English
Division by the left argument is injective: the map (a,b) ↦ (a ∣ b) is injective.
Русский
Делимость слева инъективна: отображение (a,b) ↦ (a ∣ b) инъективно.
LaTeX
$$$\text{Injective}((\cdot \mid \cdot): \mathbb{N} \to \mathbb{N} \to \text{Prop})$$$
Lean4
/-- `dvd` is injective in the left argument -/
theorem dvd_left_injective : Function.Injective ((· ∣ ·) : ℕ → ℕ → Prop) := fun _ _ h =>
dvd_right_iff_eq.mp fun a => iff_of_eq (congr_fun h a)