Simplify the notation for the relational judements

{E,E;Δ,Γ} ⊨ ... => {E;Δ,Γ} ⊨ ...
{⊤,⊤;Δ,Γ} ⊨ ... => {Δ,Γ} ⊨ ...

theories/examples/bit.v

@@ -121,8 +121,8 @@ Section heapify_refinement.
 
   Lemma heapify_refinement_ez Γ E1 b1 b2 :
     ↑logrelN ⊆ E1 →
-    {E1,E1;Δ;Γ} ⊨ b1 ≤log≤ b2 : bitτ -∗
-    {E1,E1;Δ;Γ} ⊨ heapify b1 ≤log≤ heapify b2 : bitτ.
+    {E1;Δ;Γ} ⊨ b1 ≤log≤ b2 : bitτ -∗
+    {E1;Δ;Γ} ⊨ heapify b1 ≤log≤ heapify b2 : bitτ.
   Proof.
     iIntros (?) "Hb1b2".
     iApply bin_log_related_app; eauto.

theories/examples/counter.v

@@ -77,8 +77,8 @@ Section CG_Counter.
 
   Lemma bin_log_FG_increment_l Γ K E x (n : nat) t τ :
     x ↦ᵢ #n -∗
-    (x ↦ᵢ # (S n) -∗ {E,E;Δ;Γ} ⊨ fill K #() ≤log≤ t : τ) -∗
-    {E,E;Δ;Γ} ⊨ fill K (FG_increment #x #()) ≤log≤ t : τ.
+    (x ↦ᵢ # (S n) -∗ {E;Δ;Γ} ⊨ fill K #() ≤log≤ t : τ) -∗
+    {E;Δ;Γ} ⊨ fill K (FG_increment #x #()) ≤log≤ t : τ.
   Proof.
     iIntros "Hx Hlog".
     iApply bin_log_related_wp_l.
@@ -146,7 +146,7 @@ Section CG_Counter.
        ((∃ n : nat, x ↦ᵢ #n ∗ R n) ={E2,E1}=∗ True) ∧
         (∀ m, x ↦ᵢ # (S m) ∗ R m -∗ P -∗
             {E2,E1;Δ;Γ} ⊨ fill K #() ≤log≤ t : τ))
-    -∗ ({E1,E1;Δ;Γ} ⊨ fill K ((FG_increment $/ LitV (Loc x)) #()) ≤log≤ t : τ).
+    -∗ ({E1;Δ;Γ} ⊨ fill K ((FG_increment $/ LitV (Loc x)) #()) ≤log≤ t : τ).
   Proof.
     iIntros "HP #H".
     iLöb as "IH".
@@ -189,7 +189,7 @@ Section CG_Counter.
        ((∃ n : nat, x ↦ᵢ #n ∗ R n) ={E2,E1}=∗ True) ∧
         (∀ m : nat, x ↦ᵢ #m ∗ R m -∗
             {E2,E1;Δ;Γ} ⊨ fill K #m ≤log≤ t : τ))
-    -∗ {E1,E1;Δ;Γ} ⊨ fill K ((counter_read $/ LitV (Loc x)) #()) ≤log≤ t : τ.
+    -∗ {E1;Δ;Γ} ⊨ fill K ((counter_read $/ LitV (Loc x)) #()) ≤log≤ t : τ.
   Proof.
     iIntros "#H".
     unfold counter_read. unlock. simpl.
@@ -205,7 +205,7 @@ Section CG_Counter.
   (* TODO: try to use with_lock rules *)
   Lemma FG_CG_increment_refinement l cnt cnt' Γ :
     inv counterN (counter_inv l cnt cnt') -∗
-    {⊤,⊤;Δ;Γ} ⊨ FG_increment $/ LitV (Loc cnt) ≤log≤ CG_increment $/ LitV (Loc cnt') $/ LitV (Loc l) : TArrow TUnit TUnit.
+    {Δ;Γ} ⊨ FG_increment $/ LitV (Loc cnt) ≤log≤ CG_increment $/ LitV (Loc cnt') $/ LitV (Loc l) : TArrow TUnit TUnit.
   Proof.
     iIntros "#Hinv".
     iApply bin_log_related_arrow_val.
@@ -236,7 +236,7 @@ Section CG_Counter.
 
