proposition: Lemma wordToNat_natToWord_le : forall sz n, (wordToNat (natToWord sz n) <= n)%nat.
proof: Proof. intros. case_eq (lt_dec n (pow2 sz)); intros. rewrite wordToNat_natToWord_idempotent'; auto. eapply Nat.le_trans. apply Nat.lt_le_incl. apply wordToNat_bound. match goal with H : _ = right _ |- _ => clear H end. 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