Tweak.

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|].