   Lemma counter_read_refinement l cnt cnt' Γ :
     inv counterN (counter_inv l cnt cnt') -∗
-    {⊤,⊤;Δ;Γ} ⊨ counter_read $/ LitV (Loc cnt) ≤log≤ counter_read $/ LitV (Loc cnt') : TArrow TUnit TNat.
+    {Δ;Γ} ⊨ counter_read $/ LitV (Loc cnt) ≤log≤ counter_read $/ LitV (Loc cnt') : TArrow TUnit TNat.
   Proof.
     iIntros "#Hinv".
     iApply bin_log_related_arrow_val.
@@ -262,7 +262,7 @@ Section CG_Counter.
   Qed.
 
   Lemma FG_CG_counter_refinement :
-    {⊤,⊤;Δ;∅} ⊨ FG_counter ≤log≤ CG_counter :
+    {Δ;∅} ⊨ FG_counter ≤log≤ CG_counter :
           TArrow TUnit (TProd (TArrow TUnit TUnit) (TArrow TUnit TNat)).
   Proof.
     unfold FG_counter, CG_counter.

theories/examples/lateearlychoice.v

@@ -38,8 +38,8 @@ Section Refinement.
 
   Lemma rand_l Δ Γ E1 K ρ t τ :
     ↑choiceN ⊆ E1 →
-    spec_ctx ρ -∗ (∀ b : bool, {E1,E1;Δ;Γ} ⊨ fill K #b ≤log≤ t : τ) -∗
-    {E1,E1;Δ;Γ} ⊨ fill K (rand #()) ≤log≤ t : τ.
+    spec_ctx ρ -∗ (∀ b : bool, {E1;Δ;Γ} ⊨ fill K #b ≤log≤ t : τ) -∗
+    {E1;Δ;Γ} ⊨ fill K (rand #()) ≤log≤ t : τ.
   Proof.
     iIntros (?) "#Hs Hlog".
     unfold rand. unlock. simpl.

theories/examples/lock.v

@@ -72,8 +72,8 @@ Section lockG_rules.
   Lemma bin_log_related_newlock_l (R : iProp Σ) Δ Γ E K t τ :
     R -∗
     ▷(∀ (lk : loc) γ, is_lock γ #lk R
-      -∗ ({E,E;Δ;Γ} ⊨ fill K #lk ≤log≤ t: τ)) -∗
-    {E,E;Δ;Γ} ⊨ fill K (newlock #()) ≤log≤ t: τ.
+      -∗ ({E;Δ;Γ} ⊨ fill K #lk ≤log≤ t: τ)) -∗
+    {E;Δ;Γ} ⊨ fill K (newlock #()) ≤log≤ t: τ.
   Proof.
     iIntros "HR Hlog".
     iApply bin_log_related_wp_l.
@@ -90,8 +90,8 @@ Section lockG_rules.
     is_lock γ #lk R -∗
     locked γ -∗
     R -∗
-    ▷({E,E;Δ;Γ} ⊨ fill K #() ≤log≤ t: τ) -∗
-    {E,E;Δ;Γ} ⊨ fill K (release #lk) ≤log≤ t: τ.
+    ▷({E;Δ;Γ} ⊨ fill K #() ≤log≤ t: τ) -∗
+    {E;Δ;Γ} ⊨ fill K (release #lk) ≤log≤ t: τ.
   Proof.
     iIntros (?) "Hlock Hlocked HR Hlog".
     iDestruct "Hlock" as (l) "[% #?]"; simplify_eq.
@@ -109,8 +109,8 @@ Section lockG_rules.
   Lemma bin_log_related_acquire_l (R : iProp Σ) (lk : loc) γ Δ Γ E K t τ :
     ↑N ⊆ E →
     is_lock γ #lk R -∗
-    ▷(locked γ -∗ R -∗ {E,E;Δ;Γ} ⊨ fill K #() ≤log≤ t: τ) -∗
-    {E,E;Δ;Γ} ⊨ fill K (acquire #lk) ≤log≤ t: τ.
+    ▷(locked γ -∗ R -∗ {E;Δ;Γ} ⊨ fill K #() ≤log≤ t: τ) -∗
+    {E;Δ;Γ} ⊨ fill K (acquire #lk) ≤log≤ t: τ.
   Proof.
     iIntros (?) "#Hlock Hlog".
     iLöb as "IH".
@@ -167,8 +167,8 @@ Section lock_rules_r.
   Qed.
 
