homologyMap'_comp — Mathlib

English

homologyMap' (φ1 ≫ φ2) h1 h3 = homologyMap' φ1 h1 h2 ≫ homologyMap' φ2 h2 h3.

Русский

Гомография'(составление) равна композиции гомографий.

LaTeX

$$$\mathrm{homologyMap}'(φ_1 \;≫\; φ_2)\; h_1\; h_3 = \mathrm{homologyMap}'(φ_1)\; h_1\; h_2 \;≫\; \mathrm{homologyMap}'(φ_2)\; h_2\; h_3$$$

Lean4

theorem homologyMap'_comp (φ₁ : S₁ ⟶ S₂) (φ₂ : S₂ ⟶ S₃) (h₁ : S₁.HomologyData) (h₂ : S₂.HomologyData)
    (h₃ : S₃.HomologyData) : homologyMap' (φ₁ ≫ φ₂) h₁ h₃ = homologyMap' φ₁ h₁ h₂ ≫ homologyMap' φ₂ h₂ h₃ :=
  leftHomologyMap'_comp _ _ _ _ _

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