∀ {ι : Sort u_1} {R : Type u_2} {N : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid N]
  [inst_2 : TopologicalSpace N] [inst_3 : Module R N] [inst_4 : ContinuousAdd N] [inst_5 : ContinuousConstSMul R N]
  {x : N} {f : ι → ClosedSubmodule R N}, (x ∈ ⨆ i, f i) = (x ∈ closure (⨆ i, ↑(f i)).carrier)