   Lemma bin_log_related_newlock_l_simp Γ K t τ :
-    (∀ l : loc, l ↦ᵢ #false -∗ {E1,E1;Δ;Γ} ⊨ fill K #l ≤log≤ t : τ) -∗
-    {E1,E1;Δ;Γ} ⊨ fill K (newlock #()) ≤log≤ t : τ.
+    (∀ l : loc, l ↦ᵢ #false -∗ {E1;Δ;Γ} ⊨ fill K #l ≤log≤ t : τ) -∗
+    {E1;Δ;Γ} ⊨ fill K (newlock #()) ≤log≤ t : τ.
   Proof.
     iIntros "Hlog".
     unfold newlock. unlock.
@@ -209,8 +209,8 @@ Section lock_rules_r.
 
   Lemma bin_log_related_acquire_suc_l Γ K l t τ :
     l ↦ᵢ #false -∗
-    (l ↦ᵢ #true -∗ {E1,E1;Δ;Γ} ⊨ fill K (#()) ≤log≤ t : τ) -∗
-    {E1,E1;Δ;Γ} ⊨ fill K (acquire #l) ≤log≤ t : τ.
+    (l ↦ᵢ #true -∗ {E1;Δ;Γ} ⊨ fill K (#()) ≤log≤ t : τ) -∗
+    {E1;Δ;Γ} ⊨ fill K (acquire #l) ≤log≤ t : τ.
   Proof.
     iIntros "Hl Hlog".
     unfold acquire. unlock.
@@ -226,8 +226,8 @@ Section lock_rules_r.
 
   Lemma bin_log_related_acquire_fail_l Γ K l t τ :
     l ↦ᵢ #true -∗
-    (l ↦ᵢ #false -∗ {E1,E1;Δ;Γ} ⊨ fill K (acquire #l) ≤log≤ t : τ) -∗
-    {E1,E1;Δ;Γ} ⊨ fill K (acquire #l) ≤log≤ t : τ.
+    (l ↦ᵢ #false -∗ {E1;Δ;Γ} ⊨ fill K (acquire #l) ≤log≤ t : τ) -∗
+    {E1;Δ;Γ} ⊨ fill K (acquire #l) ≤log≤ t : τ.
   Proof.
     iIntros "Hl Hlog".
     iLöb as "IH".

theories/examples/or.v

@@ -36,9 +36,9 @@ Section contents.
 
   Lemma bin_log_related_or Δ Γ E e1 e2 e1' e2' :
     ↑logrelN ⊆ E →
-    {E,E;Δ;Γ} ⊨ e1 ≤log≤ e1' : TArrow TUnit TUnit -∗
-    {E,E;Δ;Γ} ⊨ e2 ≤log≤ e2' : TArrow TUnit TUnit -∗
-    {E,E;Δ;Γ} ⊨ or e1 e2 ≤log≤ or e1' e2' : TUnit.
+    {E;Δ;Γ} ⊨ e1 ≤log≤ e1' : TArrow TUnit TUnit -∗
+    {E;Δ;Γ} ⊨ e2 ≤log≤ e2' : TArrow TUnit TUnit -∗
+    {E;Δ;Γ} ⊨ or e1 e2 ≤log≤ or e1' e2' : TUnit.
   Proof.
     iIntros (?) "He1 He2".
     iApply (bin_log_related_app with "[He1] He2").
@@ -48,8 +48,8 @@ Section contents.
 
