proposition: Lemma pow2_bound_mono: forall a b x, x < pow2 a -> a <= b -> x < pow2 b.
proof: Proof. intros. replace b with (a + (b - a)) by lia. rewrite pow2_add_mul. apply lt_mul_mono; auto. pose proof (zero_lt_pow2 (b - a)). 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