| import Mathlib | |
| import OAI.Analysis.HardSphere.Geometry.ScalarNormSqIntegral | |
| import OAI.Analysis.HardSphere.Cutoffs.DifferentialFormula | |
| namespace OAI | |
| section | |
| section | |
| noncomputable section | |
| open MeasureTheory Filter Set | |
| open scoped Topology ENNReal BigOperators | |
| open scoped RealInnerProductSpace | |
| namespace HardSphere | |
| lemma IsGroundVector.ae_gradient_phase {N : ℕ} {L : Length} {a : ℝ} {u : Jet N L} | |
| (hu : IsGroundVector N L a u) (p : Direction N) : | |
| ∀ᵐ X ∂volume, u.2 p X = u.1 X / (‖u.1 X‖ : ℂ) * (modulusJet u).2 p X := by | |
| filter_upwards [hu.ae_norm_modulusPartial p, coe_modulusPartial u.1 (u.2 p)] with X h1 h2 | |
| change u.2 p X = u.1 X / (‖u.1 X‖ : ℂ) * modulusPartial u.1 (u.2 p) X | |
| rw [h2] | |
| exact ComplexRegularization.phase_differential_of_norm_eq _ _ h1 | |
| end HardSphere | |
| end | |
| end | |
| end | |
| end OAI | |