opcyclesMap'_smul — Mathlib

English

There is an R-linear structure on RightHomologyMapData compatible with φQ and φH components.

Русский

Существует R-линейная структура на RightHomologyMapData совместимая с φQ и φH.

LaTeX

$$$\text{RightHomologyMapData}$ is $R$-linear in φ$$

Lean4

@[simp]
theorem opcyclesMap'_smul : opcyclesMap' (a • φ) h₁ h₂ = a • opcyclesMap' φ h₁ h₂ :=
  by
  have γ : RightHomologyMapData φ h₁ h₂ := default
  simp only [(γ.smul a).opcyclesMap'_eq, RightHomologyMapData.smul_φQ, γ.opcyclesMap'_eq]

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