rightHomologyMap'_neg — Mathlib

English

The combination of negation and subtraction interacts with leftHomologyMap in a predictable way.

Русский

Комбинация отрицания и вычитания взаимодействует с leftHomologyMap предсказуемым образом.

LaTeX

$$$ leftHomologyMap(-φ) = -leftHomologyMap φ $ and $ leftHomologyMap(φ - φ') = leftHomologyMap φ - leftHomologyMap φ' $$$

Lean4

@[simp]
theorem rightHomologyMap'_neg : rightHomologyMap' (-φ) h₁ h₂ = -rightHomologyMap' φ h₁ h₂ :=
  by
  have γ : RightHomologyMapData φ h₁ h₂ := default
  simp only [γ.rightHomologyMap'_eq, γ.neg.rightHomologyMap'_eq, RightHomologyMapData.neg_φH]

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