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f205175 | 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 | import Mathlib
import OAI.Probability.CriticalPercolation.GraphGeometry.VertexBall
namespace OAI
section
section
open Set MeasureTheory ProbabilityTheory
open scoped BigOperators
namespace CriticalPercolation.ClusterDeletion
variable {V : Type*}
@[simp] lemma delete_bot (U : Set V) : delete (⊥ : SimpleGraph V) U = ⊥ := by
ext v w
simp [delete]
@[simp] lemma component_bot (s : V) : component (⊥ : SimpleGraph V) s = {s} := by
ext v
simp [component, SimpleGraph.reachable_bot, eq_comm]
@[simp] lemma roots_bot (S : Set V) : roots (⊥ : SimpleGraph V) S = S := by
ext v
simp [roots, SimpleGraph.reachable_bot]
end CriticalPercolation.ClusterDeletion
end
end
end OAI
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