funext — Mathlib

English

If f,g: hatα → β are continuous and agree at all ι a, then f = g (function extensionality on hatα).

Русский

Если функции f,g: hatα → β непрерывны и совпадают на всех ι a, тогда f = g (расширенная функция).

LaTeX

$$$\\forall a, f(\\iota(a)) = g(\\iota(a)) \\Rightarrow f = g$ (assuming appropriate topological conditions).$$

Lean4

protected theorem funext [TopologicalSpace β] [T2Space β] {f g : hatα → β} (hf : Continuous f) (hg : Continuous g)
    (h : ∀ a, f (ι a) = g (ι a)) : f = g :=
  funext fun a => pkg.induction_on a (isClosed_eq hf hg) h

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