Put the quantification over Δ in the definition bin_log_related.

F_mu_ref_par/context_refinement.v

@@ -194,16 +194,12 @@ Notation "Γ ⊨ e '≤ctx≤' e' : τ" :=
 
 Section bin_log_related_under_typed_ctx.
   Context `{heapIG Σ, cfgSG Σ}.
-  Notation D := (prodC valC valC -n> iPropG lang Σ).
-  Implicit Types Δ : listC D.
 
   Lemma bin_log_related_under_typed_ctx Γ e e' τ Γ' τ' K :
     (∀ f, e.[base.iter (length Γ) up f] = e) →
     (∀ f, e'.[base.iter (length Γ) up f] = e') →
     typed_ctx K Γ τ Γ' τ' →
-    (∀ Δ (HΔ : env_PersistentP Δ), Δ ∥ Γ ⊨ e ≤log≤ e' : τ) →
-    ∀ Δ (HΔ : env_PersistentP Δ),
-      Δ ∥ Γ' ⊨ fill_ctx K e ≤log≤ fill_ctx K e' : τ'.
+    Γ ⊨ e ≤log≤ e' : τ → Γ' ⊨ fill_ctx K e ≤log≤ fill_ctx K e' : τ'.
   Proof.
     revert Γ τ Γ' τ' e e'.
     induction K as [|k K]=> Γ τ Γ' τ' e e' H1 H2; simpl.

F_mu_ref_par/examples/counter.v

@@ -253,10 +253,10 @@ Section CG_Counter.
 
   Definition counterN : namespace := nroot .@ "counter".
 
-  Lemma FG_CG_counter_refinement Δ {HΔ : env_PersistentP Δ} :
-    Δ ∥ [] ⊨ FG_counter ≤log≤ CG_counter : TProd (TArrow TUnit TUnit) (TArrow TUnit TNat).
+  Lemma FG_CG_counter_refinement :
+    [] ⊨ FG_counter ≤log≤ CG_counter : TProd (TArrow TUnit TUnit) (TArrow TUnit TNat).
   Proof.
-    iIntros { [|??] ρ} "#(Hheap & Hspec & HΓ)"; iIntros {j K} "Hj"; last first.
+    iIntros { Δ [|??] ρ ? } "#(Hheap & Hspec & HΓ)"; iIntros {j K} "Hj"; last first.
     { iDestruct (interp_env_length with "HΓ") as %[=]. }
     iClear "HΓ". cbn -[FG_counter CG_counter].
     rewrite ?empty_env_subst /CG_counter /FG_counter.

F_mu_ref_par/examples/stack/refinement.v

@@ -12,14 +12,14 @@ Section Stack_refinement.
   Notation D := (prodC valC valC -n> iPropG lang Σ).
   Implicit Types Δ : listC D.
 
-  Lemma FG_CG_counter_refinement Δ {HΔ : env_PersistentP Δ} :
-    Δ ∥ [] ⊨ FG_stack ≤log≤ CG_stack : TForall (TProd (TProd
-        (TArrow (TVar 0) TUnit)
-        (TArrow TUnit (TSum TUnit (TVar 0))))
-        (TArrow (TArrow (TVar 0) TUnit) TUnit)).
+  Lemma FG_CG_counter_refinement :
+    [] ⊨ FG_stack ≤log≤ CG_stack : TForall (TProd (TProd
+           (TArrow (TVar 0) TUnit)
+           (TArrow TUnit (TSum TUnit (TVar 0))))
+           (TArrow (TArrow (TVar 0) TUnit) TUnit)).
   Proof.
     (* executing the preambles *)
-    iIntros { [|??] ρ} "#(Hheap & Hspec & HΓ)"; iIntros {j K} "Hj"; last first.
+    iIntros { Δ [|??] ρ ? } "#(Hheap & Hspec & HΓ)"; iIntros {j K} "Hj"; last first.
     { iDestruct (interp_env_length with "HΓ") as %[=]. } 
     iClear "HΓ". cbn -[FG_stack CG_stack].
     rewrite ?empty_env_subst /CG_stack /FG_stack.
@@ -378,5 +378,5 @@ Proof.
   eapply (@binary_soundness Σ);
     eauto using FG_stack_closed, CG_stack_closed.
   all: try typeclasses eauto.
-  intros. apply FG_CG_counter_refinement, _.
+  intros. apply FG_CG_counter_refinement.
 Qed.

