constructor
case refine_2.h
x : ℝ
⊢ x ∈ ⋃₀ upper_intervals ↔ x ∈ Set.univ
case refine_2.h.mp
x : ℝ
⊢ x ∈ ⋃₀ upper_intervals → x ∈ Set.univ

case refine_2.h.mpr
x : ℝ
⊢ x ∈ Set.univ → x ∈ ⋃₀ upper_intervals