(** 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_p1_le_bpow :
forall m e1 e2 : Z,
(0 < m)%Z ->
(F2R (Float beta m e1) < bpow e2)%R ->
(F2R (Float beta (m + 1) e1) <= bpow e2)%R.