pullbackDiagonalMapIdIso_inv_snd_fst

English

The inverse of the diagonal map composed with two snds yields the second snd after diagonal alignment, expressing diagonal compatibility.

Русский

Обратная диагональная карта, примененная дважды к snd, даёт вторую snd после согласования диагонали.

LaTeX

$$$$ (diagonalMapIso\ f g i)^{−1} \circ snd \circ snd = snd $$$$

Lean4

@[reassoc (attr := simp)]
theorem pullbackDiagonalMapIdIso_inv_snd_fst :
    (pullbackDiagonalMapIdIso f g i).inv ≫ pullback.snd _ _ ≫ pullback.fst _ _ = pullback.fst _ _ :=
  by
  rw [Iso.inv_comp_eq]
  simp

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