proposition: Lemma pow2_le_S : forall sz, (pow2 sz) + 1 <= pow2 (sz + 1).
proof: Proof. induction sz; simpl; auto. repeat rewrite Nat.add_0_r. rewrite pow2_add_mul. repeat rewrite mul2_add. pose proof (zero_lt_pow2 sz). 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