proposition: Lemma subst_exp_close_exp_wrt_exp_rec_open_exp_wrt_exp_rec_mutual : (forall e2 e1 x1 x2 n1, x2 `notin` fv_exp e2 -> x2 `notin` fv_exp e1 -> x2 <> x1 -> degree_exp_wrt_exp n1 e1 -> subst_exp e1 x1 e2 = close_exp_wrt_exp_rec n1 x2 (subst_exp e1 x1 (open_exp_wrt_exp_rec n1 (var_f x2) e2))).
proof: Proof. apply_mutual_ind exp_mutrec; default_simp. Qed.
imports: Coq.Logic.FunctionalExtensionality Coq.Program.Equality Metalib.Metatheory Metalib.LibLNgen Stlc