Get rid of some unnecessary closedness conditions

theories/logrel/rules.v

@@ -202,8 +202,7 @@ Section properties.
     - by inv_head_step.
   Qed.
   
-  Lemma bin_log_related_pack_l Δ Γ E K e e' v t τ
-   (Hclosed' : Closed ∅ e') :
+  Lemma bin_log_related_pack_l Δ Γ E K e e' v t τ :
    to_val e = Some v →
    ▷ ({E,E;Δ;Γ} ⊨ fill K (App e' e) ≤log≤ t : τ)
    ⊢ {E,E;Δ;Γ} ⊨ fill K (Unpack (Pack e) e') ≤log≤ t : τ.
@@ -214,9 +213,7 @@ Section properties.
     - by inv_head_step.
   Qed.
 
-  Lemma bin_log_related_case_inl_l Δ Γ E K e v e1 e2 t τ
-   (Hclosed1 : Closed ∅ e1) 
-   (Hclosed2 : Closed ∅ e2) : 
+  Lemma bin_log_related_case_inl_l Δ Γ E K e v e1 e2 t τ :
    to_val e = Some v →
    ▷ ({E,E;Δ;Γ} ⊨ fill K (App e1 e) ≤log≤ t : τ)
    ⊢ {E,E;Δ;Γ} ⊨ fill K (Case (InjL e) e1 e2) ≤log≤ t : τ.
@@ -227,9 +224,7 @@ Section properties.
     - by inv_head_step.
   Qed.
 
-  Lemma bin_log_related_case_inr_l Δ Γ E K e v e1 e2 t τ
-   (Hclosed1 : Closed ∅ e1) 
-   (Hclosed2 : Closed ∅ e2) : 
+  Lemma bin_log_related_case_inr_l Δ Γ E K e v e1 e2 t τ :
    to_val e = Some v →
    ▷ ({E,E;Δ;Γ} ⊨ fill K (App e2 e) ≤log≤ t : τ)
    ⊢ {E,E;Δ;Γ} ⊨ fill K (Case (InjR e) e1 e2) ≤log≤ t : τ.
@@ -240,9 +235,7 @@ Section properties.
     - by inv_head_step.
   Qed.
 
-  Lemma bin_log_related_if_true_l Δ Γ E K e1 e2 t τ
-   (Hclosed1 : Closed ∅ e1) 
-   (Hclosed2 : Closed ∅ e2) : 
+  Lemma bin_log_related_if_true_l Δ Γ E K e1 e2 t τ :
    ▷ ({E,E;Δ;Γ} ⊨ fill K e1 ≤log≤ t : τ)
    ⊢ {E,E;Δ;Γ} ⊨ fill K (If #true e1 e2) ≤log≤ t : τ.
   Proof.
@@ -252,9 +245,7 @@ Section properties.
     - by inv_head_step.
   Qed.
 
-  Lemma bin_log_related_if_true_masked_l Δ Γ E1 E2 K e1 e2 t τ
-   (Hclosed1 : Closed ∅ e1) 
-   (Hclosed2 : Closed ∅ e2) : 
+  Lemma bin_log_related_if_true_masked_l Δ Γ E1 E2 K e1 e2 t τ :
    ({E1,E2;Δ;Γ} ⊨ fill K e1 ≤log≤ t : τ)
    ⊢ {E1,E2;Δ;Γ} ⊨ fill K (If #true e1 e2) ≤log≤ t : τ.
   Proof.
@@ -264,9 +255,7 @@ Section properties.
     - by inv_head_step.
   Qed.
 
-  Lemma bin_log_related_if_false_l Δ Γ E K e1 e2 t τ
-   (Hclosed1 : Closed ∅ e1) 
-   (Hclosed2 : Closed ∅ e2) : 
+  Lemma bin_log_related_if_false_l Δ Γ E K e1 e2 t τ :
    ▷ ({E,E;Δ;Γ} ⊨ fill K e2 ≤log≤ t : τ)
    ⊢ {E,E;Δ;Γ} ⊨ (fill K (If #false e1 e2)) ≤log≤ t : τ.
   Proof.
@@ -276,9 +265,7 @@ Section properties.
     - by inv_head_step.
   Qed.
 
-  Lemma bin_log_related_if_false_masked_l Δ Γ E1 E2 K e1 e2 t τ
-   (Hclosed1 : Closed ∅ e1) 
-   (Hclosed2 : Closed ∅ e2) : 
+  Lemma bin_log_related_if_false_masked_l Δ Γ E1 E2 K e1 e2 t τ :
    ({E1,E2;Δ;Γ} ⊨ fill K e2 ≤log≤ t : τ)
    ⊢ {E1,E2;Δ;Γ} ⊨ (fill K (If #false e1 e2)) ≤log≤ t : τ.
   Proof.