(** Commutation properties with addition, subtraction, multiplication. *)

Theorem BofZ_mult_2p:
forall nan x p,
Z.abs x <= 2^emax - 2^(emax-prec) ->
2^prec <= Z.abs x ->
0 <= p <= emax - 1 ->
Bmult _ _ _ Hmax nan mode_NE (BofZ x) (BofZ (2^p)) = BofZ (x * 2^p).