From 128c91254d76693d0da20e42cc576356a0f9197c Mon Sep 17 00:00:00 2001
From: Jacques-Henri Jourdan <jacques-henri.jourdan@normalesup.org>
Date: Mon, 18 Dec 2017 19:41:27 +0100
Subject: [PATCH] Tweak.

---
 theories/bi/embedding.v | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/theories/bi/embedding.v b/theories/bi/embedding.v
index ca132298d..b42903ad9 100644
--- a/theories/bi/embedding.v
+++ b/theories/bi/embedding.v
@@ -37,6 +37,7 @@ Class SbiEmbedding (PROP1 PROP2 : sbi) `{BiEmbed PROP1 PROP2} := {
 Section bi_embedding.
   Context `{BiEmbedding PROP1 PROP2}.
   Local Notation bi_embed := (bi_embed (A:=PROP1) (B:=PROP2)).
+  Local Notation "⎡ P ⎤" := (bi_embed P) : bi_scope.
   Implicit Types P Q R : PROP1.
 
   Global Instance bi_embed_proper : Proper ((≡) ==> (≡)) bi_embed.
@@ -49,7 +50,7 @@ Section bi_embedding.
     rewrite EQ //.
   Qed.
 
-  Lemma bi_embed_valid (P : PROP1) : bi_embed P ↔ P.
+  Lemma bi_embed_valid (P : PROP1) : ⎡P⎤%I ↔ P.
   Proof.
     by rewrite /bi_valid -bi_embed_emp; split=>?; [apply (inj bi_embed)|f_equiv].
   Qed.
@@ -78,7 +79,7 @@ Section bi_embedding.
     apply bi.equiv_spec; split; [|apply bi_embed_wand_2].
     apply bi.wand_intro_l. by rewrite -bi_embed_sep bi.wand_elim_r.
   Qed.
-  Lemma bi_embed_pure φ : bi_embed ⌜φ⌝ ⊣⊢ ⌜φ⌝.
+  Lemma bi_embed_pure φ : ⎡⌜φ⌝⎤ ⊣⊢ ⌜φ⌝.
   Proof.
     rewrite (@bi.pure_alt PROP1) (@bi.pure_alt PROP2) bi_embed_exist.
     do 2 f_equiv. apply bi.equiv_spec. split; [apply bi.True_intro|].
@@ -86,7 +87,7 @@ Section bi_embedding.
       last apply bi.True_intro.
     apply bi.impl_intro_l. by rewrite right_id.
   Qed.
-  Lemma bi_embed_internal_eq (A : ofeT) (x y : A) : bi_embed (x ≡ y) ⊣⊢ x ≡ y.
+  Lemma bi_embed_internal_eq (A : ofeT) (x y : A) : ⎡x ≡ y⎤ ⊣⊢ x ≡ y.
   Proof.
     apply bi.equiv_spec; split; [apply bi_embed_internal_eq_1|].
     etrans; [apply (bi.internal_eq_rewrite x y (λ y, ⎡x ≡ y⎤%I)); solve_proper|].
-- 
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