diff --git a/theories/list.v b/theories/list.v
index 33d15d59c6a2d07d52bc5578f1b9e57dbb6b8133..c1c2ede4afceadf89248547fa5e62b77a4b4485c 100644
--- a/theories/list.v
+++ b/theories/list.v
@@ -911,17 +911,17 @@ Section find.
   Lemma list_find_fmap {B : Type} (f : B → A) (l : list B) :
     list_find P (f <$> l) = prod_map id f <$> list_find (P ∘ f) l.
   Proof.
-    induction l as [|x y IH]; [done|]. simpl.
+    induction l as [|x l IH]; [done|]. simpl.
     case_decide; [done|].
-    change (list_fmap B A f y) with (f <$> y). (* FIXME it simplified too much *)
-    rewrite IH. by destruct (list_find (P ∘ f) y).
+    change (list_fmap B A f l) with (f <$> l). (* FIXME it simplified too much *)
+    rewrite IH. by destruct (list_find (P ∘ f) l).
   Qed.
 
   Lemma list_find_proper (Q : A → Prop) `{∀ x, Decision (Q x)} l :
     (∀ x, P x ↔ Q x) →
     list_find P l = list_find Q l.
   Proof.
-    intros HPQ. induction l as [|x y IH]; [done|]. simpl.
+    intros HPQ. induction l as [|x l IH]; [done|]. simpl.
     erewrite decide_iff by done. by rewrite IH.
   Qed.
 End find.