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-rw-r--r--plugins/ltac/rewrite.ml10
-rw-r--r--plugins/micromega/EnvRing.v16
-rw-r--r--plugins/setoid_ring/Field_theory.v24
-rw-r--r--plugins/setoid_ring/InitialRing.v50
-rw-r--r--plugins/setoid_ring/Ring_polynom.v16
-rw-r--r--plugins/setoid_ring/Ring_theory.v39
-rw-r--r--test-suite/success/setoid_test.v10
-rw-r--r--test-suite/success/setoid_test2.v16
-rw-r--r--theories/FSets/FSetProperties.v2
-rw-r--r--theories/QArith/Qreduction.v8
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.
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-25 16:15:15 +0000