Weak Problem RHSOf Field eq of mem H01

theorem weakProblemRHSOfField_eq_of_memH01    {Ω : Set E} (hΩ : IsOpen Ω) {F : E → E} {v : E → ℝ}    (hv0 : MemH01 v Ω) (hv : MemW1pWitness 2 v Ω) :    weakProblemRHSOfField (Ω := Ω) F v = divergenceRHSOfField F hv := by  let _ := (inferInstance : NeZero d)  rw [weakProblemRHSOfField, dif_pos hv0]  let hw0 : MemW1pWitness 2 v Ω :=    DeGiorgi.MemW1p.someWitness (MemW01p.memW1p hv0)  have hgrad_ae : hw0.weakGrad =ᵐ[volume.restrict Ω] hv.weakGrad := by    have hp2 : (1 : ENNReal) ≤ 2 := by      norm_num    have hcomp :        ∀ i : Fin d,          (fun x => hw0.weakGrad x i) =ᵐ[volume.restrict Ω] (fun x => hv.weakGrad x i) := by      intro i      exact HasWeakPartialDeriv.ae_eq hΩ (hw0.isWeakGrad i) (hv.isWeakGrad i)        ((hw0.weakGrad_component_memLp i).locallyIntegrable hp2)        ((hv.weakGrad_component_memLp i).locallyIntegrable hp2)    filter_upwards [ae_all_iff.2 hcomp] with x hx    ext i    exact hx i  have hintegral :      ∫ x in Ω, divergenceRHSIntegrandOfField F hw0 x =        ∫ x in Ω, divergenceRHSIntegrandOfField F hv x := by    apply integral_congr_ae    filter_upwards [hgrad_ae] with x hx    simpa [divergenceRHSIntegrandOfField, hw0] using      congrArg (fun g => ⟪F x, g⟫_ℝ) hx  simpa [hw0, divergenceRHSOfField] using congrArg Neg.neg hintegral