rw [_root_.abs_of_nonpos <| by exact_mod_cast Int.floor_nonpos hx.2.le]
case inr
a b x : ℝ
hx✝ : (a ≤ x ∨ b ≤ x) ∧ (x ≤ a ∨ x ≤ b)
this : |x| ≤ max |a| |b|
hx : |x| = -x ∧ x < 0
⊢ |↑⌊x⌋| ≤ max |a| |b| + 1
case inr
a b x : ℝ
hx✝ : (a ≤ x ∨ b ≤ x) ∧ (x ≤ a ∨ x ≤ b)
this : |x| ≤ max |a| |b|
hx : |x| = -x ∧ x < 0
⊢ -↑⌊x⌋ ≤ max |a| |b| + 1