(** Nan payload operations for single <-> double conversions. *)
Definition expand_pl (pl: nan_pl 24) : nan_pl 53.

(* Specifications: *)
Theorem mul_commut:
forall x y, is_nan _ _ x = false \/ is_nan _ _ y = false -> mul x y = mul y x.
Theorem mul_commut:
forall x y, is_nan _ _ x = false \/ is_nan _ _ y = false -> mul x y = mul y x.