constructor
case h
x : ℝ
a✝ : x ∈ Set.univ
⊢ Set.Ico x (x + 1) ∈ lower_intervals ∧ x ∈ Set.Ico x (x + 1)
case h.left
x : ℝ
a✝ : x ∈ Set.univ
⊢ Set.Ico x (x + 1) ∈ lower_intervals

case h.right
x : ℝ
a✝ : x ∈ Set.univ
⊢ x ∈ Set.Ico x (x + 1)