snd_invApp_t_app — Mathlib

English

The main compatibility statement of opensImagePreimageMap_app holds: the red and blue arrows commute in the overarching gluing diagram.

Русский

Основное тождество opensImagePreimageMap_app: красные и синие стрелки в большом диаграммном склейивании commute.

LaTeX

$$$\\text{opensImagePreimageMap\_app}(i,j,k,U)$$$

Lean4

/-- The red and the blue arrows in ![this diagram](https://i.imgur.com/q6X1GJ9.png) commute. -/
@[simp, reassoc]
theorem snd_invApp_t_app (i j k : D.J) (U : Opens (pullback (D.f i j) (D.f i k)).carrier) :
    (π₂⁻¹ i, j, k) U ≫ (D.t k i).c.app _ =
      (D.t' k i j).c.app _ ≫
        (π₁⁻¹ k, j, i) (unop _) ≫ (D.V (k, i)).presheaf.map (eqToHom (D.snd_invApp_t_app' i j k U).choose.symm) :=
  by
  have e := (D.snd_invApp_t_app' i j k U).choose_spec
  replace e := reassoc_of% e
  rw [← e]
  simp [eqToHom_map]

Похожие утверждения