proposition: Lemma wordToNat_wmult': forall sz (a b: word sz), (#a * #b < pow2 sz)%nat -> #(a ^* b) = #a * #b.
proof: Proof. intros. rewrite <-? wordToN_to_nat in *. rewrite <-? Nnat.N2Nat.inj_mul in *. rewrite <- Npow2_nat in *. apply Nlt_in in H. rewrite wordToN_mult by assumption. reflexivity. Qed.
imports: Coq.Classes.Morphisms Coq.Classes.Morphisms_Prop Coq.Classes.Equivalence Coq.Arith.PeanoNat Coq.ZArith.BinInt  Coq.Arith.Arith Coq.NArith.NArith Coq.Bool.Bool Coq.ZArith.ZArith Coq.Logic.Eqdep_dec Coq.Logic.EqdepFacts Coq.Program.Tactics Coq.Program.Equality Coq.setoid_ring.Ring Coq.setoid_ring.Ring_polynom bbv.Nomega bbv.ZLib bbv.NatLib bbv.NLib bbv.N_Z_nat_conversions bbv.DepEq bbv.DepEqNat bbv.ReservedNotations Coq.micromega.Lia