mpullbackWithin_smul — Mathlib

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]

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