(** 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.

(** Bounded complement and other operations *)
Lemma lor_ones_low : forall a n, log2 a < n ->
lor a (ones n) == ones n.