| 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 | |