proposition: Theorem eq_rect_split1_eq2 : forall n1 n2 n2' (w: word (n1 + n2)) Heq, split1 n1 n2 w = split1 n1 n2' (eq_rect (n1 + n2) (fun y : nat => word y) w (n1 + n2') Heq).
proof: Proof. intros. assert (n2 = n2') as H' by lia. generalize dependent w. generalize dependent Heq. rewrite H'; intros. 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