proposition: Lemma wplus_wplus_pow2 sz (x1 x2 y1 y2: word (sz + 1)): x1 = y1 ^+ $(pow2 sz) -> x2 = y2 ^+ $(pow2 sz) -> x1 ^+ x2 = y1 ^+ y2.
proof: Proof. intros. rewrite H. rewrite <- wplus_assoc. rewrite wplus_comm. rewrite wplus_comm in H0. rewrite H0. rewrite wplus_assoc. rewrite pow2_wplus_wzero. rewrite wzero_wplus. rewrite wplus_comm. 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