leftHomologyMap'_add — Mathlib

English

Negation commutes with leftHomologyMap: leftHomologyMap of the negated morphism is the negation of leftHomologyMap.

Русский

Налоговая карта leftHomologyMap сохраняет знак: левая гомологическая карта от отрицательного морфизма равна отрицанию карты от морфизма.

LaTeX

$$$ leftHomologyMap(-\varphi) = - leftHomologyMap(\varphi) $$$

Lean4

@[simp]
theorem leftHomologyMap'_add : leftHomologyMap' (φ + φ') h₁ h₂ = leftHomologyMap' φ h₁ h₂ + leftHomologyMap' φ' h₁ h₂ :=
  by
  have γ : LeftHomologyMapData φ h₁ h₂ := default
  have γ' : LeftHomologyMapData φ' h₁ h₂ := default
  simp only [γ.leftHomologyMap'_eq, γ'.leftHomologyMap'_eq, (γ.add γ').leftHomologyMap'_eq, LeftHomologyMapData.add_φH]

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