mpullbackWithin_apply — Mathlib

English

The pullback within s is linear in the vector argument: mpullbackWithin I I' f (c·V) s x = c · mpullbackWithin I I' f V s x.

Русский

Вытягивание внутри области сохраняет линейность по вектору: mpullbackWithin I I' f (c·V) s x = c · mpullbackWithin I I' f V s x.

LaTeX

$$$$ \mathrm{mpullbackWithin}\ I\ I'\ f\ (c\cdot V)\ s\ x = c\cdot \mathrm{mpullbackWithin}\ I\ I'\ f\ V\ s\ x $$$$

Lean4

theorem mpullbackWithin_apply : mpullbackWithin I I' f V s x = (mfderivWithin I I' f s x).inverse (V (f x)) :=
  rfl

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