diff --git a/theories/collections.v b/theories/collections.v
index 6f4e526e3127119b3688ce7cc10081640443a48e..3a49b8deb7e39928a11456bf7098b49468c1c2e0 100644
--- a/theories/collections.v
+++ b/theories/collections.v
@@ -390,7 +390,7 @@ Section simple_collection.
     split.
     - induction Xs; simpl; intros HXs; [by apply elem_of_empty in HXs|].
       setoid_rewrite elem_of_cons. apply elem_of_union in HXs. naive_solver.
-    - intros [X []]. induction 1; simpl; [by apply elem_of_union_l |].
+    - intros [X [Hx]]. induction Hx; simpl; [by apply elem_of_union_l |].
       intros. apply elem_of_union_r; auto.
   Qed.
 
diff --git a/theories/list.v b/theories/list.v
index 59b7bda9e163ca67ae0ac65fc67e7cb712b78b87..ab08c510c7a112db57efdde80a6da8940361405d 100644
--- a/theories/list.v
+++ b/theories/list.v
@@ -926,7 +926,7 @@ Proof. by destruct n. Qed.
 Lemma drop_length l n : length (drop n l) = length l - n.
 Proof. revert n. by induction l; intros [|i]; f_equal/=. Qed.
 Lemma drop_ge l n : length l ≤ n → drop n l = [].
-Proof. revert n. induction l; intros [|??]; simpl in *; auto with lia. Qed.
+Proof. revert n. induction l; intros [|?]; simpl in *; auto with lia. Qed.
 Lemma drop_all l : drop (length l) l = [].
 Proof. by apply drop_ge. Qed.
 Lemma drop_drop l n1 n2 : drop n1 (drop n2 l) = drop (n2 + n1) l.
@@ -2828,7 +2828,7 @@ Section fmap.
     (∀ x, f x = y) → f <$> l = replicate (length l) y.
   Proof. intros; induction l; f_equal/=; auto. Qed.
   Lemma list_lookup_fmap l i : (f <$> l) !! i = f <$> (l !! i).
-  Proof. revert i. induction l; by intros [|]. Qed.
+  Proof. revert i. induction l; intros [|n]; by try revert n. Qed.
   Lemma list_lookup_fmap_inv l i x :
     (f <$> l) !! i = Some x → ∃ y, x = f y ∧ l !! i = Some y.
   Proof.