uniformContinuous_eval_const — Mathlib

English

The uniform-continuity of the coefficient function implies uniform continuity of the underlying function.

Русский

Градиентная равномерная непрерывность коэффициентной функции вносит равномерную непрерывность базовой функции.

LaTeX

$$UniformContinuous (ContinuousMultilinearMap.funLike.coe)$$

Lean4

theorem uniformContinuous_eval_const [∀ i, ContinuousSMul 𝕜 (E i)] (x : Π i, E i) :
    UniformContinuous fun f : ContinuousMultilinearMap 𝕜 E F ↦ f x :=
  uniformContinuous_pi.1 uniformContinuous_coe_fun x

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