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Diffstat (limited to 'theories/Reals/LegacyRfield.v')
-rw-r--r-- | theories/Reals/LegacyRfield.v | 40 |
1 files changed, 40 insertions, 0 deletions
diff --git a/theories/Reals/LegacyRfield.v b/theories/Reals/LegacyRfield.v new file mode 100644 index 00000000..b33274af --- /dev/null +++ b/theories/Reals/LegacyRfield.v @@ -0,0 +1,40 @@ +(************************************************************************) +(* v * The Coq Proof Assistant / The Coq Development Team *) +(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *) +(* \VV/ **************************************************************) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(************************************************************************) + +(*i $Id$ i*) + +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. |