zero — Mathlib

English

If ω is a constant linear map along the segment, then the curve integral over the segment equals the constant applied to the difference b−a.

Русский

Если ω постоянна вдоль сегмента, то интеграл по сегменту равен ω(b−a).

LaTeX

$$$\\text{curveIntegralSegmentConst}(\\omega, a, b) : \\int_{\\text{segment}(a,b)} ω = ω(b-a)$$$

Lean4

theorem zero : CurveIntegrable (0 : E → E →L[𝕜] F) γ := by simp [CurveIntegrable, IntervalIntegrable.zero]

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