mpullbackWithin_univ — Mathlib

English

Under standard Euclidean model, mpullbackWithin equals pullbackWithin: mpullbackWithin (modelWithCornersSelf 𝕜 E) (modelWithCornersSelf 𝕜 E') f V s = pullbackWithin 𝕜 f V s.

Русский

В обычной евклидовой модели mpullbackWithin равен pullbackWithin: mpullbackWithin (modelWithCornersSelf 𝕜 E) (modelWithCornersSelf 𝕜 E') f V s = pullbackWithin 𝕜 f V s.

LaTeX

$$$$ \mathrm{mpullbackWithin}\ I\ I' f V s = \mathrm{pullbackWithin}\ 𝕜 f V s $$$$

Lean4

@[simp]
theorem mpullbackWithin_univ : mpullbackWithin I I' f V univ = mpullback I I' f V :=
  by
  ext x
  simp [mpullback_apply, mpullbackWithin_apply]

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