uniformEquicontinuous_unique — Mathlib

English

If ι is unique, uniform equicontinuity of F is equivalent to uniform continuity of the unique F_i.

Русский

Если ι уникално, униформная эконтинуальность F эквивалентна униформной непрерывности единственной F_i.

LaTeX

$$$$ [Unique ι] \{F : ι \to β \to α\} : \operatorname{UniformEquicontinuous} F \iff \operatorname{UniformContinuous}(F default). $$$$

Lean4

theorem uniformEquicontinuous_unique [Unique ι] {F : ι → β → α} :
    UniformEquicontinuous F ↔ UniformContinuous (F default) :=
  uniformEquicontinuous_finite.trans Unique.forall_iff

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