   Lemma bin_log_or_choice_1_r_val Δ Γ E (v1 v1' v2 : val) :
     ↑logrelN ⊆ E →
-    {E,E;Δ;Γ} ⊨ v1 ≤log≤ v1' : TArrow TUnit TUnit -∗
-    {E,E;Δ;Γ} ⊨ v1 #() ≤log≤ or v1' v2 : TUnit.
+    {E;Δ;Γ} ⊨ v1 ≤log≤ v1' : TArrow TUnit TUnit -∗
+    {E;Δ;Γ} ⊨ v1 #() ≤log≤ or v1' v2 : TUnit.
   Proof.
     iIntros (?) "Hlog".
     unlock or. repeat rel_rec_r.
@@ -64,7 +64,7 @@ Section contents.
   Lemma bin_log_or_choice_1_r_val_typed Δ Γ E (v1 v2 : val) :
     ↑logrelN ⊆ E →
     Γ ⊢ₜ v1 : TArrow TUnit TUnit →
-    {E,E;Δ;Γ} ⊨ v1 #() ≤log≤ or v1 v2 : TUnit.
+    {E;Δ;Γ} ⊨ v1 #() ≤log≤ or v1 v2 : TUnit.
   Proof.
     iIntros (??).
     iApply bin_log_or_choice_1_r_val; eauto.
@@ -73,8 +73,8 @@ Section contents.
 
   Lemma bin_log_or_choice_1_r Δ Γ E (e1 e1' : expr) (v2 : val) :
     ↑logrelN ⊆ E →
-    {E,E;Δ;Γ} ⊨ e1 ≤log≤ e1' : TArrow TUnit TUnit -∗
-    {E,E;Δ;Γ} ⊨ e1 #() ≤log≤ or e1' v2 : TUnit.
+    {E;Δ;Γ} ⊨ e1 ≤log≤ e1' : TArrow TUnit TUnit -∗
+    {E;Δ;Γ} ⊨ e1 #() ≤log≤ or e1' v2 : TUnit.
   Proof.
     iIntros (?) "Hlog".
     rel_bind_l e1.
@@ -90,7 +90,7 @@ Section contents.
     ↑logrelN ⊆ E →
     Closed ∅ e1 →
     Γ ⊢ₜ e1 : TUnit →
-    {E,E;Δ;Γ} ⊨ e1 ≤log≤ or (λ: <>, e1) v2 : TUnit.
+    {E;Δ;Γ} ⊨ e1 ≤log≤ or (λ: <>, e1) v2 : TUnit.
   Proof.
     iIntros (???).
     unlock or. repeat rel_rec_r.
@@ -118,9 +118,9 @@ Section contents.
   Lemma bin_log_or_commute Δ Γ E (v1 v1' v2 v2' : val) :
     ↑orN ⊆ E →
     ↑logrelN ⊆ E →
-    {E,E;Δ;Γ} ⊨ v1 ≤log≤ v1' : TArrow TUnit TUnit -∗
-    {E,E;Δ;Γ} ⊨ v2 ≤log≤ v2' : TArrow TUnit TUnit -∗
-    {E,E;Δ;Γ} ⊨ or v2 v1 ≤log≤ or v1' v2' : TUnit.
+    {E;Δ;Γ} ⊨ v1 ≤log≤ v1' : TArrow TUnit TUnit -∗
+    {E;Δ;Γ} ⊨ v2 ≤log≤ v2' : TArrow TUnit TUnit -∗
+    {E;Δ;Γ} ⊨ or v2 v1 ≤log≤ or v1' v2' : TUnit.
   Proof.
     iIntros (??) "Hv1 Hv2".
     unlock or. repeat rel_rec_r. repeat rel_rec_l.
@@ -155,8 +155,8 @@ Section contents.
 
