homologyIso_hom_comp_ι — Mathlib

English

For h : S.RightHomologyData, the equation h.homologyIso.inv ≫ S.homologyι = h.ι ≫ h.opcyclesIso.inv holds.

Русский

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

LaTeX

$$$h.homologyIso.inv \circ S.homology\\iota = h.\\iota \\circ h.opcyclesIso.inv$$$

Lean4

@[reassoc (attr := simp)]
theorem homologyIso_hom_comp_ι (h : S.RightHomologyData) : h.homologyIso.hom ≫ h.ι = S.homologyι ≫ h.opcyclesIso.hom :=
  by
  dsimp only [homologyι, homologyIso]
  simp only [Iso.trans_hom, Iso.symm_hom, assoc, rightHomologyIso_hom_comp_ι]

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