pullbackDiagonalMapIdIso_hom_snd — Mathlib

English

The inverse of a diagonalObjPullbackFstIso composed with fst yields a canonical fst composition, illustrating the interaction of diagonal with pullback projections.

Русский

Обратное diagonalObjPullbackFstIso, композиция с fst, даёт каноническую композицию fst, иллюстрируя взаимодействие диагонали с проекциями предела.

LaTeX

$$$$ (diagonalObjPullbackFstIso\ f\ g).inv \circ fst = fst \circ fst $$$$

Lean4

@[reassoc (attr := simp)]
theorem pullbackDiagonalMapIdIso_hom_snd :
    (pullbackDiagonalMapIdIso f g i).hom ≫ pullback.snd _ _ = pullback.snd _ _ ≫ pullback.snd _ _ :=
  by
  delta pullbackDiagonalMapIdIso
  simp

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