| import Mathlib | |
| import OAI.Geometry.Cannon.Flows.Domain | |
| namespace OAI | |
| section | |
| section | |
| section | |
| noncomputable section | |
| section | |
| section | |
| section | |
| namespace CannonApprox | |
| open CannonMagnification CannonCrossEnergy Set Metric Filter Topology MeasureTheory | |
| lemma onDomain_image_eq {X : Type*} [TopologicalSpace X] {Ω : Set X} | |
| (u : C(Ω,ℝ)) (A : Set X) (hA : A ⊆ Ω) : | |
| onDomain u '' A = u '' (Subtype.val ⁻¹' A) := by | |
| ext t | |
| constructor | |
| · rintro ⟨x,hx,rfl⟩ | |
| exact ⟨⟨x,hA hx⟩,hx,(onDomain_eq u x (hA hx)).symm⟩ | |
| · rintro ⟨x,hx,rfl⟩ | |
| exact ⟨x,hx,onDomain_eq u x x.property⟩ | |
| end CannonApprox | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end OAI | |