[ltac] Warning for deprecated `Add Setoid` and `Add Morphism` forms.

The manual has long stated that these forms are deprecated. We add a
warning for them, as indeed `Add Morphism` is an "proof evil" [*]
command, and we may want to remove it in the future.

We've also fixed the stdlib not to emit the warning.

[*] https://ncatlab.org/nlab/show/principle+of+equivalence

10 files changed, 128 insertions, 63 deletions

diff --git a/plugins/ltac/rewrite.ml b/plugins/ltac/rewrite.ml
index fd791a910..1809f0fcd 100644
--- a/plugins/ltac/rewrite.ml
+++ b/plugins/ltac/rewrite.ml
@@ -1935,7 +1935,12 @@ let default_morphism sign m =
   let evars, mor = resolve_one_typeclass env (goalevars evars) morph in
     mor, proper_projection sigma mor morph
 
+let warn_add_setoid_deprecated =
+  CWarnings.create ~name:"add-setoid" ~category:"deprecated" (fun () ->
+      Pp.(str "Add Setoid is deprecated, please use Add Parametric Relation."))
+
 let add_setoid global binders a aeq t n =
+  warn_add_setoid_deprecated ?loc:a.CAst.loc ();
   init_setoid ();
   let _lemma_refl = declare_instance_refl global binders a aeq n (mkappc "Seq_refl" [a;aeq;t]) in
   let _lemma_sym = declare_instance_sym global binders a aeq n (mkappc "Seq_sym" [a;aeq;t]) in
@@ -1954,7 +1959,12 @@ let make_tactic name =
   let tacname = Qualid (Loc.tag tacpath) in
   TacArg (Loc.tag @@ TacCall (Loc.tag (tacname, [])))
 
+let warn_add_morphism_deprecated =
+  CWarnings.create ~name:"add-morphism" ~category:"deprecated" (fun () ->
+      Pp.(str "Add Morphism f : id is deprecated, please use Add Morphism f with signature (...) as id"))
+
 let add_morphism_infer glob m n =
+  warn_add_morphism_deprecated ?loc:m.CAst.loc ();
   init_setoid ();
   let poly = Flags.is_universe_polymorphism () in
   let instance_id = add_suffix n "_Proper" in
diff --git a/plugins/micromega/EnvRing.v b/plugins/micromega/EnvRing.v
index 56b3d480e..ae4857a77 100644
--- a/plugins/micromega/EnvRing.v
+++ b/plugins/micromega/EnvRing.v
@@ -56,10 +56,18 @@ Section MakeRingPol.
  Infix "?=!" := ceqb. Notation "[ x ]" := (phi x).
 
  (* Useful tactics *)
- Add Morphism radd : radd_ext. exact (Radd_ext Reqe). Qed.
- Add Morphism rmul : rmul_ext. exact (Rmul_ext Reqe). Qed.
- Add Morphism ropp : ropp_ext. exact (Ropp_ext Reqe). Qed.
- Add Morphism rsub : rsub_ext. exact (ARsub_ext Rsth Reqe ARth). Qed.
+ Add Morphism radd with signature (req ==> req ==> req) as radd_ext.
+ Proof. exact (Radd_ext Reqe). Qed.
+
+ Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext.
+ Proof. exact (Rmul_ext Reqe). Qed.
+
+ Add Morphism ropp with signature (req ==> req) as ropp_ext.
+ Proof. exact (Ropp_ext Reqe). Qed.
+
+ Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext.
+ Proof. exact (ARsub_ext Rsth Reqe ARth). Qed.
+
  Ltac rsimpl := gen_srewrite Rsth Reqe ARth.
 
  Ltac add_push := gen_add_push radd Rsth Reqe ARth.
diff --git a/plugins/setoid_ring/Field_theory.v b/plugins/setoid_ring/Field_theory.v
index 56b985aa3..88e2cb1da 100644
--- a/plugins/setoid_ring/Field_theory.v
+++ b/plugins/setoid_ring/Field_theory.v
@@ -56,11 +56,16 @@ Let rI_neq_rO := AFth.(AF_1_neq_0).
 Let rdiv_def := AFth.(AFdiv_def).
 Let rinv_l := AFth.(AFinv_l).
 
