∀ {ι : Type u_1} (s : Set (ι → ℝ)) [inst : Finite ι] {c : ℝ} (hc : c ≠ 0) (x : ι → ℝ),
  x ∈ s ∩ c⁻¹ • ↑(Submodule.span ℤ (Set.range ⇑(Pi.basisFun ℝ ι))) ↔
    (Equiv.smulRight hc) x ∈ c • s ∩ ↑(Submodule.span ℤ (Set.range ⇑(Pi.basisFun ℝ ι)))