proposition: Lemma pow2_inc : forall n m, n < m -> pow2 n < pow2 m.
proof: Proof. intros n m; revert n; induction m as [|m IH]; intros n nLm; [lia|]. destruct n; [now apply one_lt_pow2|]. assert (H : pow2 n < pow2 m) by (apply IH; lia). simpl; lia. Qed.
imports: Coq.Classes.Morphisms Coq.Classes.Morphisms_Prop Coq.Bool.Bool Coq.Arith.Arith Coq.micromega.Lia Coq.NArith.NArith Coq.ZArith.ZArith bbv.N_Z_nat_conversions bbv.Nomega