-Add Morphism radd : radd_ext. Proof. exact (Radd_ext Reqe). Qed.
-Add Morphism rmul : rmul_ext. Proof. exact (Rmul_ext Reqe). Qed.
-Add Morphism ropp : ropp_ext. Proof. exact (Ropp_ext Reqe). Qed.
-Add Morphism rsub : rsub_ext. Proof. exact (ARsub_ext Rsth Reqe ARth). Qed.
-Add Morphism rinv : rinv_ext. Proof. exact SRinv_ext. Qed.
+Add Morphism radd with signature (req ==> req ==> req) as radd_ext.
+Proof. exact (Radd_ext Reqe). Qed.
+Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext.
+Proof. exact (Rmul_ext Reqe). Qed.
+Add Morphism ropp with signature (req ==> req) as ropp_ext.
+Proof. exact (Ropp_ext Reqe). Qed.
+Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext.
+Proof. exact (ARsub_ext Rsth Reqe ARth). Qed.
+Add Morphism rinv with signature (req ==> req) as rinv_ext.
+Proof. exact SRinv_ext. Qed.
 
 Let eq_trans := Setoid.Seq_trans _ _ Rsth.
 Let eq_sym := Setoid.Seq_sym _ _ Rsth.
@@ -1609,9 +1614,12 @@ Section Complete.
  Variable Rsth : Setoid_Theory R req.
    Add Setoid R req Rsth as R_setoid3.
  Variable Reqe : ring_eq_ext radd rmul ropp req.
-   Add Morphism radd : radd_ext3.  exact (Radd_ext Reqe). Qed.
-   Add Morphism rmul : rmul_ext3.  exact (Rmul_ext Reqe). Qed.
-   Add Morphism ropp : ropp_ext3.  exact (Ropp_ext Reqe). Qed.
+   Add Morphism radd with signature (req ==> req ==> req) as radd_ext3.
+   Proof. exact (Radd_ext Reqe). Qed.
+   Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext3.
+   Proof. exact (Rmul_ext Reqe). Qed.
+   Add Morphism ropp with signature (req ==> req) as ropp_ext3.
+   Proof. exact (Ropp_ext Reqe). Qed.
 
 Section AlmostField.
 
diff --git a/plugins/setoid_ring/InitialRing.v b/plugins/setoid_ring/InitialRing.v
index 98ffff432..bd4e94687 100644
--- a/plugins/setoid_ring/InitialRing.v
+++ b/plugins/setoid_ring/InitialRing.v
@@ -51,9 +51,12 @@ Section ZMORPHISM.
      Add Setoid R req Rsth as R_setoid3.
      Ltac rrefl := gen_reflexivity Rsth.
  Variable Reqe : ring_eq_ext radd rmul ropp req.
-   Add Morphism radd : radd_ext3.  exact (Radd_ext Reqe). Qed.
-   Add Morphism rmul : rmul_ext3.  exact (Rmul_ext Reqe). Qed.
-   Add Morphism ropp : ropp_ext3.  exact (Ropp_ext Reqe). Qed.
+   Add Morphism radd with signature (req ==> req ==> req) as radd_ext3.
+   Proof. exact (Radd_ext Reqe). Qed.
+   Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext3.
+   Proof. exact (Rmul_ext Reqe). Qed.
+   Add Morphism ropp with signature (req ==> req) as ropp_ext3.
+   Proof. exact (Ropp_ext Reqe). Qed.
 
  Fixpoint gen_phiPOS1 (p:positive) : R :=
   match p with
@@ -103,7 +106,8 @@ Section ZMORPHISM.
 
  Section ALMOST_RING.
  Variable ARth : almost_ring_theory 0 1 radd rmul rsub ropp req.
-   Add Morphism rsub : rsub_ext3. exact (ARsub_ext Rsth Reqe ARth). Qed.
+   Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext3.
+   Proof. exact (ARsub_ext Rsth Reqe ARth). Qed.
    Ltac norm := gen_srewrite Rsth Reqe ARth.
    Ltac add_push := gen_add_push radd Rsth Reqe ARth.
 
@@ -151,7 +155,8 @@ Section ZMORPHISM.
 
