proposition: Lemma wordToNat_natToWord_eqn sz: forall n, wordToNat (natToWord sz n) = n mod (pow2 sz).
proof: Proof. intros. pose proof (wordToNat_natToWord sz n). destruct H as [? [? ?]]. rewrite H. assert (sth: pow2 sz * x = x * pow2 sz) by (apply Nat.mul_comm). rewrite <- sth in *. clear sth. pose proof (wordToNat_bound (natToWord sz n)). apply (Nat.mod_unique n (pow2 sz) x (n - pow2 sz * x)); try 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