.always_and_sep_l.
-  rewrite inv_open. 2: eassumption.
-  subst e.
-  rewrite -(bin_log_related_load_l Δ' Γ E1 E2).
-  rewrite fupd_frame_r.
-  rewrite -(fupd_trans E1 E2 E2).
-  subst E2.
-  apply fupd_mono.  
-  rewrite -H8.
-  subst Δ2.
-  rewrite (envs_snoc_sound Δ1 false nam (▷P)) /=. 2: eassumption.
-  rewrite comm.
-  rewrite assoc.
-  rewrite uPred.wand_elim_l.
-  rewrite (envs_snoc_sound (envs_snoc Δ1 false nam (▷ P)) false nam_cl (▷ P ={E1 ∖ ↑N,E1}=∗ True)) //;
-          last first.
-  { rewrite (envs_lookup_snoc_ne Δ1); eassumption. }
-  rewrite uPred.wand_elim_l.
-  done.
-Qed.
-
-Tactic Notation "rel_load_l" "under" constr(N) "as" constr(nam) constr(nam_cl) :=
-  iStartProof;
-  eapply (tac_rel_load_l nam nam_cl);
-    [solve_ndisj || fail "rel_load_l: cannot prove 'nclose " N " ⊆ ?'"
-    |iAssumptionCore || fail "rel_load_l: cannot find inv " N " ?" 
-    |try fast_done (* E2 = E1 \ ↑N *)
-    |tac_bind_helper (* e = fill K' .. *)
-    |try fast_done (* nam fresh *)
-    |try fast_done (* nam_cl fresh *)
-    |eauto (* nam =/= nam_cl *)
-    |env_cbv; reflexivity || fail "rel_load_l: this should not happen"
-    |(* new goal *)].
+Tactic Notation "rel_load_l_atomic" := rel_apply_l bin_log_related_load_l.
 
 Lemma tac_rel_load_l_simp `{logrelG Σ} Δ1 Δ2 E1 i1 l v K' Γ e t Δ' τ :
   e = fill K' (Load (Loc l)) →
@@ -341,58 +269,7 @@ Tactic Notation "rel_load_l" :=
     |iAssumptionCore || fail 3 "rel_load_l: cannot find ? ↦ᵢ ?"
     | (* new goal *)].
 
