liftCochain_descCochain — Mathlib

English

The lift and descent operations yield a cochain that is the sum of compatible lifts of α,β.

Русский

Подъём и спуск дают коохайн, который есть сумма совместимых подъемов α,β.

LaTeX

$$$ liftCochain(φ,α,β,h) \\circ descCochain(φ,α',β',h') = α \\circ α' + β \\circ β' $$$

Lean4

@[simp]
theorem liftCochain_descCochain :
    (liftCochain φ α β h).comp (descCochain φ α' β' h') hp = α.comp α' (by cutsat) + β.comp β' (by cutsat) := by
  simp [liftCochain, descCochain, Cochain.comp_assoc α (inl φ) _ _ (show -1 + n' = m' by cutsat) (by linarith)]

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