From 9043add656177eeac1491a73d2f3ab92bec0013c Mon Sep 17 00:00:00 2001
From: Benjamin Barenblat <bbaren@debian.org>
Date: Sat, 29 Dec 2018 14:31:27 -0500
Subject: Imported Upstream version 8.8.2

---
 plugins/setoid_ring/Ring_theory.v | 57 ++++++++++++++++++++++++++++-----------
 1 file changed, 42 insertions(+), 15 deletions(-)

(limited to 'plugins/setoid_ring/Ring_theory.v')

diff --git a/plugins/setoid_ring/Ring_theory.v b/plugins/setoid_ring/Ring_theory.v
index f7757a18..d67a8d8d 100644
--- a/plugins/setoid_ring/Ring_theory.v
+++ b/plugins/setoid_ring/Ring_theory.v
@@ -1,9 +1,11 @@
 (************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
 (*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
 (************************************************************************)
 
 Require Import Setoid Morphisms BinPos BinNat.
@@ -254,12 +256,16 @@ 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 :
-        -x = x and x - y = x + y *)
+        [-x = x] and [x - y = x + y] *)
  Definition SRopp (x:R) := x. Notation "- x" := (SRopp x).
 
  Definition SRsub x y := x + -y. Infix "-" := SRsub.
@@ -323,9 +329,15 @@ 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 +405,29 @@ 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 Parametric Relation : C ceq
+     reflexivity  proved by Csth.(@Equivalence_Reflexive _ _)
+     symmetry     proved by Csth.(@Equivalence_Symmetric _ _)
+     transitivity proved by Csth.(@Equivalence_Transitive _ _)
+    as C_setoid.
+
+   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]).
-- 
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