proposition: Theorem wbit_or_same : forall sz sz' (n : word sz'), (wordToNat n < sz)%nat -> (wbit sz n) ^| (wbit sz n) <> wzero sz.
proof: Proof. unfold not. induction sz; intros; try lia. unfold wbit, wzero, wor in *. simpl in *. destruct (zero_or_wordToNat_S n). subst; rewrite roundTrip_0 in *. discriminate. destruct H1. destruct H1. rewrite H1 in *. inversion H0. apply (inj_pair2_eq_dec _ eq_nat_dec) in H5. rewrite div2_pow2_twice in H5. repeat rewrite <- H2 in H5. eapply IHsz; eauto. 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