  Variable Rth : ring_theory 0 1 radd rmul rsub ropp req.
  Let ARth := Rth_ARth Rsth Reqe Rth.
-   Add Morphism rsub : rsub_ext4. exact (ARsub_ext Rsth Reqe ARth). Qed.
+   Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext4.
+   Proof. exact (ARsub_ext Rsth Reqe ARth). Qed.
    Ltac norm := gen_srewrite Rsth Reqe ARth.
    Ltac add_push := gen_add_push radd Rsth Reqe ARth.
 
@@ -265,8 +270,10 @@ Section NMORPHISM.
  Let rsub := (@SRsub R radd).
   Notation "x - y " := (rsub x y).  Notation "- x" := (ropp x).
   Notation "x == y" := (req x y).
-   Add Morphism radd : radd_ext4.  exact (Radd_ext Reqe). Qed.
-   Add Morphism rmul : rmul_ext4.  exact (Rmul_ext Reqe). Qed.
+   Add Morphism radd with signature (req ==> req ==> req) as radd_ext4.
+   Proof. exact (Radd_ext Reqe). Qed.
+   Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext4.
+   Proof. exact (Rmul_ext Reqe). Qed.
    Ltac norm := gen_srewrite_sr Rsth Reqe ARth.
 
  Definition gen_phiN1 x :=
@@ -377,12 +384,16 @@ Section NWORDMORPHISM.
      Add Setoid R req Rsth as R_setoid5.
      Ltac rrefl := gen_reflexivity Rsth.
  Variable Reqe : ring_eq_ext radd rmul ropp req.
-   Add Morphism radd : radd_ext5.  exact (Radd_ext Reqe). Qed.
-   Add Morphism rmul : rmul_ext5.  exact (Rmul_ext Reqe). Qed.
-   Add Morphism ropp : ropp_ext5.  exact (Ropp_ext Reqe). Qed.
+   Add Morphism radd with signature (req ==> req ==> req) as radd_ext5.
+   Proof. exact (Radd_ext Reqe). Qed.
+   Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext5.
+   Proof. exact (Rmul_ext Reqe). Qed.
+   Add Morphism ropp with signature (req ==> req) as ropp_ext5.
+   Proof. exact (Ropp_ext Reqe). Qed.
 
  Variable ARth : almost_ring_theory 0 1 radd rmul rsub ropp req.
-   Add Morphism rsub : rsub_ext7. exact (ARsub_ext Rsth Reqe ARth). Qed.
+   Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext7.
+   Proof. exact (ARsub_ext Rsth Reqe ARth). Qed.
    Ltac norm := gen_srewrite Rsth Reqe ARth.
    Ltac add_push := gen_add_push radd Rsth Reqe ARth.
 
@@ -557,10 +568,14 @@ Section GEN_DIV.
   (* Useful tactics *)
   Add Setoid R req Rsth as R_set1.
  Ltac rrefl := gen_reflexivity Rsth.
-  Add Morphism radd : radd_ext.  exact (Radd_ext Reqe). Qed.
-  Add Morphism rmul : rmul_ext.  exact (Rmul_ext Reqe). Qed.
-  Add Morphism ropp : ropp_ext.  exact (Ropp_ext Reqe). Qed.
-  Add Morphism rsub : rsub_ext. exact (ARsub_ext Rsth Reqe ARth). Qed.
+  Add Morphism radd with signature (req ==> req ==> req) as radd_ext.
+  Proof. exact (Radd_ext Reqe). Qed.
+  Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext.
+  Proof. exact (Rmul_ext Reqe). Qed.
+  Add Morphism ropp with signature (req ==> req) as ropp_ext.
+  Proof. exact (Ropp_ext Reqe). Qed.
+  Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext.
+  Proof. exact (ARsub_ext Rsth Reqe ARth). Qed.
  Ltac rsimpl := gen_srewrite Rsth Reqe ARth.
 
  Definition triv_div x y :=
@@ -859,8 +874,3 @@ Ltac isZcst t :=
   (* *)
   | _ => constr:(false)
   end.
-
-
-
-
-
diff --git a/plugins/setoid_ring/Ring_polynom.v b/plugins/setoid_ring/Ring_polynom.v
index ac54d862c..a94f8d8df 100644
--- a/plugins/setoid_ring/Ring_polynom.v
+++ b/plugins/setoid_ring/Ring_polynom.v
@@ -59,10 +59,18 @@ Section MakeRingPol.
  Infix "?=!" := ceqb. Notation "[ x ]" := (phi x).
 
