Module Import ShiftNotations.
Notation "l ^<< r" := (@wlshift' _ l%word r) : word_scope.
Notation "l ^>> r" := (@wrshift' _ l%word r) : word_scope.
End ShiftNotations.
(** * Setting an individual bit *)
Definition wbit sz sz' (n : word sz') := natToWord sz (pow2 (wordToNat n)).
(*! Facts *)
Hint Rewrite div2_double div2_S_double: div2.
Local Hint Resolve mod2_S_double mod2_double.
induction w as [|b]; rewrite wordToNat_wordToNat'; intuition; f_equal; unfold natToWord, wordToNat'; fold natToWord; fold wordToNat';
destruct b; f_equal; autorewrite with div2; intuition.
Qed.
induction sz; simpl; intuition.
Qed.
Hint Rewrite roundTrip_0 : wordToNat.

Lemma wordToNat_natToWord' : forall sz w, exists k, wordToNat (natToWord sz w) + k * pow2 sz = w.