Better notation for autosubst substitution and liftings

theories/examples/symbol.v

@@ -250,7 +250,7 @@ Section proof.
   Context `{!logrelG Σ, !msizeG Σ, !lockG Σ}.
 
   Lemma eqKey_refinement Δ Γ γ :
-    {⊤,⊤;tableR γ :: Δ;Autosubst_Classes.subst (ren (+1)) <$> Γ} ⊨
+    {⊤,⊤;tableR γ :: Δ;⤉Γ} ⊨
       eqKey
     ≤log≤
       eqKey : TArrow (TVar 0) (TArrow (TVar 0) TBool).

theories/logrel/fundamental_binary.v

@@ -338,7 +338,7 @@ Section masked.
     Closed (dom _ Γ) e →
     Closed (dom _ Γ) e' →
     ↑ logrelN ⊆ E →
-    (∀ (τi : D), ⌜∀ ww, Persistent (τi ww)⌝ → □ ({E;(τi::Δ);Autosubst_Classes.subst (ren (+1)) <$> Γ} ⊨ e ≤log≤ e' : τ)) -∗
+    (∀ (τi : D), ⌜∀ ww, Persistent (τi ww)⌝ → □ ({E;(τi::Δ);⤉Γ} ⊨ e ≤log≤ e' : τ)) -∗
     {E;Δ;Γ} ⊨ TLam e ≤log≤ TLam e' : TForall τ.
   Proof.
     rewrite bin_log_related_eq.
@@ -376,7 +376,7 @@ Section masked.
   Lemma bin_log_related_tapp (τi : D) Δ Γ e e' τ :
     (∀ ww, Persistent (τi ww)) →
     {E;Δ;Γ} ⊨ e ≤log≤ e' : TForall τ -∗
-    {E;τi::Δ;Autosubst_Classes.subst (ren (+1)) <$> Γ} ⊨ TApp e ≤log≤ TApp e' : τ.
+    {E;τi::Δ;⤉Γ} ⊨ TApp e ≤log≤ TApp e' : τ.
   Proof.
     rewrite bin_log_related_eq.
     iIntros (?) "IH".
@@ -435,7 +435,7 @@ Section masked.
 
   Lemma bin_log_related_pack (τi : D) Δ Γ e e' τ :
     (∀ ww, Persistent (τi ww)) →
-    {E;τi::Δ;Autosubst_Classes.subst (ren (+1)) <$> Γ} ⊨ e ≤log≤ e' : τ -∗
+    {E;τi::Δ;⤉Γ} ⊨ e ≤log≤ e' : τ -∗
     {E;Δ;Γ} ⊨ Pack e ≤log≤ Pack e' : TExists τ.
   Proof.
     rewrite bin_log_related_eq.
@@ -457,8 +457,8 @@ Section masked.
     (Hmasked : ↑ logrelN ⊆ E) :
     {E;Δ;Γ} ⊨ e1 ≤log≤ e1' : TExists τ -∗
     (∀ τi : D, ⌜∀ ww, Persistent (τi ww)⌝ →
-      {E;τi::Δ;Autosubst_Classes.subst (ren (+1)) <$> Γ} ⊨
-        e2 ≤log≤ e2' : TArrow τ (Autosubst_Classes.subst (ren (+1)) τ2)) -∗
+      {E;τi::Δ;⤉Γ} ⊨
+        e2 ≤log≤ e2' : TArrow τ (asubst (ren (+1)) τ2)) -∗
     {E;Δ;Γ} ⊨ Unpack e1 e2 ≤log≤ Unpack e1' e2' : τ2.
   Proof.
     rewrite bin_log_related_eq.
@@ -630,7 +630,7 @@ Section masked.
     - by iApply (bin_log_related_app with "[] []").
     - assert (Closed (dom _ Γ) e).
       { apply typed_X_closed in Ht.
-        pose (K:=(dom_fmap (Autosubst_Classes.subst (ren (+1))) Γ (D:=stringset))).
+        pose (K:=(dom_fmap (asubst (ren (+1))) Γ (D:=stringset))).
         fold_leibniz. by rewrite -K. }
       iApply bin_log_related_tlam; eauto.
     - by iApply bin_log_related_tapp'.

theories/logrel/logrel_binary.v

@@ -139,7 +139,7 @@ Section interp_env_facts.
   Qed.
 
   Lemma interp_env_ren Δ (Γ : stringmap type) E1 E2 (vvs : stringmap (val * val)) (τi : D) :
-    interp_env (Autosubst_Classes.subst (ren (+1)) <$> Γ) E1 E2 (τi :: Δ) vvs
+    interp_env (⤉Γ) E1 E2 (τi :: Δ) vvs
                ⊣⊢
     interp_env Γ E1 E2 Δ vvs.
   Proof.
@@ -209,7 +209,7 @@ Section related_facts.
 
   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)].
+    {τi::Δ;⤉Γ} ⊨ e1 ≤log≤ e2 : τ.[ren (+1)].
   Proof.
     rewrite bin_log_related_eq /bin_log_related_def.
     iIntros "Hlog" (vvs ρ) "#Hs #HΓ".

theories/prelude/base.v

@@ -40,3 +40,7 @@ Ltac properness :=
 Reserved Notation "⟦ τ ⟧" (at level 0, τ at level 70).
 Reserved Notation "⟦ τ ⟧ₑ" (at level 0, τ at level 70).
 Reserved Notation "⟦ Γ ⟧*" (at level 0, Γ at level 70).
+
+Notation asubst := Autosubst_Classes.subst.
+Notation "⤉ Γ" := (asubst (ren (+1)) <$> Γ)
+                    (at level 10, format "⤉ Γ").