equicontinuousOn_unique — Mathlib

English

If ι is unique, equicontinuity on S is equivalent to continuity of the unique F_i on S.

Русский

Если ι уникално, эконтинуальность на S эквивалентна непрерывности единственной F_i на S.

LaTeX

$$$$ [Unique ι] \{F : ι \to X \to α\} {S : Set X} : \operatorname{EquicontinuousOn} F S \iff \operatorname{ContinuousOn} (F default) S. $$$$

Lean4

theorem equicontinuousOn_unique [Unique ι] {F : ι → X → α} {S : Set X} :
    EquicontinuousOn F S ↔ ContinuousOn (F default) S :=
  equicontinuousOn_finite.trans Unique.forall_iff

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