curveIntegralFun_zero — Mathlib

English

The curve integral along a segment from a to b equals the interval integral of the function t ↦ ω(lineMap(a,b,t))(b−a) over t in [0,1].

Русский

Интеграл по кривой вдоль сегмента от a до b равен интегралу по времени t ∈ [0,1] функции t ↦ ω(lineMap(a,b,t))(b−a).

LaTeX

$$$\\int_{\\text{segment}(a,b)} ω(x) \\, dx = \\int_{0}^{1} ω(\\text{lineMap}(a,b,t))(b-a) \\, dt$$$

Lean4

@[simp]
theorem curveIntegralFun_zero : curveIntegralFun (0 : E → E →L[𝕜] F) γ = 0 := by ext; simp [curveIntegralFun]

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