  (* Useful tactics *)
- Add Morphism radd : radd_ext. exact (Radd_ext Reqe). Qed.
- Add Morphism rmul : rmul_ext. exact (Rmul_ext Reqe). Qed.
- Add Morphism ropp : ropp_ext. exact (Ropp_ext Reqe). Qed.
- Add Morphism rsub : rsub_ext. exact (ARsub_ext Rsth Reqe ARth). Qed.
+ Add Morphism radd with signature (req ==> req ==> req) as radd_ext.
+ Proof. exact (Radd_ext Reqe). Qed.
+
+ Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext.
+ Proof. exact (Rmul_ext Reqe). Qed.
+
+ Add Morphism ropp with signature (req ==> req) as ropp_ext.
+ Proof. exact (Ropp_ext Reqe). Qed.
+
+ Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext.
+ Proof. exact (ARsub_ext Rsth Reqe ARth). Qed.
+
  Ltac rsimpl := gen_srewrite Rsth Reqe ARth.
 
  Ltac add_push := gen_add_push radd Rsth Reqe ARth.
diff --git a/plugins/setoid_ring/Ring_theory.v b/plugins/setoid_ring/Ring_theory.v
index 8dda5ecd3..335a68d70 100644
--- a/plugins/setoid_ring/Ring_theory.v
+++ b/plugins/setoid_ring/Ring_theory.v
@@ -254,8 +254,12 @@ Section ALMOST_RING.
  Section SEMI_RING.
  Variable SReqe : sring_eq_ext radd rmul req.
 
-   Add Morphism radd : radd_ext1.  exact (SRadd_ext SReqe). Qed.
-   Add Morphism rmul : rmul_ext1.  exact (SRmul_ext SReqe). Qed.
+   Add Morphism radd with signature (req ==> req ==> req) as radd_ext1.
+   Proof. exact (SRadd_ext SReqe). Qed.
+
+   Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext1.
+   Proof. exact (SRmul_ext SReqe). Qed.
+
  Variable SRth : semi_ring_theory 0 1 radd rmul req.
 
  (** Every semi ring can be seen as an almost ring, by taking :
@@ -323,9 +327,15 @@ Section ALMOST_RING.
  Notation "- x" := (ropp x).
 
  Variable Reqe : ring_eq_ext radd rmul ropp req.
-   Add Morphism radd : radd_ext2.  exact (Radd_ext Reqe). Qed.
-   Add Morphism rmul : rmul_ext2.  exact (Rmul_ext Reqe). Qed.
-   Add Morphism ropp : ropp_ext2.  exact (Ropp_ext Reqe). Qed.
+
+   Add Morphism radd with signature (req ==> req ==> req) as radd_ext2.
+   Proof. exact (Radd_ext Reqe). Qed.
+
+   Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext2.
+   Proof. exact (Rmul_ext Reqe). Qed.
+
+   Add Morphism ropp with signature (req ==> req) as ropp_ext2.
+   Proof. exact (Ropp_ext Reqe). Qed.
 
