rightHomologyIso_hom_comp_homologyIso_inv

English

For h : S.RightHomologyData, h.rightHomologyIso.inv ≫ S.homologyι = h.ι ≫ h.opcyclesIso.inv.

Русский

Для h : S.RightHomologyData выполняется h.rightHomologyIso.inv ≫ S.homologyι = h.ι ≫ h.opcyclesIso.inv.

LaTeX

$$$h.rightHomologyIso.inv \circ S.homologyι = h.\iota \\circ h.opcyclesIso.inv$$$

Lean4

@[reassoc (attr := simp)]
theorem rightHomologyIso_hom_comp_homologyIso_inv (h : S.RightHomologyData) :
    h.rightHomologyIso.hom ≫ h.homologyIso.inv = S.rightHomologyIso.hom :=
  by
  dsimp only [homologyIso]
  simp only [Iso.trans_inv, Iso.symm_inv, Iso.hom_inv_id_assoc]

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