gluedLiftPullbackMap_fst — Mathlib

English

Cocycle identity with two snd maps; shows compatibility of second projections in the overlap.

Русский

Кокосовое тождество с двумя snd; совместимость вторых проекций на перекрытии.

LaTeX

$$$ t'_{\\mathcal{U}} f g i j k \\;\\gg\\; \\mathrm{snd} \\_ \\_ \\;\\gg\\; \\mathrm{snd} \\_ \\_ = \\mathrm{snd} \\_ \\_ \\;\\gg\\; \\mathrm{snd} \\_ \\_ $$

Lean4

@[reassoc]
theorem gluedLiftPullbackMap_fst (i j : 𝒰.I₀) :
    gluedLiftPullbackMap 𝒰 f g s i j ≫ pullback.fst _ _ =
      pullback.fst _ _ ≫
        (pullbackSymmetry _ _).hom ≫ pullback.map _ _ _ _ (𝟙 _) s.snd f (Category.id_comp _).symm s.condition :=
  by simp [gluedLiftPullbackMap]

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