proposition: Lemma wzero_wones: forall sz, sz >= 1 -> natToWord sz 0 <> wones sz.
proof: Proof. intros. unfold not. intros. pose proof (f_equal (@wordToNat sz) H0) as sth. unfold wzero in *. rewrite roundTrip_0 in *. rewrite wones_pow2_minus_one in sth. destruct sz; [lia | ]. pose proof (NatLib.one_lt_pow2 sz). 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