rw [_root_.abs_of_nonneg <| by exact_mod_cast Int.floor_nonneg.mpr hx.2]
case inl
a b x : ℝ
hx✝ : (a ≤ x ∨ b ≤ x) ∧ (x ≤ a ∨ x ≤ b)
this : |x| ≤ max |a| |b|
hx : |x| = x ∧ 0 ≤ x
⊢ |↑⌊x⌋| ≤ max |a| |b| + 1
case inl
a b x : ℝ
hx✝ : (a ≤ x ∨ b ≤ x) ∧ (x ≤ a ∨ x ≤ b)
this : |x| ≤ max |a| |b|
hx : |x| = x ∧ 0 ≤ x
⊢ ↑⌊x⌋ ≤ max |a| |b| + 1