diff --git a/theories/tactics.v b/theories/tactics.v
index 62f8ff4aa02303fd6e777d0bb34cacc697eb2c20..6869a1681ba3aa996b6a29b8f5e1b1accef40a4e 100644
--- a/theories/tactics.v
+++ b/theories/tactics.v
@@ -375,36 +375,36 @@ Ltac f_equiv :=
   | H : ?R ?x ?y |- ?R2 (match ?x with _ => _ end) (match ?y with _ => _ end) =>
      destruct H
   (* First assume that the arguments need the same relation as the result *)
-  | |- ?R (?f _) _ => simple apply (_ : Proper (R ==> R) f)
-  | |- ?R (?f _ _) _ => simple apply (_ : Proper (R ==> R ==> R) f)
-  | |- ?R (?f _ _ _) _ => simple apply (_ : Proper (R ==> R ==> R ==> R) f)
-  | |- ?R (?f _ _ _ _) _ => simple apply (_ : Proper (R ==> R ==> R ==> R ==> R) f)
-  | |- ?R (?f _ _ _ _ _) _ => simple apply (_ : Proper (R ==> R ==> R ==> R ==> R ==> R) f)
+  | |- ?R (?f _) (?f _) => simple apply (_ : Proper (R ==> R) f)
+  | |- ?R (?f _ _) (?f _ _) => simple apply (_ : Proper (R ==> R ==> R) f)
+  | |- ?R (?f _ _ _) (?f _ _ _) => simple apply (_ : Proper (R ==> R ==> R ==> R) f)
+  | |- ?R (?f _ _ _ _) (?f _ _ _ _) => simple apply (_ : Proper (R ==> R ==> R ==> R ==> R) f)
+  | |- ?R (?f _ _ _ _ _) (?f _ _ _ _ _) => simple apply (_ : Proper (R ==> R ==> R ==> R ==> R ==> R) f)
   (* For the case in which R is polymorphic, or an operational type class,
   like equiv. *)
-  | |- (?R _) (?f _) _ => simple apply (_ : Proper (R _ ==> _) f)
-  | |- (?R _ _) (?f _) _ => simple apply (_ : Proper (R _ _ ==> _) f)
-  | |- (?R _ _ _) (?f _) _ => simple apply (_ : Proper (R _ _ _ ==> _) f)
-  | |- (?R _) (?f _ _) _ => simple apply (_ : Proper (R _ ==> R _ ==> _) f)
-  | |- (?R _ _) (?f _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> _) f)
-  | |- (?R _ _ _) (?f _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> _) f)
-  | |- (?R _) (?f _ _ _) _ => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> _) f)
-  | |- (?R _ _) (?f _ _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> _) f)
-  | |- (?R _ _ _) (?f _ _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ R _ _ _ ==> _) f)
-  | |- (?R _) (?f _ _ _ _) _ => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> _) f)
-  | |- (?R _ _) (?f _ _ _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> _) f)
-  | |- (?R _ _ _) (?f _ _ _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> _) f)
-  | |- (?R _) (?f _ _ _ _ _) _ => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> R _ ==> _) f)
-  | |- (?R _ _) (?f _ _ _ _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> _) f)
-  | |- (?R _ _ _) (?f _ _ _ _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> _) f)
+  | |- (?R _) (?f _) (?f _) => simple apply (_ : Proper (R _ ==> _) f)
+  | |- (?R _ _) (?f _) (?f _) => simple apply (_ : Proper (R _ _ ==> _) f)
+  | |- (?R _ _ _) (?f _) (?f _) => simple apply (_ : Proper (R _ _ _ ==> _) f)
+  | |- (?R _) (?f _ _) (?f _ _) => simple apply (_ : Proper (R _ ==> R _ ==> _) f)
+  | |- (?R _ _) (?f _ _) (?f _ _) => simple apply (_ : Proper (R _ _ ==> R _ _ ==> _) f)
+  | |- (?R _ _ _) (?f _ _) (?f _ _) => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> _) f)
+  | |- (?R _) (?f _ _ _) (?f _ _ _) => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> _) f)
+  | |- (?R _ _) (?f _ _ _) (?f _ _ _) => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> _) f)
+  | |- (?R _ _ _) (?f _ _ _) (?f _ _ _) => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ R _ _ _ ==> _) f)
+  | |- (?R _) (?f _ _ _ _) (?f _ _ _ _) => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> _) f)
+  | |- (?R _ _) (?f _ _ _ _) (?f _ _ _ _) => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> _) f)
+  | |- (?R _ _ _) (?f _ _ _ _) (?f _ _ _ _) => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> _) f)
+  | |- (?R _) (?f _ _ _ _ _) (?f _ _ _ _ _) => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> R _ ==> _) f)
+  | |- (?R _ _) (?f _ _ _ _ _) (?f _ _ _ _ _) => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> _) f)
+  | |- (?R _ _ _) (?f _ _ _ _ _) (?f _ _ _ _ _) => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> _) f)
   (* Next, try to infer the relation. Unfortunately, very often, it will turn
      the goal into a Leibniz equality so we get stuck. *)
   (* TODO: Can we exclude that instance? *)
-  | |- ?R (?f _) _ => simple apply (_ : Proper (_ ==> R) f)
-  | |- ?R (?f _ _) _ => simple apply (_ : Proper (_ ==> _ ==> R) f)
-  | |- ?R (?f _ _ _) _ => simple apply (_ : Proper (_ ==> _ ==> _ ==> R) f)
-  | |- ?R (?f _ _ _ _) _ => simple apply (_ : Proper (_ ==> _ ==> _ ==> _ ==> R) f)
-  | |- ?R (?f _ _ _ _ _) _ => simple apply (_ : Proper (_ ==> _ ==> _ ==> _ ==> _ ==> R) f)
+  | |- ?R (?f _) (?f _) => simple apply (_ : Proper (_ ==> R) f)
+  | |- ?R (?f _ _) (?f _ _) => simple apply (_ : Proper (_ ==> _ ==> R) f)
+  | |- ?R (?f _ _ _) (?f _ _ _) => simple apply (_ : Proper (_ ==> _ ==> _ ==> R) f)
+  | |- ?R (?f _ _ _ _) (?f _ _ _ _) => simple apply (_ : Proper (_ ==> _ ==> _ ==> _ ==> R) f)
+  | |- ?R (?f _ _ _ _ _) (?f _ _ _ _ _) => simple apply (_ : Proper (_ ==> _ ==> _ ==> _ ==> _ ==> R) f)
   (* In case the function symbol differs, but the arguments are the same,
      maybe we have a relation about those functions in our context. *)
   (* TODO: If only some of the arguments are the same, we could also