(** ** Algebraic identities *)
(** Commutativity of addition and multiplication *)

(* Specifications: *)
Theorem Bplus_commut:
forall plus_nan mode (x y: binary_float),
plus_nan x y = plus_nan y x ->
Bplus _ _ _ Hmax plus_nan mode x y = Bplus _ _ _ Hmax plus_nan mode y x.
Theorem Bmult_commut:
forall mult_nan mode (x y: binary_float),
mult_nan x y = mult_nan y x ->
Bmult _ _ _ Hmax mult_nan mode x y = Bmult _ _ _ Hmax mult_nan mode y x.
Theorem Bplus_commut:
forall plus_nan mode (x y: binary_float),
plus_nan x y = plus_nan y x ->
Bplus _ _ _ Hmax plus_nan mode x y = Bplus _ _ _ Hmax plus_nan mode y x.
Theorem Bmult_commut:
forall mult_nan mode (x y: binary_float),
mult_nan x y = mult_nan y x ->
Bmult _ _ _ Hmax mult_nan mode x y = Bmult _ _ _ Hmax mult_nan mode y x.