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/RealField.v | 31 +++++++++++++++++++++++++------
 1 file changed, 25 insertions(+), 6 deletions(-)

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

diff --git a/plugins/setoid_ring/RealField.v b/plugins/setoid_ring/RealField.v
index 29372212..38bc58a6 100644
--- a/plugins/setoid_ring/RealField.v
+++ b/plugins/setoid_ring/RealField.v
@@ -1,3 +1,13 @@
+(************************************************************************)
+(*         *   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          *)
+(*         *     (see LICENSE file for the text of the license)         *)
+(************************************************************************)
+
 Require Import Nnat.
 Require Import ArithRing.
 Require Export Ring Field.
@@ -59,11 +69,12 @@ Notation Rset := (Eqsth R).
 Notation Rext := (Eq_ext Rplus Rmult Ropp).
 
 Lemma Rlt_0_2 : 0 < 2.
+Proof.
 apply Rlt_trans with (0 + 1).
  apply Rlt_n_Sn.
  rewrite Rplus_comm.
    apply Rplus_lt_compat_l.
-    replace 1 with (0 + 1).
+    replace R1 with (0 + 1).
   apply Rlt_n_Sn.
   apply Rplus_0_l.
 Qed.
@@ -126,9 +137,17 @@ Ltac Rpow_tac t :=
   | _ => constr:(N.of_nat t)
   end.
 
-Add Field RField : Rfield
-   (completeness Zeq_bool_complete, power_tac R_power_theory [Rpow_tac]).
-
-
-
+Ltac IZR_tac t :=
+  match t with
+  | R0 => constr:(0%Z)
+  | R1 => constr:(1%Z)
+  | IZR ?u =>
+    match isZcst u with
+    | true => u
+    | _ => constr:(InitialRing.NotConstant)
+    end
+  | _ => constr:(InitialRing.NotConstant)
+  end.
 
+Add Field RField : Rfield
+   (completeness Zeq_bool_complete, constants [IZR_tac], power_tac R_power_theory [Rpow_tac]).
-- 
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