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theorem proved term proof

realizedDefectAnnularExcessBounded_of_ringRegularErrorBound

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formal statement (Lean)

 242theorem realizedDefectAnnularExcessBounded_of_ringRegularErrorBound
 243    (fam : DefectSampledFamily) (hreg : RingRegularErrorBound fam) :
 244    RealizedDefectAnnularExcessBounded fam := by

proof body

Term-mode proof.

 245  obtain ⟨K, hK⟩ := hreg.total_error_bounded
 246  refine ⟨K, ?_⟩
 247  intro N
 248  exact le_trans
 249    (annularExcess_le_sum_of_ringCost_le_topologicalFloor_plus_regularError fam hreg N)
 250    (hK N)
 251
 252/-- A uniform total-cost bound immediately gives a uniform excess bound, since
 253the topological floor is nonnegative. -/

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depends on (19)

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