(** This file is part of the Flocq formalization of floating-point arithmetic in Coq: http://flocq.gforge.inria.fr/  Copyright (C) 2010-2013 Sylvie Boldo #<br /># Copyright (C) 2010-2013 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. *)
(** * Basic properties of floating-point formats: lemmas about mantissa, exponent... *)
Section Float_prop.
Variable beta : radix.
Notation bpow e := (bpow beta e).

Theorem F2R_lt_bpow :
forall f : float beta, forall e',
(Zabs (Fnum f) < Zpower beta (e' - Fexp f))%Z ->
(Rabs (F2R f) < bpow e')%R.