Is Closable add continuous

lemma IsClosable.add_continuous    (h₁ : U₁.IsClosable) (h₂ : Continuous U₂) (h : U₁.domain ≤ U₂.domain) :    (U₁ + U₂).IsClosable := by  use (U₁ + U₂).graph.topologicalClosure.toLinearPMap  refine (toLinearPMap_graph_eq _ fun ⟨x₁, x₂⟩ hx hx₁ ↦ ?_).symm  subst hx₁  refine graph_fst_eq_zero_snd U₁.closure ?_ rfl  rw [← h₁.graph_closure_eq_closure_graph]  apply mem_closure_iff_seq_limit.mpr  obtain ⟨b, hb, hbx⟩ := mem_closure_iff_seq_limit.mp hx  simp only [coe_toAddSubmonoid, SetLike.mem_coe, mem_graph_iff, add_domain, add_apply,    Subtype.exists, exists_and_left, exists_eq_left, nhds_prod_eq] at *  refine ⟨fun n ↦ ((b n).1, (b n).2 - U₂ ⟨(b n).1, h (hb n).choose.1⟩), fun n ↦ ?_, ?_⟩  · exact ⟨(hb n).choose.1, eq_sub_of_add_eq (hb n).choose_spec⟩  · refine Filter.Tendsto.prodMk hbx.fst ?_    refine sub_zero x₂ ▸ hbx.snd.sub ?_    exact map_zero U₂ ▸ (h₂.tendsto 0).comp (tendsto_subtype_rng.mpr hbx.fst)