Derivative of K sin²θ
ProvedExactVacuumAtlas.Deriv.mul_sin_sqeinstein-maxwellexact-spacetime-atlas-ivexact-vacuum-atlasgeneral-relativity
Derivative of K sin²θ
HasDerivAt (t ↦ K sin²t) (K · 2 sin θ cos θ) at θ.
Scope. Exactly the hypotheses printed in the formal statement.
中文摘要 导数引理 d(K sin²θ)。
Preamble
import Mathlib open Real
Formal statement
theorem ExactVacuumAtlas.Deriv.mul_sin_sq (K θ : ℝ) :
HasDerivAt (fun t => K * sin t ^ 2) (K * (2 * sin θ * cos θ)) θ := by sorrySource
He Wang, Exact Spacetime Atlas IV: Certified Einstein–Maxwell Backgrounds and First Variations. Local source, no public repository; commit 543904bfcfa3bb169f43fc4d9dbd569999b71886; Atlas/Core/Deriv.lean#L66-L70; SHA-256 dc49ec3a0b39ea3e075312c79b8b14e378ffdc0688d2931d08c6421ec4264e95. Registered definitions and literature: mission/PHYSICS_BOUNDARY.md (§H–§J); Müller–Grave arXiv:0904.4184; Newman et al., J. Math. Phys. 6 (1965) 918.
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.