(** Multiplication by 2 is diagonal addition. *)

Theorem Bmult2_Bplus:
forall plus_nan mult_nan mode (f: binary_float),
(forall (x y: binary_float),
is_nan _ _ x = true -> is_finite _ _ y = true -> plus_nan x x = mult_nan x y) ->
Bplus _ _ _ Hmax plus_nan mode f f = Bmult _ _ _ Hmax mult_nan mode f (BofZ 2%Z).