OAI/Probability/SLE/Gauge/SerpentineInfiniteArray.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

The finite serpentine remains embedded after continuing its last column vertically to infinity.

  1. lemma OAI.SLEExactGauge.Serpentine.array_normal_terminal line 14
  2. lemma OAI.SLEExactGauge.Serpentine.array_normal_finite_terminal_disjoint line 24
  3. theorem OAI.SLEExactGauge.Serpentine.array_normal_injective_infinite line 57

    Source documentation

    The complete upward-continued array is embedded on the whole closed width-one normal strip.

    theorem array_normal_injective_infinite {m : ℕ} (hm : 0 < m) :
        InjOn (normalRibbon (arraySpine m (2 * m)) (arrayTangent m (2 * m)))
          {z : ℂ | 0 ≤ z.re ∧ |z.im| ≤ 1} := by
    …

    Mentions: OAI.SLEExactGauge.Serpentine.normalRibbon, OAI.SLEExactGauge.Serpentine.arraySpine, OAI.SLEExactGauge.Serpentine.arrayTangent