(* "two_power" and "zero_lt_pow" are copied from 
    contribs/BORDEAUX/Additions/two_power.v
    to avoid Requiring the contribution *)
Fixpoint two_power (m : nat) : nat :=
  match m with
  | O => 1
  | S n => 2 * two_power n
  end.

Lemma zero_lt_pow : forall a : nat, 0 < two_power a.