Imported Upstream version 8.4~betaupstream/8.4_beta

1 files changed, 34 insertions, 0 deletions

diff --git a/plugins/setoid_ring/Rings_R.v b/plugins/setoid_ring/Rings_R.v
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+++ b/plugins/setoid_ring/Rings_R.v
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+Require Export Cring.
+Require Export Integral_domain.
+
+(* Real numbers *)
+Require Import Reals.
+Require Import RealField.
+
+Lemma Rsth : Setoid_Theory R (@eq R).
+constructor;red;intros;subst;trivial.
+Qed.
+
+Instance Rops: (@Ring_ops R 0%R 1%R Rplus Rmult Rminus Ropp (@eq R)).
+
+Instance Rri : (Ring (Ro:=Rops)).
+constructor;
+try (try apply Rsth;
+   try (unfold respectful, Proper; unfold equality; unfold eq_notation in *;
+  intros; try rewrite H; try rewrite H0; reflexivity)).
+ exact Rplus_0_l. exact Rplus_comm. symmetry. apply Rplus_assoc.
+ exact Rmult_1_l.  exact Rmult_1_r. symmetry. apply Rmult_assoc.
+ exact Rmult_plus_distr_r. intros; apply Rmult_plus_distr_l. 
+exact Rplus_opp_r.
+Defined.
+
+Instance Rcri: (Cring (Rr:=Rri)).
+red. exact Rmult_comm. Defined.
+
+Lemma R_one_zero: 1%R <> 0%R.
+discrR.
+Qed.
+
+Instance Rdi : (Integral_domain (Rcr:=Rcri)). 
+constructor. 
+exact Rmult_integral. exact R_one_zero. Defined.