  Section RING.
  Variable Rth : ring_theory 0 1 radd rmul rsub ropp req.
@@ -393,14 +403,25 @@ Section ALMOST_RING.
   Notation "?=!" := ceqb. Notation "[ x ]" := (phi x).
  Variable Csth : Equivalence ceq.
  Variable Ceqe : ring_eq_ext cadd cmul copp ceq.
+
    Add Setoid C ceq Csth as C_setoid.
-   Add Morphism cadd : cadd_ext.  exact (Radd_ext Ceqe). Qed.
-   Add Morphism cmul : cmul_ext.  exact (Rmul_ext Ceqe). Qed.
-   Add Morphism copp : copp_ext.  exact (Ropp_ext Ceqe). Qed.
+
+   Add Morphism cadd with signature (ceq ==> ceq ==> ceq) as cadd_ext.
+   Proof. exact (Radd_ext Ceqe). Qed.
+
+   Add Morphism cmul with signature (ceq ==> ceq ==> ceq) as cmul_ext.
+   Proof. exact (Rmul_ext Ceqe). Qed.
+
+   Add Morphism copp with signature (ceq ==> ceq) as copp_ext.
+   Proof. exact (Ropp_ext Ceqe). Qed.
+
  Variable Cth : ring_theory cO cI cadd cmul csub copp ceq.
  Variable Smorph : semi_morph 0 1 radd rmul req cO cI cadd cmul ceqb phi.
  Variable phi_ext : forall x y, ceq x y -> [x] == [y].
-   Add Morphism phi : phi_ext1.  exact phi_ext. Qed.
+
+   Add Morphism phi with signature (ceq ==> req) as phi_ext1.
+   Proof. exact phi_ext. Qed.
+
  Lemma Smorph_opp x : [-!x] == -[x].
  Proof.
   rewrite <-  (Rth.(Radd_0_l) [-!x]).
diff --git a/test-suite/success/setoid_test.v b/test-suite/success/setoid_test.v
index 1f24ef2a6..c8dfcd2cb 100644
--- a/test-suite/success/setoid_test.v
+++ b/test-suite/success/setoid_test.v
@@ -33,7 +33,8 @@ Qed.
 
 Add Setoid set same setoid_set as setsetoid.
 
-Add Morphism In : In_ext.
+Add Morphism In with signature (eq ==> same ==> iff) as In_ext.
+Proof.
 unfold same; intros a s t H; elim (H a); auto.
 Qed.
 
@@ -50,10 +51,9 @@ simpl; right.
 apply (H2 H1).
 Qed.
 
-Add Morphism Add : Add_ext.
+Add Morphism Add with signature (eq ==> same ==> same) as Add_ext.
 split; apply add_aux.
 assumption.
-
 rewrite H.
 reflexivity.
 Qed.
@@ -90,7 +90,7 @@ Qed.
 Parameter P : set -> Prop.
 Parameter P_ext : forall s t : set, same s t -> P s -> P t.
 
-Add Morphism P : P_extt.
+Add Morphism P with signature (same ==> iff) as P_extt.
 intros; split; apply P_ext; (assumption || apply (Seq_sym _ _ setoid_set); assumption).
 Qed.
 
@@ -113,7 +113,7 @@ Definition f: forall A : Set, A -> A := fun A x => x.
 
 Add Relation (id A) (rel A) as eq_rel.
 
-Add Morphism (@f A) : f_morph.
+Add Morphism (@f A) with signature (eq ==> eq) as f_morph.
 Proof.
 unfold rel, f. trivial.
 Qed.
diff --git a/test-suite/success/setoid_test2.v b/test-suite/success/setoid_test2.v
index 6baf79701..79467e549 100644
--- a/test-suite/success/setoid_test2.v
+++ b/test-suite/success/setoid_test2.v
@@ -134,8 +134,8 @@ Axiom SetoidS2 : Setoid_Theory S2 eqS2.
 Add Setoid S2 eqS2 SetoidS2 as S2setoid.
 
 Axiom f : S1 -> nat -> S2.
-Add Morphism f : f_compat. Admitted.
-Add Morphism f : f_compat2. Admitted.
+Add Morphism f with signature (eqS1 ==> eq ==> eqS2) as f_compat. Admitted.
+Add Morphism f with signature (eqS1 ==> eq ==> eqS2) as f_compat2. Admitted.
 
 Theorem test1: forall x y, (eqS1 x y) -> (eqS2 (f x 0) (f y 0)).
  intros.
@@ -151,7 +151,7 @@ Theorem test1': forall x y, (eqS1 x y) -> (eqS2 (f x 0) (f y 0)).
 Qed.
 
 Axiom g : S1 -> S2 -> nat.
-Add Morphism g : g_compat. Admitted.
+Add Morphism g with signature (eqS1 ==> eqS2 ==> eq) as g_compat. Admitted.
 
 Axiom P : nat -> Prop.
 Theorem test2:
@@ -190,13 +190,13 @@ Theorem test5:
 Qed.
 
