ofMkLEMk_refl — Mathlib

English

For a mono f, the self-witnessing MkLEMk is the identity on A.

Русский

Для монофункции f присутствует тождественный MkLEMk.

LaTeX

$$$\operatorname{ofMkLEMk} f f \;\mathrm{le\_rfl} = \mathrm{id}$$$

Lean4

@[simp]
theorem ofMkLEMk_refl {B A₁ : C} (f : A₁ ⟶ B) [Mono f] : ofMkLEMk f f le_rfl = 𝟙 _ :=
  by
  apply (cancel_mono f).mp
  simp
    -- As with `ofLE`, we have `X` and `Y` as explicit arguments for readability.

Похожие утверждения