inr_f_descCochain_v — Mathlib

English

The p-th component of the degree-0 cochain built from ψ matches ψ at p.

Русский

Компонента p в нулевом коохайн из ψ совпадает с ψ(p).

LaTeX

$$$ (\\operatorname{ofHoms}(ψ)).v(p,p;\\mathrm{add\\,zero}\,p) = ψ(p) $$$

Lean4

@[reassoc (attr := simp)]
theorem inr_f_descCochain_v (p₁ p₂ : ℤ) (h₁₂ : p₁ + n = p₂) :
    (inr φ).f p₁ ≫ (descCochain φ α β h).v p₁ p₂ h₁₂ = β.v p₁ p₂ h₁₂ := by
  simpa only [Cochain.comp_v _ _ (zero_add n) p₁ p₁ p₂ (add_zero p₁) h₁₂, Cochain.ofHom_v] using
    Cochain.congr_v (inr_descCochain φ α β h) p₁ p₂ (by cutsat)

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