 Axiom f_test6 : S2 -> Prop.
-Add Morphism f_test6 : f_test6_compat. Admitted.
+Add Morphism f_test6 with signature (eqS2 ==> iff) as f_test6_compat. Admitted.
 
 Axiom g_test6 : bool -> S2.
-Add Morphism g_test6 : g_test6_compat. Admitted.
+Add Morphism g_test6 with signature (eq ==> eqS2) as g_test6_compat. Admitted.
 
 Axiom h_test6 : S1 -> bool.
-Add Morphism h_test6 : h_test6_compat. Admitted.
+Add Morphism h_test6 with signature (eqS1 ==> eq) as h_test6_compat. Admitted.
 
 Theorem test6:
  forall E1 E2, (eqS1 E1 E2) -> (f_test6 (g_test6 (h_test6 E2))) ->
@@ -223,7 +223,7 @@ Add Setoid S1_test8 eqS1_test8 SetoidS1_test8 as S1_test8setoid.
 Instance eqS1_test8_default : DefaultRelation eqS1_test8.
 
 Axiom f_test8 : S2 -> S1_test8.
-Add Morphism f_test8 : f_compat_test8. Admitted.
+Add Morphism f_test8 with signature (eqS2 ==> eqS1_test8) as f_compat_test8. Admitted.
 
 Axiom eqS1_test8': S1_test8 -> S1_test8 -> Prop.
 Axiom SetoidS1_test8' : Setoid_Theory S1_test8 eqS1_test8'.
@@ -233,7 +233,7 @@ Add Setoid S1_test8 eqS1_test8' SetoidS1_test8' as S1_test8setoid'.
   (S1_test8, eqS1_test8'). However this does not happen and
   there is still no syntax for it ;-( *)
 Axiom g_test8 : S1_test8 -> S2.
-Add Morphism g_test8 : g_compat_test8. Admitted.
+Add Morphism g_test8 with signature (eqS1_test8 ==> eqS2) as g_compat_test8. Admitted.
 
 Theorem test8:
  forall x x': S2, (eqS2 x x') ->
diff --git a/theories/FSets/FSetProperties.v b/theories/FSets/FSetProperties.v
index 25b042ca9..0041bfa1c 100644
--- a/theories/FSets/FSetProperties.v
+++ b/theories/FSets/FSetProperties.v
@@ -762,7 +762,7 @@ Module WProperties_fun (Import E : DecidableType)(M : WSfun E).
   rewrite (cardinal_2 (s:=remove x s') (s':=s') (x:=x)); eauto with set.
   Qed.
 
-  Add Morphism cardinal : cardinal_m.
+  Add Morphism cardinal with signature (Equal ==> Logic.eq) as cardinal_m.
   Proof.
   exact Equal_cardinal.
   Qed.
diff --git a/theories/QArith/Qreduction.v b/theories/QArith/Qreduction.v
index 88e1298fb..5d055b547 100644
--- a/theories/QArith/Qreduction.v
+++ b/theories/QArith/Qreduction.v
@@ -101,7 +101,7 @@ Proof.
  - apply Qred_complete.
 Qed.
 
-Add Morphism Qred : Qred_comp.
+Add Morphism Qred with signature (Qeq ==> Qeq) as Qred_comp.
 Proof.
   intros. now rewrite !Qred_correct.
 Qed.
@@ -125,19 +125,19 @@ Proof.
   intros; unfold Qminus'; apply Qred_correct; auto.
 Qed.
 
-Add Morphism Qplus' : Qplus'_comp.
+Add Morphism Qplus' with signature (Qeq ==> Qeq ==> Qeq) as Qplus'_comp.
 Proof.
   intros; unfold Qplus'.
   rewrite H, H0; auto with qarith.
 Qed.
 
-Add Morphism Qmult' : Qmult'_comp.
+Add Morphism Qmult' with signature (Qeq ==> Qeq ==> Qeq) as Qmult'_comp.
 Proof.
   intros; unfold Qmult'.
   rewrite H, H0; auto with qarith.
 Qed.
 
-Add Morphism Qminus' : Qminus'_comp.
+Add Morphism Qminus' with signature (Qeq ==> Qeq ==> Qeq) as Qminus'_comp.
 Proof.
   intros; unfold Qminus'.
   rewrite H, H0; auto with qarith.