proposition: Lemma uwordToZ_ZToWord_mod: forall (sz : nat) (z : Z), (0 <= z)%Z -> uwordToZ (ZToWord sz z) = (z mod 2 ^ (Z.of_nat sz))%Z.
proof: Proof. intros. pose proof (uwordToZ_ZToWord_k sz H) as P. destruct P as [k [P Q]]. pose proof (uwordToZ_bound (ZToWord sz z)) as B. rewrite P in *. clear P. rewrite Zmod_eq by (apply Zpow2_pos). pose proof (Z.div_unique_pos z (2 ^ Z.of_nat sz) k (z - k * 2 ^ Z.of_nat sz)) as U. rewrite U. - reflexivity. - lia. - rewrite Z.mul_comm. 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