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theorem proved term proof

honestPhaseFamily_charge_zero_of_costBounded

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formal statement (Lean)

 219theorem honestPhaseFamily_charge_zero_of_costBounded
 220    (zfd : ZetaPhaseFamilyData)
 221    (hcost : RealizedDefectAnnularCostBounded (zfd.phaseFamily.toSampledFamily)) :
 222    zfd.sensor.charge = 0 := by

proof body

Term-mode proof.

 223  have hzero :=
 224    (realizedDefectCostBounded_iff_charge_zero_and_excessBounded
 225      (zfd.phaseFamily.toSampledFamily)).mp hcost
 226  simpa [DefectPhaseFamily.toSampledFamily, zfd.family_sensor] using hzero.1
 227
 228/-- For the current honest phase package, bounded total cost is equivalent to
 229zero charge. The perturbation/excess part is already proved; only the bounded-cost
 230upgrade remains genuinely open. -/

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