rcases hlege with ⟨h12ge, h28le⟩
case h.mpr
x : ℝ
hlege : 12 ≤ x ∧ x ≤ 28
⊢ ∃ x_1, (3 ≤ x_1 ∧ x_1 ≤ 5) ∧ x_1 ^ 2 + 3 = x
case h.mpr.intro
x : ℝ
h12ge : 12 ≤ x
h28le : x ≤ 28
⊢ ∃ x_1, (3 ≤ x_1 ∧ x_1 ≤ 5) ∧ x_1 ^ 2 + 3 = x