proposition: Lemma wplus_one_neq: forall {sz} (w: word (S sz)), w ^+ (natToWord (S sz) 1) <> w.
proof: Proof. intros; intro Hx. rewrite wplus_comm in Hx. assert ((natToWord (S sz) 1) ^+ w ^- w = w ^- w) by (rewrite Hx; reflexivity). clear Hx. do 2 rewrite wminus_def in H. rewrite <-wplus_assoc in H. rewrite wminus_inv in H. rewrite wplus_comm, wplus_unit in H. inversion H. 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