-Lemma tac_rel_store_l `{logrelG Σ} nam nam_cl Δ1 Δ2 E1 E2 p i1 N P l e' v' K' Γ e t Δ' τ :
-  nclose N ⊆ E1 →
-  envs_lookup i1 Δ1 = Some (p, inv N P) →
-  E2 = E1 ∖ ↑N →
-  e = fill K' (Store (Loc l) e') →
-  to_val e' = Some v' →
-  envs_lookup nam Δ1 = None →
-  envs_lookup nam_cl Δ1 = None →
-  nam_cl ≠ nam →
-  Δ2 = envs_snoc (envs_snoc Δ1 false nam (▷ P)%I) false nam_cl (▷ P ={E1 ∖ ↑N,E1}=∗ True)%I →
-  (Δ2 ⊢ |={E2}=> ∃ v, ▷ (l ↦ᵢ v) ∗
-     ▷(l ↦ᵢ v' -∗ bin_log_related E2 E1 Δ' Γ (fill K' (Lit Unit)) t τ)) →
-  (Δ1 ⊢ bin_log_related E1 E1 Δ' Γ e t τ).
-Proof.
-  intros ??????????.
-  rewrite -(idemp uPred_and Δ1).
-  rewrite {1}envs_lookup_sound'. 2: eassumption.
-  rewrite uPred.sep_elim_l uPred.always_and_sep_l.
-  rewrite inv_open. 2: eassumption.
-  subst e.
-  rewrite -(bin_log_related_store_l Δ' Γ E1 E2). 2: eassumption.
-  rewrite fupd_frame_r.
-  rewrite -(fupd_trans E1 E2 E2).
-  subst E2.
-  apply fupd_mono.  
-  rewrite -H9.
-  subst Δ2.
-  rewrite (envs_snoc_sound Δ1 false nam (▷P)) /=. 2: eassumption.
-  rewrite comm.
-  rewrite assoc.
-  rewrite uPred.wand_elim_l.
-  rewrite (envs_snoc_sound (envs_snoc Δ1 false nam (▷ P)) false nam_cl (▷ P ={E1 ∖ ↑N,E1}=∗ True)) //;
-          last first.
-  { rewrite (envs_lookup_snoc_ne Δ1); eassumption. }
-  rewrite uPred.wand_elim_l.
-  done.
-Qed.
-
-Tactic Notation "rel_store_l" "under" constr(N) "as" constr(nam) constr(nam_cl) :=
-  iStartProof;
-  eapply (tac_rel_store_l nam nam_cl);
-    [solve_ndisj || fail "rel_store_l: cannot prove 'nclose " N " ⊆ ?'"
-    |iAssumptionCore || fail "rel_store_l: cannot find inv " N " ?" 
-    |try fast_done (* E2 = E1 \ ↑N *)
-    |tac_bind_helper (* e = fill K' (Store (Loc l) e') *)
-    |solve_to_val (* to_val e' = Some v *)
-    |try fast_done (* nam fresh *)
-    |try fast_done (* nam_cl fresh *)
-    |eauto (* nam =/= nam_cl *)
-    |env_cbv; reflexivity || fail "rel_store_l: this should not happen"
-    |(* new goal *)].
-
+Tactic Notation "rel_store_l_atomic" := rel_apply_l bin_log_related_store_l.
 
 Lemma tac_rel_store_l_simp `{logrelG Σ} Δ1 Δ2 i1 E1 l v e' v' K' Γ e t Δ' τ :
   e = fill K' (Store (Loc l) e') →
@@ -421,67 +298,7 @@ Tactic Notation "rel_store_l" :=
     |env_cbv; reflexivity || fail "rel_store_l: this should not happen"
     | (* new goal *)].
 
