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def definition def or abbrev

gradient_squared

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formal statement (Lean)

  76noncomputable def gradient_squared (φ : ScalarField) (g : MetricTensor) (x : Fin 4 → ℝ) : ℝ :=

proof body

Definition body.

  77  Finset.sum (Finset.univ : Finset (Fin 4)) (fun μ =>
  78    Finset.sum (Finset.univ : Finset (Fin 4)) (fun ν =>
  79      (inverse_metric g) x (fun i => if (i : ℕ) = 0 then μ else ν) (fun _ => 0) *
  80      (gradient φ x μ) * (gradient φ x ν)))
  81
  82/-- Gradient squared for Minkowski metric. -/

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