proposition: Lemma wneg_wplus_distr: forall sz (w1 w2: word sz), wneg (w1 ^+ w2) = wneg w1 ^+ wneg w2.
proof: Proof. intros. apply wplus_cancel with (c:= w1 ^+ w2). rewrite wplus_comm, wminus_inv. rewrite wplus_comm, wplus_assoc. rewrite <-wplus_assoc with (x:= w1). rewrite wplus_comm with (x:= w2). rewrite wplus_assoc. rewrite wminus_inv. rewrite wplus_wzero_2. rewrite wminus_inv. 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