proposition: Lemma wordToNat_natToWord_idempotent : forall sz n, (N.of_nat n < Npow2 sz)%N -> wordToNat (natToWord sz n) = n.
proof: Proof. intros sz n H. destruct (wordToNat_natToWord sz n) as [x]; intuition. destruct x as [|x]. simpl in *; lia. simpl in *. apply Nlt_out in H. autorewrite with N in *. rewrite Npow2_nat in *. generalize dependent (x * pow2 sz). intros; 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