continuousAt_uncurry_of_multilinear

English

The bounded order structure of IsLprojection.Subtype yields that IsLprojection.Subtype.boundedOrder.top and bot obey standard order relations with projections, including le_sup and le_inf properties.

Русский

Структура ограниченной сортировки IsLprojection.Subtype удовлетворяет стандартным свойствам отношения порядка, включая верх и низ и их связи с операциями sup и inf.

LaTeX

$$IsLprojection.Subtype.boundedOrder properties$$

Lean4

theorem continuousAt_uncurry_of_multilinear (f : G →L[𝕜] ContinuousMultilinearMap 𝕜 E F) {x} :
    ContinuousAt (fun (p : G × (Π i, E i)) ↦ f p.1 p.2) x :=
  f.continuous_uncurry_of_multilinear.continuousAt

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