   Lemma bin_log_or_idem_r Δ Γ E (v v' : val) :
     ↑logrelN ⊆ E →
-    {E,E;Δ;Γ} ⊨ v ≤log≤ v' : TArrow TUnit TUnit -∗
-    {E,E;Δ;Γ} ⊨ v #() ≤log≤ or v' v' : TUnit.
+    {E;Δ;Γ} ⊨ v ≤log≤ v' : TArrow TUnit TUnit -∗
+    {E;Δ;Γ} ⊨ v #() ≤log≤ or v' v' : TUnit.
   Proof.
     iIntros (?) "Hlog".
     by iApply bin_log_or_choice_1_r_val.
@@ -166,7 +166,7 @@ Section contents.
     Closed ∅ e →
     ↑logrelN ⊆ E →
     Γ ⊢ₜ e : TUnit →
-    {E,E;Δ;Γ} ⊨ e ≤log≤ or (λ: <>, e) (λ: <>, e) : TUnit.
+    {E;Δ;Γ} ⊨ e ≤log≤ or (λ: <>, e) (λ: <>, e) : TUnit.
   Proof.
     iIntros (???).
     iPoseProof (bin_log_or_choice_1_r_body Δ _ _ e (λ: <>, e)) as "HZ"; eauto.
@@ -176,8 +176,8 @@ Section contents.
   Lemma bin_log_or_idem_l Δ Γ E (v v' : val) :
     ↑orN ⊆ E →
     ↑logrelN ⊆ E →
-    {E,E;Δ;Γ} ⊨ v ≤log≤ v' : TArrow TUnit TUnit -∗
-    {E,E;Δ;Γ} ⊨ or v v ≤log≤ v' #() : TUnit.
+    {E;Δ;Γ} ⊨ v ≤log≤ v' : TArrow TUnit TUnit -∗
+    {E;Δ;Γ} ⊨ or v v ≤log≤ v' #() : TUnit.
   Proof.
     iIntros (??) "Hlog".
     unlock or. repeat rel_rec_l.
@@ -203,8 +203,8 @@ Section contents.
   Lemma bin_log_or_bot_l Δ Γ E (v v' : val) :
     ↑orN ⊆ E →
     ↑logrelN ⊆ E →
-    {E,E;Δ;Γ} ⊨ v ≤log≤ v' : TArrow TUnit TUnit -∗
-    {E,E;Δ;Γ} ⊨ or v bot ≤log≤ v' #() : TUnit.
+    {E;Δ;Γ} ⊨ v ≤log≤ v' : TArrow TUnit TUnit -∗
+    {E;Δ;Γ} ⊨ or v bot ≤log≤ v' #() : TUnit.
   Proof.
     iIntros (??) "Hlog".
     unlock or. repeat rel_rec_l.
@@ -228,8 +228,8 @@ Section contents.
 
