proposition: Theorem combine_split_eq_rect2 : forall n1 n2 n2' (w : word (n1 + n2)) Heq, combine (split1 n1 n2 w) (eq_rect n2 (fun n => word n) (split2 n1 n2 w) n2' Heq) = eq_rect (n1 + n2) (fun n => word n) w (n1 + n2') (eq_rect_split2_helper _ Heq).
proof: Proof. intros. assert (n2 = n2') by lia. generalize dependent Heq. generalize dependent w. rewrite <- H; intros. repeat rewrite <- (eq_rect_eq_dec eq_nat_dec). apply combine_split. 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