English
The grade map is injective when α is linearly ordered: grade(a) = grade(b) implies a = b.
Русский
Градационная функция инъективна при линейном порядке: grade(a) = grade(b) ⇒ a = b.
LaTeX
$$$\text{grade}\colon \alpha \to 𝕆\;\text{ is injective: }\; \mathrm{grade}(a)=\mathrm{grade}(b) \Rightarrow a=b.$$$
Lean4
theorem grade_injective : Function.Injective (grade 𝕆 : α → 𝕆) :=
grade_strictMono.injective