(** We cannot have a function complementing all bits of a number, otherwise it would have an infinity of bit 1. Nonetheless, we can design a bounded complement *)
Definition lnot a n := lxor a (ones n).
#[global]
Instance ones_wd : Proper (eq==>eq) ones.

Lemma lxor_lnot_lnot : forall a b n,
lxor (lnot a n) (lnot b n) == lxor a b.