English
The pullback is additive in the vector argument: mpullbackWithin I I' f (V + V1) s x = mpullbackWithin I I' f V s x + mpullbackWithin I I' f V1 s x.
Русский
Вытягивание по сумме векторов равно сумме вытягиваний: mpullbackWithin I I' f (V + V1) s x = mpullbackWithin I I' f V s x + mpullbackWithin I I' f V1 s x.
LaTeX
$$$$ \mathrm{mpullbackWithin}\ I\ I'\ f\ (V + V1)\ s\ x = \mathrm{mpullbackWithin}\ I\ I'\ f\ V\ s\ x + \mathrm{mpullbackWithin}\ I\ I'\ f\ V1\ s\ x $$$$
Lean4
theorem mpullbackWithin_smul : mpullbackWithin I I' f (c • V) s = c • mpullbackWithin I I' f V s :=
by
ext x
simp [mpullbackWithin_apply]