structure
definition
def or abbrev
ZeroWindingCert
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formal statement (Lean)
123structure ZeroWindingCert where
124 center : ℂ
125 radius : ℝ
126 radius_pos : 0 < radius
127 cert : ComplexCarrierCert
128 cert_match : cert.center = center ∧ cert.radius = radius
129 zero_winding : ∀ (r : ℝ), 0 < r → r < radius →
130 contourWinding cert r = 0
131
132/-- Extract a `ZeroWindingCert` from a `ComplexCarrierCert`. -/
133def ComplexCarrierCert.toZeroWindingCert (cert : ComplexCarrierCert) :
134 ZeroWindingCert where
135 center := cert.center
proof body
Definition body.
136 radius := cert.radius
137 radius_pos := cert.radius_pos
138 cert := cert
139 cert_match := ⟨rfl, rfl⟩
140 zero_winding := carrier_zero_winding cert
141
142/-- The Euler carrier's zero-winding certificate for any σ₀ > 1/2. -/
used by (16)
-
carrier_trace_charge_zero -
zeroWindingData -
zeroWindingFromCert -
zeroWindingFromCert_charge -
ComplexCarrierCert -
eulerZeroWindingCert -
mkSampledMesh -
mkSampledMesh_charge_zero -
mkSampledRing -
sampledBudgetedCarrier -
sampledBudgetedCarrier_scale_zero -
SampledMesh -
SampledRing -
sampledTraceToAnnularTrace -
sampledTraceToAnnularTrace_charge_zero -
sampledTraceToAnnularTrace_excess_zero