diff --git a/prelude/tactics.v b/prelude/tactics.v
index 9e70ba94a458219a1fc9f641c37e686f6357dbed..c55f53d667bbf3f8d2765f35bd431e48131eab48 100644
--- a/prelude/tactics.v
+++ b/prelude/tactics.v
@@ -292,9 +292,9 @@ Ltac f_equiv :=
end.
(** auto_proper solves goals of the form "f _ = f _", for any relation and any
- number of arguments, by repeatedly apply f_equiv and handling trivial cases.
+ number of arguments, by repeatedly applying f_equiv and handling trivial cases.
If it cannot solve an equality, it will leave that to the user. *)
-Ltac auto_proper :=
+Ltac auto_equiv :=
(* Deal with "pointwise_relation" *)
repeat lazymatch goal with
| |- pointwise_relation _ _ _ _ => intros ?
@@ -302,10 +302,10 @@ Ltac auto_proper :=
(* Normalize away equalities. *)
simplify_eq;
(* repeatedly apply congruence lemmas and use the equalities in the hypotheses. *)
- try (f_equiv; fast_done || auto_proper).
+ try (f_equiv; fast_done || auto_equiv).
(** solve_proper solves goals of the form "Proper (R1 ==> R2)", for any
- number of relations. All the actual work is done by f_equiv;
+ number of relations. All the actual work is done by auto_equiv;
solve_proper just introduces the assumptions and unfolds the first
head symbol. *)
Ltac solve_proper :=
@@ -328,7 +328,7 @@ Ltac solve_proper :=
| |- ?R (?f _ _) (?f _ _) => unfold f
| |- ?R (?f _) (?f _) => unfold f
end;
- solve [ auto_proper ].
+ solve [ auto_equiv ].
(** The tactic [intros_revert tac] introduces all foralls/arrows, performs tac,
and then reverts them. *)