subtype_comp_d₀₁ — Mathlib

English

Let i be the inclusion of the invariants A^{\\rho} into A. Then the 0→1 differential composed with i is zero.

Русский

Пусть i — включение инвариантов A^{\\rho} в A. Тогда композиция d01 с i равна нулю.

LaTeX

$$$d_{01}(A) \\circ i = 0$, where $i: A^{\\rho} \\hookrightarrow A$ is the inclusion.$$

Lean4

@[reassoc (attr := simp), elementwise (attr := simp)]
theorem subtype_comp_d₀₁ : ModuleCat.ofHom (A.ρ.invariants.subtype) ≫ d₀₁ A = 0 :=
  by
  ext ⟨x, hx⟩ g
  replace hx := hx g
  rw [← sub_eq_zero] at hx
  exact hx

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