proposition: Theorem split2_iter : forall n1 n2 n3 Heq w, split2 n2 n3 (split2 n1 (n2 + n3) w) = split2 (n1 + n2) n3 (match Heq in _ = N return word N with | refl_equal => w end).
proof: Proof. induction n1 as [|n1 IHn1]; simpl; intros n2 n3 Heq w; intuition. rewrite (UIP_dec eq_nat_dec Heq (refl_equal _)); reflexivity. rewrite (IHn1 _ _ (Nat.add_assoc _ _ _)). f_equal. apply wtl_match. 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