op_pOpcycles_opcyclesOpIso_hom — Mathlib

English

As above, the equation h.rightHomologyIso.inv ≫ S.rightHomologyι = h.ι ≫ h.opcyclesIso.inv holds.

Русский

Как выше, выполняется равенство h.rightHomologyIso.inv ≫ S.rightHomologyι = h.ι ≫ h.opcyclesIso.inv.

LaTeX

$$h.rightHomologyIso.inv \circ S.rightHomologyι = h.ι \circ h.opcyclesIso.inv$$

Lean4

@[reassoc (attr := simp)]
theorem op_pOpcycles_opcyclesOpIso_hom [S.HasLeftHomology] : S.op.pOpcycles ≫ S.opcyclesOpIso.hom = S.iCycles.op :=
  by
  dsimp [opcyclesOpIso]
  rw [← S.leftHomologyData.op.p_comp_opcyclesIso_inv, assoc, Iso.inv_hom_id, comp_id]
  rfl

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