proposition: Lemma wxor_assoc : forall sz (w1 w2 w3 : word sz), wxor w1 (wxor w2 w3) = wxor (wxor w1 w2) w3.
proof: Proof. unfold wxor. induction sz; intros; rewrite (shatter_word w1), (shatter_word w2), (shatter_word w3); auto. simpl; f_equal. rewrite xorb_assoc_reverse; auto. rewrite IHsz. 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