proposition: Lemma wor_r_wzero_1 sz: forall w1 w2, w1 ^| w2 = natToWord sz 0 -> w2 = natToWord sz 0.
proof: Proof. induction w1; simpl; auto; intros. pose proof (shatter_word w2) as sth. simpl in sth. rewrite sth in *. unfold wor in H. simpl in H. unfold natToWord in H. unfold natToWord. fold (natToWord n (Nat.div2 0)) in *. unfold Nat.div2, mod2 in *. inversion H. destruct_existT. rewrite (IHw1 _ H2). f_equal. destruct b, (whd w2); auto. 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