   Lemma bin_log_or_bot_r Δ Γ E (v v' : val) :
     ↑logrelN ⊆ E →
-    {E,E;Δ;Γ} ⊨ v ≤log≤ v' : TArrow TUnit TUnit -∗
-    {E,E;Δ;Γ} ⊨ v #() ≤log≤ or v' bot : TUnit.
+    {E;Δ;Γ} ⊨ v ≤log≤ v' : TArrow TUnit TUnit -∗
+    {E;Δ;Γ} ⊨ v #() ≤log≤ or v' bot : TUnit.
   Proof.
     iIntros (?) "Hlog".
     iApply bin_log_or_choice_1_r_val; eauto.
@@ -238,10 +238,10 @@ Section contents.
   Lemma bin_log_or_assoc1 Δ Γ E (v1 v1' v2 v2' v3 v3' : val) :
     ↑orN ⊆ E →
     ↑logrelN ⊆ E →
-    {E,E;Δ;Γ} ⊨ v1 ≤log≤ v1' : TArrow TUnit TUnit -∗
-    {E,E;Δ;Γ} ⊨ v2 ≤log≤ v2' : TArrow TUnit TUnit -∗
-    {E,E;Δ;Γ} ⊨ v3 ≤log≤ v3' : TArrow TUnit TUnit -∗
-    {E,E;Δ;Γ} ⊨ or v1 (λ: <>, or v2 v3) ≤log≤ or (λ: <>, or v1' v2') v3' : TUnit.
+    {E;Δ;Γ} ⊨ v1 ≤log≤ v1' : TArrow TUnit TUnit -∗
+    {E;Δ;Γ} ⊨ v2 ≤log≤ v2' : TArrow TUnit TUnit -∗
+    {E;Δ;Γ} ⊨ v3 ≤log≤ v3' : TArrow TUnit TUnit -∗
+    {E;Δ;Γ} ⊨ or v1 (λ: <>, or v2 v3) ≤log≤ or (λ: <>, or v1' v2') v3' : TUnit.
   Proof.
     iIntros (??) "Hv1 Hv2 Hv3".
     unlock or. simpl.
@@ -304,7 +304,7 @@ Section contents.
     Closed {["x"]} e →
     ↑logrelN ⊆ E →
     Γ ⊢ₜ subst "x" v e : τ →
-    {E,E;Δ;Γ} ⊨ let: "x" := v in e ≤log≤ subst "x" v e : τ.
+    {E;Δ;Γ} ⊨ let: "x" := v in e ≤log≤ subst "x" v e : τ.
   Proof.
     iIntros (?? Hτ).
     assert (Closed ∅ (Rec BAnon "x" e)).
@@ -317,7 +317,7 @@ Section contents.
     Closed {["x"]} e →
     ↑logrelN ⊆ E →
     Γ ⊢ₜ subst "x" v e : τ →
-    {E,E;Δ;Γ} ⊨ subst "x" v e ≤log≤ (let: "x" := v in e) : τ.
+    {E;Δ;Γ} ⊨ subst "x" v e ≤log≤ (let: "x" := v in e) : τ.
   Proof.
     iIntros (?? Hτ).
     assert (Closed ∅ (Rec BAnon "x" e)).

theories/examples/par.v

@@ -26,9 +26,9 @@ Section compatibility.
 
   Lemma bin_log_related_par Δ Γ E e1 e2 e1' e2' τ1 τ2 :
     ↑logrelN ⊆ E →
-    {E,E;Δ;Γ} ⊨ e1 ≤log≤ e1' : TArrow TUnit τ1 -∗
-    {E,E;Δ;Γ} ⊨ e2 ≤log≤ e2' : TArrow TUnit τ2 -∗
-    {E,E;Δ;Γ} ⊨ par e1 e2 ≤log≤ par e1' e2' : TProd τ1 τ2.
+    {E;Δ;Γ} ⊨ e1 ≤log≤ e1' : TArrow TUnit τ1 -∗
+    {E;Δ;Γ} ⊨ e2 ≤log≤ e2' : TArrow TUnit τ2 -∗
+    {E;Δ;Γ} ⊨ par e1 e2 ≤log≤ par e1' e2' : TProd τ1 τ2.
   Proof.
     iIntros (?) "He1 He2".
     iApply (bin_log_related_app with "[He1] He2").

theories/examples/various.v

@@ -199,8 +199,8 @@ Section refinement.
 
