uniformCauchySeqOn — Mathlib

English

A variant of tendsto/HasBasis equivalences for TendstoUniformlyOn: TendstoUniformlyOn F f l s is characterized by HasBasis data on l and l'.

Русский

Вариант эквивалентностей TendstoUniformlyOn с базисом HasBasis по l и l'.

LaTeX

$$$TendstoUniformlyOnFilter F f l l' \iff \dots$$$

Lean4

/-- A sequence that converges uniformly is also uniformly Cauchy -/
theorem uniformCauchySeqOn (hF : TendstoUniformlyOn F f p s) : UniformCauchySeqOn F p s :=
  uniformCauchySeqOn_iff_uniformCauchySeqOnFilter.mpr hF.tendstoUniformlyOnFilter.uniformCauchySeqOnFilter

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