repeat rw [not_or] at hne
case h.mp.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
hne :
  ¬(x = -7 ∨
      x = -6 ∨
        x = -5 ∨ x = -4 ∨ x = -3 ∨ x = -2 ∨ x = -1 ∨ x = 0 ∨ x = 1 ∨ x = 2 ∨ x = 3 ∨ x = 4 ∨ x = 5 ∨ x = 6 ∨ x = 7)
⊢ False
case h.mp.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
hne :
  ¬x = -7 ∧
    ¬x = -6 ∧
      ¬x = -5 ∧
        ¬x = -4 ∧ ¬x = -3 ∧ ¬x = -2 ∧ ¬x = -1 ∧ ¬x = 0 ∧ ¬x = 1 ∧ ¬x = 2 ∧ ¬x = 3 ∧ ¬x = 4 ∧ ¬x = 5 ∧ ¬x = 6 ∧ ¬x = 7
⊢ False