   Definition bot : val := rec: "bot" <> := "bot" #().
   Lemma bot_l ϕ Δ Γ E K t τ :
-    (ϕ -∗ {E,E;Δ;Γ} ⊨ fill K (bot #()) ≤log≤ t : τ) -∗
-    {E,E;Δ;Γ} ⊨ fill K (bot #()) ≤log≤ t : τ.
+    (ϕ -∗ {E;Δ;Γ} ⊨ fill K (bot #()) ≤log≤ t : τ) -∗
+    {E;Δ;Γ} ⊨ fill K (bot #()) ≤log≤ t : τ.
   Proof.
     iIntros "Hlog".
     iLöb as "IH".
@@ -320,7 +320,7 @@ Section refinement.
   Lemma profiled_g `{oneshotG Σ} `{inG Σ (exclR unitR)} γ γ' c1 c2 g1 g2 Δ Γ :
     inv shootN (i6 c1 c2 γ γ') -∗
     ⟦ τg ⟧ Δ (g1, g2) -∗
-    {⊤,⊤;Δ;Γ} ⊨
+    {Δ;Γ} ⊨
       (FG_increment #c1 #() ;; g1 #())
     ≤log≤
       (FG_increment #c2 #() ;; g2 #()) : TUnit.
@@ -405,7 +405,7 @@ Section refinement.
   Lemma profiled_g' `{oneshotG Σ} `{inG Σ (exclR unitR)} γ γ' c1 c2 g1 g2 Δ Γ :
     inv shootN (i6 c1 c2 γ γ') -∗
     ⟦ τg ⟧ Δ (g1, g2) -∗
-    {⊤,⊤;Δ;Γ} ⊨
+    {Δ;Γ} ⊨
       (λ: <>, FG_increment #c1 #() ;; g1 #())
     ≤log≤
       (λ: <>, FG_increment #c2 #() ;; g2 #()) : τg.

theories/logrel/logrel_binary.v

@@ -36,12 +36,17 @@ Notation "⟦ Γ ⟧*" := (interp_env Γ).
 
 Notation "'{' E1 ',' E2 ';' Δ ';' Γ '}' ⊨ e '≤log≤' e' : τ" :=
   (bin_log_related E1 E2 Δ Γ e%E e'%E τ)
-  (at level 74, E1,E2, e, e', τ at next level,
-   format "'[hv' '{' E1 ',' E2 ';' Δ ';' Γ '}'  ⊨  '/  ' e  '/' '≤log≤'  '/  ' e'  :  τ ']'").
-Notation "'{' E1 ',' E2 ';' Γ '}' ⊨ e '≤log≤' e' : τ" :=
-  (∀ Δ, bin_log_related E1 E2 Δ Γ e%E e'%E τ)%I
-  (at level 74, E1,E2, e, e', τ at next level,
-   format "'[hv' '{' E1 ',' E2 ';' Γ '}'  ⊨  '/  ' e  '/' '≤log≤'  '/  ' e'  :  τ ']'").
+  (at level 74, E1 at level 50, E2 at next level,
+   Δ at next level, Γ at next level, e, e', τ at next level,
+   format "'[hv' '{' E1 ',' E2 ';'  Δ ';'  Γ '}'  ⊨  '/  ' e  '/' '≤log≤'  '/  ' e'  :  τ ']'").
+Notation "'{' E ';' Δ ';' Γ '}' ⊨ e '≤log≤' e' : τ" :=
+  (bin_log_related E E Δ Γ e%E e'%E τ)
+  (at level 74, E at level 50, Δ at next level, Γ at next level, e, e', τ at next level,
+   format "'[hv' '{' E ';'  Δ ';'  Γ '}'  ⊨  '/  ' e  '/' '≤log≤'  '/  ' e'  :  τ ']'").
+Notation "'{' Δ ';' Γ '}' ⊨ e '≤log≤' e' : τ" :=
+  (bin_log_related ⊤ ⊤ Δ Γ e%E e'%E τ)
+  (at level 74, Δ at level 50, Γ at next level, e, e', τ at next level,
+   format "'[hv' '{' Δ ';'  Γ '}'  ⊨  '/  ' e  '/' '≤log≤'  '/  ' e'  :  τ ']'").
 Notation "Γ ⊨ e '≤log≤' e' : τ" :=
   (∀ Δ, bin_log_related ⊤ ⊤ Δ Γ e%E e'%E τ)%I
   (at level 74, e, e', τ at next level,
@@ -163,7 +168,7 @@ Section related_facts.
 
