(** If two numbers produce the same stream of bits, they are equal. *)

Lemma bits_inj_iff' : forall a b, (forall n, 0<=n -> a.[n] = b.[n]) <-> a == b.
Tactic Notation "bitwise" "as" simple_intropattern(m) simple_intropattern(Hm)
:= apply bits_inj'; intros m Hm; autorewrite with bitwise.