diff --git a/theories/tactics.v b/theories/tactics.v
index 7097ce22269664b4190bcf6d013ec42a2fb48c02..7916a6022ccbdc594183251b67afd1742e2bc38e 100644
--- a/theories/tactics.v
+++ b/theories/tactics.v
@@ -382,21 +382,25 @@ Ltac f_equiv :=
   | |- ?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 _) (?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)
+  | |- (?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)
+
+  | |- (?R _) (?f _ _ _ _ _) (?f _ _ _ _ _) => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> R _ ==> R _) f)
+  | |- (?R _ _) (?f _ _ _ _ _) (?f _ _ _ _ _) => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> R _ _) f)
+  | |- (?R _ _ _) (?f _ _ _ _ _) (?f _ _ _ _ _) => simple apply (_ : Proper (R _ _ _ ==> 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? *)