proposition: Lemma wminus_plus_distr: forall {sz} (x y z: word sz), x ^- (y ^+ z) = x ^- y ^- z.
proof: Proof. intros. apply wplus_cancel with (c:= y ^+ z). rewrite wminus_def, <-wplus_assoc. rewrite wplus_comm with (y:= y ^+ z), wminus_inv. rewrite wplus_comm with (x:= x), wplus_unit. rewrite !wminus_def, <-wplus_assoc. rewrite wplus_assoc with (x:= ^~ z). rewrite wplus_comm with (x:= ^~ z). rewrite <-wplus_assoc with (x:= y). rewrite wplus_comm with (x:= ^~ z), wminus_inv. rewrite wplus_comm with (x:= y), wplus_unit. rewrite <-wplus_assoc. rewrite wplus_comm with (x:= ^~ y), wminus_inv. rewrite wplus_comm, wplus_unit. 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