File size: 1,410 Bytes
8e4d533 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 | import Mathlib
import OAI.Geometry.Cannon.PlanarGraphs.Region
namespace OAI
section
section
section
noncomputable section
open Set unitInterval Topology
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open Set Topology unitInterval
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open Set Metric Topology unitInterval
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open Set Metric Topology
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open Set unitInterval
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noncomputable section
open Set Metric Topology
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open Set Metric Topology
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open Set Metric Topology
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open Set Topology
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open Set Topology
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open Set Topology
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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
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