proposition: Lemma mult_pow2_bound_ex: forall a c x y, x < pow2 a -> y < pow2 (c - a) -> c >= a -> x * y < pow2 c.
proof: Proof. intros. replace c with (a + (c - a)) by lia. apply mult_pow2_bound; auto. 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