proposition: Theorem wordToNat_plusone: forall sz w w', w < w' -> wordToNat (w ^+ natToWord sz 1) = S (wordToNat w).
proof: Proof. intros. destruct sz. exfalso. rewrite word0 with (w:=w') in H. rewrite word0 with (w:=w) in H. apply wlt_lt in H. lia. rewrite wplus_alt. unfold wplusN, wordBinN. rewrite wordToNat_natToWord_idempotent'. rewrite roundTrip_1. lia. eapply Nat.le_lt_trans; [| eapply wordToNat_bound ]. rewrite wordToNat_natToWord_idempotent'; [| erewrite <- roundTrip_1 at 1; apply wordToNat_bound ]. apply wlt_lt in H. instantiate (1:=w'). 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