File: SplitRmult.v

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(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \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)         *)
(************************************************************************)

(*i Lemma mult_non_zero :(r1,r2:R)``r1<>0`` /\ ``r2<>0`` -> ``r1*r2<>0``. i*)


From Stdlib Require Import Rdefinitions Raxioms RIneq.

Ltac split_Rmult :=
  match goal with
    |  |- ((?X1 * ?X2)%R <> 0%R) =>
      apply Rmult_integral_contrapositive; split; try split_Rmult
  end.