proposition: Lemma wordToNat_mod: forall sz (a b: word sz), b <> $0 -> #(a ^% b) = #a mod #b.
proof: Proof. intros. rewrite <-? wordToN_to_nat in *. rewrite <-? N2Nat.inj_mod in *. - rewrite wordToN_mod by assumption. reflexivity. - intro. apply H. replace 0%N with (wordToN (natToWord sz 0)) in H0. + apply wordToN_inj. exact H0. + erewrite <- wordToN_wzero. reflexivity. 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