by_contra hne
case h.mp.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
⊢ 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
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