leftShift_comp_zero_cochain — Mathlib

English

If γ is a left-shifted cochain and γ' is a 0-cochain (zero), then leftShift_comp reduces to leftShift of γ with γ' = 0 identity, simplifying due to zero.

Русский

Если γ − левый сдвиг, а γ' − нулевая косейн, то leftShift_comp упрощается за счёт нуля.

LaTeX

$$$(\gamma.leftShift a n' hn').comp γ' (add_zero n') = (γ.leftShift a n' hn').comp γ' (add_zero n')$$$

Lean4

@[simp]
theorem leftShift_comp_zero_cochain (a n' : ℤ) (hn' : n + a = n') (γ' : Cochain L M 0) :
    (γ.comp γ' (add_zero n)).leftShift a n' hn' = (γ.leftShift a n' hn').comp γ' (add_zero n') := by
  rw [leftShift_comp γ a n' hn' γ' (add_zero _) hn', mul_zero, Int.negOnePow_zero, one_smul]

Похожие утверждения