mpullback_smul_apply — Mathlib

English

If g is differentiable with invertible mfderivWithin and hf' condition holds, then mpullbackWithin I I'' (g ∘ f) V s x = mpullbackWithin I I' f (mpullbackWithin I' I'' g V t) s x.

Русский

Если g дифференцируемо, mfderivWithin обратимо, то 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_smul_apply : mpullback I I' f (c • V) x = c • mpullback I I' f V x := by simp [mpullback]

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