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lemma proved term proof

identity_in_ball

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formal statement (Lean)

  85lemma identity_in_ball (c : Config) (hr : r > modal_distance c (identity_config c.time)) :
  86    ∃ t : ℕ, identity_config t ∈ PossibilityBall c r := by

proof body

Term-mode proof.

  87  use c.time
  88  simp only [PossibilityBall, Set.mem_setOf_eq]
  89  exact le_of_lt hr
  90
  91/-- **CONNECTIVITY**: Every configuration connects to identity.
  92
  93    This gives possibility space a "star" topology with identity at the center. -/

depends on (7)

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