F_mu_ref_par/soundness_binary.v

@@ -12,7 +12,7 @@ Section soundness.
   Local Opaque to_heap.
 
   Lemma wp_basic_soundness e e' τ :
-    (∀ `{heapIG Σ, cfgSG Σ} Δ (HΔ : env_PersistentP Δ), Δ ∥ [] ⊨ e ≤log≤ e' : τ) →
+    (∀ `{heapIG Σ, cfgSG Σ}, [] ⊨ e ≤log≤ e' : τ) →
     ownP (Σ:=globalF Σ) ∅
     ⊢ WP e {{ _, ■ ∃ thp' h v, rtc step ([e'], ∅) (# v :: thp', h) }}.
   Proof.
@@ -30,7 +30,8 @@ Section soundness.
       iPureIntro. rewrite from_to_cfg; constructor. }
     iPvs (inv_alloc specN with "[Hinv]") as "#Hcfg"; trivial.
     { iNext. iExact "Hinv". }
-    iPoseProof (bin_log_related_alt (H1 h (@CFGSG _ _ γ) [] _) [] _ 0 [] with "[Hcfg2]") as "HBR".
+    iPoseProof (bin_log_related_alt (H1 h (@CFGSG _ _ γ)) [] [] _ 0 [] with "[Hcfg2]") as "HBR".
+    { apply _. }
     { rewrite /spec_ctx /auth_ctx /tpool_mapsto /auth_own empty_env_subst /=.
       iFrame "Hheap Hcfg Hcfg2". by rewrite -interp_env_nil. }
     rewrite /= empty_env_subst.
@@ -60,29 +61,21 @@ Section soundness.
   Qed.
 
   Lemma basic_soundness e e' τ v thp hp :
-    (∀ `{heapIG Σ, cfgSG Σ} Δ (HΔ : env_PersistentP Δ), Δ ∥ [] ⊨ e ≤log≤ e' : τ) →
+    (∀ `{heapIG Σ, cfgSG Σ}, [] ⊨ e ≤log≤ e' : τ) →
     rtc step ([e], ∅) (# v :: thp, hp) →
     (∃ thp' hp' v', rtc step ([e'], ∅) (# v' :: thp', hp')).
   Proof.
-    intros H1 H2.
-    match goal with
-      |- ?A =>
-      eapply (@wp_adequacy_result lang _ ⊤ (λ _, A) e v thp ∅ ∅ hp); eauto
-    end.
-    - apply ucmra_unit_valid.
-    - iIntros "[Hp Hg]".
-      iApply wp_wand_l; iSplitR; [| iApply wp_basic_soundness]; auto.
-      by iIntros {w} "H".
+    intros. eapply wp_adequacy_result; eauto using ucmra_unit_valid.
+    iIntros "[??]". by iApply wp_basic_soundness.
   Qed.
 
   Lemma binary_soundness Γ e e' τ :
     (∀ f, e.[base.iter (length Γ) up f] = e) →
     (∀ f, e'.[base.iter (length Γ) up f] = e') →
-    (∀ `{heapIG Σ, cfgSG Σ} Δ (HΔ : env_PersistentP Δ), Δ ∥ Γ ⊨ e ≤log≤ e' : τ) →
+    (∀ `{heapIG Σ, cfgSG Σ}, Γ ⊨ e ≤log≤ e' : τ) →
     Γ ⊨ e ≤ctx≤ e' : τ.
   Proof.
-    intros H1 K HK htp hp v Hstp Hc Hc'.
-    eapply basic_soundness; eauto.
+    intros H1 K HK htp hp v Hstp Hc Hc'; eapply basic_soundness; eauto.
     intros H' H'' N Δ HΔ.
     eapply (bin_log_related_under_typed_ctx _ _ _ _ []); eauto.
   Qed.