∀ {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}
  {S : Set (ClosedSubmodule R N)}, (x ∈ sSup S) = (x ∈ closure (⨆ s ∈ S, ↑s).carrier)