Research proof index

The Euler Lagrange operator, for a trajectory q : Time → X, and a lagrangian Time → X → X → ℝ, the Euler-Lagrange operator is ∂L/∂q - dₜ(∂L/∂(dₜ q)). -/ noncomputable def eulerLagrangeOp (L : Time → X → X → ℝ) (q : Time → X) : Time → X := fun t => gradient (L t · (∂ₜ q t)) (q t) - ∂ₜ (fun t' => gradient (L t' (q t') ·) (∂ₜ q t')) t lemma eulerLagran...