(**
This file is part of the Coquelicot formalization of real
analysis in Coq: http://coquelicot.saclay.inria.fr/

Copyright (C) 2011-2015 Sylvie Boldo
#<br />#
Copyright (C) 2011-2015 Catherine Lelay
#<br />#
Copyright (C) 2011-2015 Guillaume Melquiond

This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 3 of the License, or (at your option) any later version.

This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
COPYING file for more details.
*)

(** * This file describes basic missing facts about the standard library of reals and a few concerning ssreflect.seq. It also contains a definition of the [sign] function. *)

(** Tactic for changing the last argument of a property to an evar,
    in order to apply theorems modulo equality. *)

Ltac evar_last :=
  match goal with
  | |- ?f ?x =>
    let tx := type of x in
    let tx := eval simpl in tx in
    let tmp := fresh "tmp" in
    evar (tmp : tx) ;
    refine (@eq_ind tx tmp f _ x _) ;
    unfold tmp ; clear tmp
  end.

Lemma floor_ex : forall x : R, {n : Z | IZR n <= x < IZR n + 1}.