English
If two degreewise split cochains agree on all components v, then they are equal as cochains.
Русский
Если две степеней‑разложенные коцепаны согласуются во всех компонентах v, то они равны как коцепаны.
LaTeX
$$$\forall z_1,z_2: Cochain F G n,\ (\forall p,q, hpq, z_1.v p q hpq = z_2.v p q hpq) \Rightarrow z_1 = z_2$$$
Lean4
@[simp]
theorem cocycleOfDegreewiseSplit_triangleRotateShortComplexSplitting_v (p : ℤ) :
(cocycleOfDegreewiseSplit _ (triangleRotateShortComplexSplitting φ)).1.v p _ rfl = -φ.f _ := by
simp [cocycleOfDegreewiseSplit, d_snd_v φ p (p + 1) rfl]
