lieBracketWithin_zero_left — Mathlib

English

lieBracket 𝕜 (V + V1) W x = lieBracket 𝕜 V W x + lieBracket 𝕜 V1 W x when V, V1 are differentiable at x.

Русский

При сложении левых полей: [V+V1, W](x) = [V,W](x) + [V1,W](x).

LaTeX

$$$\operatorname{lieBracket} 𝕜 (V + V_1) W x = \operatorname{lieBracket} 𝕜 V W x + \operatorname{lieBracket} 𝕜 V_1 W x$$$

Lean4

/-- We have `[0, W] = 0` for all vector fields `W`: this depends on the junk value 0
if `W` is not differentiable. Version within a set. -/
@[simp]
theorem lieBracketWithin_zero_left : lieBracketWithin 𝕜 0 W s = 0 := by ext; simp [lieBracketWithin]

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