English
If g, f are differentiable with invertible mfderivWithin together with the required hypotheses, then mpullbackWithin I I'' (g ∘ f) V s x equals VectorField.mpullbackWithin I I' f (VectorField.mpullbackWithin I' I'' g V t) s x.
Русский
При подходящих условиях дифференцируемости и обратимости mfderivWithin, вытягивание внутри композиции равно вложенному вытягиванию: mpullbackWithin I I'' (g ∘ f) V s x = mpullbackWithin I I' f (mpullbackWithin I' I'' g V t) s x.
LaTeX
$$$$ \mathrm{mpullbackWithin}\ I\ I'' (g \circ f)\ V\ s\ x = \mathrm{mpullbackWithin}\ I I' f\left( \mathrm{mpullbackWithin}\ I' I'' g\ V t\right)\ s x $$$$
Lean4
theorem mpullback_add : mpullback I I' f (V + V₁) = mpullback I I' f V + mpullback I I' f V₁ :=
by
ext x
simp [mpullback_apply]
