instIsManifoldMinSmoothnessOfNatWithTopENat

English

The pullback commutes with Lie bracket: mpullback_mlieBracketWithin states equality under pullback.

Русский

Подстановка вверх по отображению совместима со скобкой Ли: mpullback_mlieBracketWithin равенство.

LaTeX

$$$\mathrm{mpullbackWithin}(I, I', f, \mathrm{mlieBracketWithin}(I', V, W, t), s, x_0) = \mathrm{mlieBracketWithin}(I, \mathrm{mpullbackWithin}(I, I', f, V, s), \mathrm{mpullbackWithin}(I, I', f, W, s), s, x_0)$$$

Lean4

instance [IsManifold I (minSmoothness 𝕜 3) M] : IsManifold I (minSmoothness 𝕜 2) M :=
  IsManifold.of_le (n := minSmoothness 𝕜 3) (minSmoothness_monotone (by norm_cast))

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