proposition: Lemma wlshift_mul_Zpow2: forall sz n (a: word sz), (0 <= n)%Z -> wlshift a (Z.to_nat n) = a ^* ZToWord sz (2 ^ n).
proof: Proof. intros. rewrite wlshift_mul_pow2. f_equal. change 2 with (Z.to_nat 2). rewrite <- Z2Nat.inj_pow by lia. apply natToWord_Z_to_nat. apply Z.pow_nonneg. lia. 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