-Lemma tac_rel_cas_l `{logrelG Σ} nam nam_cl Δ1 Δ2 E1 E2 p i1 N P l e1 e2 v1 v2 K' Γ e t Δ' τ :
-  nclose N ⊆ E1 →
-  envs_lookup i1 Δ1 = Some (p, inv N P) →
-  E2 = E1 ∖ ↑N →
-  e = fill K' (CAS (Loc l) e1 e2) →
-  to_val e1 = Some v1 →
-  to_val e2 = Some v2 →
-  envs_lookup nam Δ1 = None →
-  envs_lookup nam_cl Δ1 = None →
-  nam_cl ≠ nam →
-  Δ2 = envs_snoc (envs_snoc Δ1 false nam (▷ P)%I) false nam_cl (▷ P ={E1 ∖ ↑N,E1}=∗ True)%I →
-  (Δ2 ⊢ |={E2}=> ∃ v, ▷ (l ↦ᵢ v) ∗
-     ((⌜v ≠ v1⌝ ∗ ▷ (l ↦ᵢ v  -∗ {E2,E1;Δ';Γ} ⊨ fill K' (#♭ false) ≤log≤ t : τ)) ∨
-      (⌜v = v1⌝ ∗ ▷ (l ↦ᵢ v2 -∗ {E2,E1;Δ';Γ} ⊨ fill K' (#♭ true) ≤log≤ t : τ)))) →
-  (Δ1 ⊢ bin_log_related E1 E1 Δ' Γ e t τ).
-Proof.
-  intros ???????????.
-  rewrite -(idemp uPred_and Δ1).
-  rewrite {1}envs_lookup_sound'. 2: eassumption.
-  rewrite uPred.sep_elim_l uPred.always_and_sep_l.
-  rewrite inv_open. 2: eassumption.
-  subst e.
-  rewrite -(bin_log_related_cas_l Δ' Γ E1 E2); try eassumption.
-  rewrite fupd_frame_r.
-  rewrite -(fupd_trans E1 E2 E2).
-  subst E2.
-  apply fupd_mono.  
-  subst Δ2.
-  rewrite (envs_snoc_sound Δ1 false nam (▷P)) /=. 2: eassumption.
-  rewrite comm.
-  rewrite assoc.
-  rewrite uPred.wand_elim_l.
-  rewrite (envs_snoc_sound (envs_snoc Δ1 false nam (▷ P)) false nam_cl (▷ P ={E1 ∖ ↑N,E1}=∗ True)) //;
-          last first.
-  { rewrite (envs_lookup_snoc_ne Δ1); eassumption. }
-  rewrite H10.
-  rewrite uPred.wand_elim_l.
-  apply fupd_mono.
-  iDestruct 1 as (v) "[Hl Hv]". iExists v. iFrame "Hl".
-  iDestruct "Hv" as "[[% Hv] | [% Hv]]"; subst.
-  - iSplitL; last first; iIntros "%". by exfalso.
-    done.
-  - iSplitR; iIntros "%". by exfalso.
-    done.
-Qed.
-
-Tactic Notation "rel_cas_l" "under" constr(N) "as" constr(nam) constr(nam_cl) :=
-  iStartProof;
-  eapply (tac_rel_cas_l nam nam_cl);
-    [solve_ndisj || fail "rel_store_l: cannot prove 'nclose " N " ⊆ ?'"
-    |iAssumptionCore || fail "rel_store_l: cannot find inv " N " ?" 
-    |try fast_done (* E2 = E1 \ ↑N *)
-    |tac_bind_helper (* e = fill K' ... *)
-    |solve_to_val (* to_val e1 = Some .. *)
-    |solve_to_val (* to_val e2 = Some .. *)
-    |try fast_done (* nam fresh *)
-    |try fast_done (* nam_cl fresh *)
-    |eauto (* nam =/= nam_cl *)
-    |env_cbv; reflexivity || fail "rel_store_l: this should not happen"
-    |(* new goal *)].
-
+Tactic Notation "rel_cas_l_atomic" := rel_apply_l bin_log_related_cas_l.
 
 (********************************)
 
@@ -663,9 +480,9 @@ Section test.
 
   Definition storeFalse : val := λ: "y", "y" <- #♭ false.
 
-  Lemma test_store Γ y y':
+  Lemma test_store Γ Δ y y':
     inv choiceN (choice_inv y y')
-    -∗ Γ ⊨ (storeFalse (Fst (#y, 3))) ≤log≤ (storeFalse #y') : TUnit.
+    -∗ {⊤,⊤;Δ;Γ} ⊨ (storeFalse (Fst (#y, 3))) ≤log≤ (storeFalse #y') : TUnit.
   Proof.
     iIntros "#Hinv".
     unfold storeFalse. unlock.
@@ -673,15 +490,17 @@ Section test.
     rel_rec_l.
     rel_rec_r.
 
-    rel_store_l under choiceN as "Hs" "Hcl".
-      iDestruct "Hs" as (f) "[>Hy >Hy']". iExists _. iFrame "Hy".
-      iModIntro. iNext. iIntros "Hy".
-      rel_store_r. simpl.
+    rel_apply_l bin_log_related_store_l.
+    iInv choiceN as (f) ">[Hy Hy']" "Hcl".
+    iExists _. iFrame "Hy".
+    iModIntro. iNext. iIntros "Hy".
+    rel_store_r. simpl.
 
     iMod ("Hcl" with "[Hy Hy']").
     { iNext. iExists _. iFrame. }
 
-    iApply bin_log_related_val; eauto.
+
+    rel_vals; eauto.
   Qed.
 
 End test.