   (* We need this to be able to open and closed invariants in front of logrels *)
   Lemma fupd_logrel E1 E2 Δ Γ e e' τ :
-    ((|={E1,E2}=> ({E2,E2;Δ;Γ} ⊨ e ≤log≤ e' : τ))
+    ((|={E1,E2}=> ({E2;Δ;Γ} ⊨ e ≤log≤ e' : τ))
      -∗ {E1,E2;Δ;Γ} ⊨ e ≤log≤ e' : τ)%I.
   Proof.
     rewrite bin_log_related_eq.
@@ -186,7 +191,7 @@ Section related_facts.
 
   Global Instance elim_modal_logrel E1 E2 Δ Γ e e' P τ :
    ElimModal (|={E1,E2}=> P) P
-     ({E1,E2;Δ;Γ} ⊨ e ≤log≤ e' : τ) ({E2,E2;Δ;Γ} ⊨ e ≤log≤ e' : τ) | 10.
+     ({E1,E2;Δ;Γ} ⊨ e ≤log≤ e' : τ) ({E2;Δ;Γ} ⊨ e ≤log≤ e' : τ) | 10.
   Proof.
     rewrite /ElimModal.
     iIntros "[HP HI]". iApply fupd_logrel.
@@ -203,8 +208,8 @@ Section related_facts.
   Qed.
 
   Lemma bin_log_related_weaken_2 τi Δ Γ e1 e2 τ :
-    {⊤,⊤;Δ;Γ} ⊨ e1 ≤log≤ e2 : τ -∗
-    {⊤,⊤;τi::Δ;Autosubst_Classes.subst (ren (+1)) <$>Γ} ⊨ e1 ≤log≤ e2 : τ.[ren (+1)].
+    {Δ;Γ} ⊨ e1 ≤log≤ e2 : τ -∗
+    {τi::Δ;Autosubst_Classes.subst (ren (+1)) <$>Γ} ⊨ e1 ≤log≤ e2 : τ.[ren (+1)].
   Proof.
     rewrite bin_log_related_eq /bin_log_related_def.
     iIntros "Hlog" (vvs ρ) "#Hs #HΓ".
@@ -227,7 +232,7 @@ Section monadic.
   Context `{logrelG Σ}.
 
   Lemma related_ret E1 E2 Δ Γ e1 e2 τ `{Closed ∅ e1} `{Closed ∅ e2} :
-    interp_expr E1 E1 ⟦ τ ⟧ Δ (e1,e2) -∗ {E2,E2;Δ;Γ} ⊨ e1 ≤log≤ e2 : τ%I.
+    interp_expr E1 E1 ⟦ τ ⟧ Δ (e1,e2) -∗ {E2;Δ;Γ} ⊨ e1 ≤log≤ e2 : τ%I.
   Proof.
     iIntros "Hτ".
     rewrite bin_log_related_eq /bin_log_related_def.
@@ -239,9 +244,9 @@ Section monadic.
   Qed.
 
   Lemma related_bind E Δ Γ (e1 e2 : expr) (τ τ' : type) (K K' : list ectx_item) :
-    ({E,E;Δ;Γ} ⊨ e1 ≤log≤ e2 : τ) -∗
-    (∀ vv, ⟦ τ ⟧ Δ vv -∗ {E,E;Δ;Γ} ⊨ fill K (of_val (vv.1)) ≤log≤ fill K' (of_val (vv.2)) : τ') -∗
-    ({E,E;Δ;Γ} ⊨ fill K e1 ≤log≤ fill K' e2 : τ').
+    ({E;Δ;Γ} ⊨ e1 ≤log≤ e2 : τ) -∗
+    (∀ vv, ⟦ τ ⟧ Δ vv -∗ {E;Δ;Γ} ⊨ fill K (of_val (vv.1)) ≤log≤ fill K' (of_val (vv.2)) : τ') -∗
+    ({E;Δ;Γ} ⊨ fill K e1 ≤log≤ fill K' e2 : τ').
   Proof.
     iIntros "Hm Hf".
     rewrite bin_log_related_eq /bin_log_related_def.