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theorem proved term proof

sampledTraceToAnnularTrace_excess_zero

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formal statement (Lean)

 145theorem sampledTraceToAnnularTrace_excess_zero (cert : ZeroWindingCert) (N : ℕ) :
 146    annularExcess ((sampledTraceToAnnularTrace cert).mesh N) = 0 := by

proof body

Term-mode proof.

 147  unfold annularExcess annularCost annularTopologicalFloor
 148  rw [sub_eq_zero]
 149  apply Finset.sum_congr rfl
 150  intro n _
 151  show ringCost _ = topologicalFloor _ _
 152  unfold sampledTraceToAnnularTrace SampledMesh.toAnnularMesh mkSampledMesh
 153    mkSampledRing SampledRing.toAnnularRingSample
 154  simp only
 155  unfold ringCost topologicalFloor
 156  simp [phiCost_zero, Finset.sum_const_zero]
 157
 158/-! ### §6. Building a BudgetedCarrier from sampled traces -/
 159
 160/-- Build a `BudgetedCarrier` from a `ZeroWindingCert` and carrier regularity data.
 161This replaces the synthetic `eulerBudgetedCarrier` with one built from actual
 162zero-winding certificates. -/

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