(** Properties of [lxor] and others, directly deduced from properties of [xorb] and others. *)
#[global]
Instance land_wd : Proper (eq ==> eq ==> eq) land.
#[global]
Instance lor_wd : Proper (eq ==> eq ==> eq) lor.
#[global]
Instance ldiff_wd : Proper (eq ==> eq ==> eq) ldiff.

Lemma land_odd_r :
forall a b, land a (2 * b + 1) == 2 * (land (div2 a) b) + odd a.