diff --git a/Nevanlinna/laplace2.lean b/Nevanlinna/laplace2.lean index b6cee8b..f36cb58 100644 --- a/Nevanlinna/laplace2.lean +++ b/Nevanlinna/laplace2.lean @@ -27,6 +27,8 @@ noncomputable def Laplace₂ E → F := fun z ↦ ∑ i, iteratedFDeriv ℝ 2 f z ![v i, v i] +#check ContinuousMultilinearMap.map_sum_finset + theorem LaplaceIndep [Fintype ι] (v₁ : Basis ι ℝ E) @@ -49,5 +51,20 @@ theorem LaplaceIndep right arg 2 intro i - rw [ContinuousMultilinearMap.map_sum_finset] + --rw [ContinuousMultilinearMap.map_sum_finset] + + have v : E := by sorry + let t := ![∑ j, ⟪v₁ j, v⟫_ℝ • (v₁ j), ∑ j, ⟪v₁ j, v⟫_ℝ • (v₁ j)] + simp at t + have L : ContinuousMultilinearMap ℝ (fun (_ : Fin 2) ↦ E) F := by exact iteratedFDeriv ℝ 2 f z + --have α : Fin 2 → Type* := by exact fun _ ↦ ι + have g : (i : Fin 2) → ι → E := by exact fun _ ↦ (fun j ↦ ⟪v₁ j, v⟫_ℝ • (v₁ j)) + have A : (i : Fin 2) → Finset ι := by exact fun _ ↦ Finset.univ + + let X := ContinuousMultilinearMap.map_sum_finset + (iteratedFDeriv ℝ 2 f z) + (fun _ ↦ (fun j ↦ ⟪v₁ j, v⟫_ℝ • (v₁ j))) + (fun _ ↦ Finset.univ) + simp at X + sorry