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theorem proved term proof

separating_singleton_cells

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formal statement (Lean)

  66theorem separating_singleton_cells (r : Recognizer C E) (h : IsSeparating r) (c : C) :
  67    ResolutionCell r c = {c} := by

proof body

Term-mode proof.

  68  ext x
  69  simp only [ResolutionCell, Set.mem_setOf_eq, Set.mem_singleton_iff]
  70  constructor
  71  · intro hx; exact h hx
  72  · intro hx; subst hx; rfl
  73
  74/-! ## Two-Recognizer Separation -/
  75
  76/-- Two recognizers together separate if their composite distinguishes all configs. -/

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