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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
Require Export Raxioms.
Require Export LegacyField.
Import LegacyRing_theory.
Section LegacyRfield.
Open Scope R_scope.
Lemma RLegacyTheory : Ring_Theory Rplus Rmult 1 0 Ropp (fun x y:R => false).
split.
exact Rplus_comm.
symmetry in |- *; apply Rplus_assoc.
exact Rmult_comm.
symmetry in |- *; apply Rmult_assoc.
intro; apply Rplus_0_l.
intro; apply Rmult_1_l.
exact Rplus_opp_r.
intros.
rewrite Rmult_comm.
rewrite (Rmult_comm n p).
rewrite (Rmult_comm m p).
apply Rmult_plus_distr_l.
intros; contradiction.
Defined.
End LegacyRfield.
Add Legacy Field
R Rplus Rmult 1%R 0%R Ropp (fun x y:R => false) Rinv RLegacyTheory Rinv_l
with minus := Rminus div := Rdiv.
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