proposition: Lemma wmult_wmultZ: forall (sz : nat) (w1 w2 : word sz), w1 ^* w2 = wmultZ w1 w2.
proof: Proof. unfold wmultZ, wmult, wordBinZ, wordBin. intros. do 2 rewrite wordToZ_wordToN. destruct (else_0_to_ex_N (wmsb w1 false) (Npow2 sz)) as [k1 E1]. rewrite E1. clear E1. destruct (else_0_to_ex_N (wmsb w2 false) (Npow2 sz)) as [k2 E2]. rewrite E2. clear E2. do 2 rewrite N2Z.inj_mul. rewrite wmultZ_helper. rewrite <- N2Z.inj_mul. rewrite ZToWord_Npow2_sub_z. rewrite ZToWord_Z_of_N. 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