(** 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 ldiff_odd_l :
forall a b, ldiff (2 * a + 1) b == 2 * ldiff a (div2 b) + even b.