(** 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 lnot_spec_low : forall a n m, m<n ->
(lnot a n).[m] = negb a.[m].