proposition: Theorem split1_iter : forall n1 n2 n3 Heq w, split1 n1 n2 (split1 (n1 + n2) n3 w) = split1 n1 (n2 + n3) (match Heq in _ = N return word N with | refl_equal => w end).
proof: Proof. induction n1; simpl; intuition. f_equal. apply whd_match. assert (n1 + n2 + n3 = n1 + (n2 + n3)) as Heq' by lia. rewrite IHn1 with (Heq:=Heq'). 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