proposition: Theorem wbit_and_not: forall sz sz' (n : word sz'), (wordToNat n < sz)%nat -> (wbit sz n) ^& wnot (wbit sz n) = wzero sz.
proof: Proof. induction sz; intros; try lia. unfold wbit, wzero, wand, wnot. simpl. f_equal. apply andb_negb_r. destruct (zero_or_wordToNat_S n); subst. rewrite roundTrip_0; simpl. apply wand_kill. do 2 destruct H0. rewrite H0; simpl. rewrite div2_pow2_twice. fold wnot. rewrite <- H1. eapply IHsz. 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