diff --git a/theories/bi/embedding.v b/theories/bi/embedding.v
index bbf87f95dfbc71b2f9277ad45185f87e5776cf6d..92bce3d7b52b5747d7a5f9c81b6dbd6fbbe1fb69 100644
--- a/theories/bi/embedding.v
+++ b/theories/bi/embedding.v
@@ -324,4 +324,4 @@ End sbi_embed.
 [class_apply @bi_embed_plainly] shelves the [BiPlainly] premise, making proof
 search for the other premises fail. See the proof of [monPred_objectively_plain]
 for an example where it would fail with a regular [Instance].*)
-Hint Extern 4 (Plain ⎡_⎤) => eapply @embed_plain : typeclass_instances.
+Hint Extern 4 (Plain _) => notypeclasses refine (embed_plain _ _) : typeclass_instances.
diff --git a/theories/bi/plainly.v b/theories/bi/plainly.v
index e957761743aff18bb61a54637df262a05d6a3075..093b731bd444200e23b37944c9da484cb3207129 100644
--- a/theories/bi/plainly.v
+++ b/theories/bi/plainly.v
@@ -633,4 +633,4 @@ Hint Immediate plain_persistent : typeclass_instances.
 [class_apply @impl_persistent] shelves the [BiPlainly] premise, making proof
 search for the other premises fail. See the proof of [coreP_persistent] for an
 example where it would fail with a regular [Instance].*)
-Hint Extern 4 (Persistent (_ → _)) => eapply @impl_persistent : typeclass_instances.
+Hint Extern 4 (Persistent _) => notypeclasses refine (impl_persistent _ _ _ _ _) : typeclass_instances.