have inverse_image_open := continuous_def.mp hlc _ (infinite_interval_lower_open (f z))
f : ℝ → ℝ
huc : Continuous f
hlc : Continuous f
z b : ℝ
hz : z ≤ b
x : ℝ
hx : x ∈ f ⁻¹' Set.Ici (f z)
⊢ ∃ y, x < y ∧ Set.Ico x y ⊆ f ⁻¹' Set.Ici (f z)
f : ℝ → ℝ
huc : Continuous f
hlc : Continuous f
z b : ℝ
hz : z ≤ b
x : ℝ
hx : x ∈ f ⁻¹' Set.Ici (f z)
inverse_image_open : IsOpen (f ⁻¹' Set.Ici (f z))
⊢ ∃ y, x < y ∧ Set.Ico x y ⊆ f ⁻¹' Set.Ici (f z)