proposition: Lemma wordToNat_wplus sz (w1 w2: word sz): #(w1 ^+ w2) = (#w1 + #w2) mod (pow2 sz).
proof: Proof. rewrite <- (natToWord_wordToNat w1) at 1. rewrite <- (natToWord_wordToNat w2) at 1. rewrite <- natToWord_plus. rewrite wordToNat_natToWord_eqn. auto. 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