mpullback_id — Mathlib

English

If hf, h maps with invertible derivatives, then mpullbackWithin I I'' (g ∘ f) V s x = mpullbackWithin I I' f (mpullbackWithin I' I'' g V t) s x.

Русский

Если hf и h удовлетворяют условиям инвертируемости производной, 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

@[simp]
theorem mpullback_id {V : Π (x : M), TangentSpace I x} : mpullback I I id V = V :=
  by
  ext x
  simp [mpullback]

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