diff --git a/prelude/lexico.v b/prelude/lexico.v
index 1b92f9825d5cc13de58f467b6f8ce0295afbda05..43ecf2cdfef5ce020c264d22cecafbbce1c3e40e 100644
--- a/prelude/lexico.v
+++ b/prelude/lexico.v
@@ -52,7 +52,7 @@ Proof.
   - intros [x y]. apply prod_lexico_irreflexive.
     by apply (irreflexivity lexico y).
   - intros [??] [??] [??] ??.
-    eapply prod_lexico_transitive; eauto. apply trans.
+    eapply prod_lexico_transitive; eauto. apply transitivity.
 Qed.
 Instance prod_lexico_trichotomyT `{Lexico A, tA : !TrichotomyT (@lexico A _)}
   `{Lexico B, tB : !TrichotomyT (@lexico B _)}: TrichotomyT (@lexico (A * B) _).
diff --git a/prelude/list.v b/prelude/list.v
index 8541aa18ced733122230d68af2296ea17d516b8b..025e8c27868a3bcafb2e4fd56231fc8fa2474f26 100644
--- a/prelude/list.v
+++ b/prelude/list.v
@@ -2493,7 +2493,7 @@ Section Forall2_order.
   Global Instance: Symmetric R → Symmetric (Forall2 R).
   Proof. intros. induction 1; constructor; auto. Qed.
   Global Instance: Transitive R → Transitive (Forall2 R).
-  Proof. intros ????. apply Forall2_transitive. by apply @trans. Qed.
+  Proof. intros ????. apply Forall2_transitive. by apply @transitivity. Qed.
   Global Instance: Equivalence R → Equivalence (Forall2 R).
   Proof. split; apply _. Qed.
   Global Instance: PreOrder R → PreOrder (Forall2 R).