proposition: Theorem eq_rect_combine : forall n1 n2 n2' (w1 : word n1) (w2 : word n2') Heq, eq_rect (n1 + n2') (fun n => word n) (combine w1 w2) (n1 + n2) Heq = combine w1 (eq_rect n2' (fun n => word n) w2 n2 (Private_plus_reg_l _ _ _ Heq)).
proof: Proof. intros. generalize (Private_plus_reg_l n2' n2 n1 Heq); intros. generalize dependent Heq. generalize dependent w2. rewrite e; intros. repeat rewrite <- (eq_rect_eq_dec eq_nat_dec). 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