union — Mathlib

English

Derived from the union property: if f is continuous within s and within t at x, then it is continuous within s ∪ t at x.

Русский

Из объединения следует: если f непрерывна на s и на t в x, то она непрерывна на s ∪ t в x.

LaTeX

$$$$\text{ContinuousWithinAt}(f, s, x) \land \text{ContinuousWithinAt}(f, t, x) \Rightarrow \text{ContinuousWithinAt}(f, s \cup t, x)$$$$

Lean4

theorem union (hs : ContinuousWithinAt f s x) (ht : ContinuousWithinAt f t x) : ContinuousWithinAt f (s ∪ t) x :=
  continuousWithinAt_union.2 ⟨hs, ht⟩

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