| import Mathlib | |
| import OAI.Geometry.Cannon.PlanarGraphs.Region | |
| namespace OAI | |
| section | |
| section | |
| section | |
| noncomputable section | |
| open Set unitInterval Topology | |
| noncomputable section | |
| noncomputable section | |
| noncomputable section | |
| open Set Topology unitInterval | |
| noncomputable section | |
| open Set Metric Topology unitInterval | |
| noncomputable section | |
| open Set Metric Topology | |
| noncomputable section | |
| noncomputable section | |
| open Set unitInterval | |
| noncomputable section | |
| noncomputable section | |
| open Set Metric Topology | |
| noncomputable section | |
| open Set Metric Topology | |
| noncomputable section | |
| open Set Metric Topology | |
| noncomputable section | |
| open Set Topology | |
| noncomputable section | |
| open Set Topology | |
| noncomputable section | |
| open Set Topology | |
| noncomputable section | |
| open Set Topology unitInterval | |
| namespace CannonFaceIncidence | |
| open Set Topology | |
| variable {X D : Type*} [TopologicalSpace X] [TopologicalSpace D] [DiscreteTopology D] | |
| omit [TopologicalSpace D] [DiscreteTopology D] in | |
| lemma incident_subset_of_patch {V W : Set X} {π : V → D} (hW : IsOpen W) | |
| {d : D} (hl : W∩V⊆region V π d) {x : X} (hx : x∈W) : | |
| incident V π x⊆{d} := by | |
| intro e he | |
| obtain ⟨y,hyW,hyR⟩ := (mem_closure_iff_nhds.mp he) W (hW.mem_nhds hx) | |
| have hy := hl ⟨hyW,region_subset _ _ _ hyR⟩ | |
| exact hyR.2.symm.trans hy.2 | |
| end CannonFaceIncidence | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end | |
| end OAI | |