of_dslope — Mathlib

English

If b ≠ a, then dslope f a is continuous at b with respect to s if and only if f is continuous at b with respect to s.

Русский

При b ≠ a долг dslope f a непрерывна в b относительно s эквивалентно непрерывности f в b относительно s.

LaTeX

$$$\text{ContinuousWithinAt}( dslope\ f\ a, s, b) \iff \text{ContinuousWithinAt}( f, s, b) \quad (b \neq a)$$$

Lean4

theorem of_dslope (h : ContinuousAt (dslope f a) b) : ContinuousAt f b :=
  (continuousWithinAt_univ _ _).1 h.continuousWithinAt.of_dslope

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