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theorem proved tactic proof

honestPhaseFamily_cost_bounded_iff_charge_zero

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formal statement (Lean)

 231theorem honestPhaseFamily_cost_bounded_iff_charge_zero
 232    (zfd : ZetaPhaseFamilyData) :
 233    RealizedDefectAnnularCostBounded (zfd.phaseFamily.toSampledFamily) ↔
 234      zfd.sensor.charge = 0 := by

proof body

Tactic-mode proof.

 235  constructor
 236  · intro hcost
 237    exact honestPhaseFamily_charge_zero_of_costBounded zfd hcost
 238  · intro hzero
 239    have hzero' : (zfd.phaseFamily.toSampledFamily).sensor.charge = 0 := by
 240      simpa [DefectPhaseFamily.toSampledFamily, zfd.family_sensor] using hzero
 241    exact realizedDefectCostBounded_of_charge_zero_and_excessBounded
 242      (zfd.phaseFamily.toSampledFamily) hzero'
 243      (honestPhaseFamily_excess_bounded zfd)
 244
 245end
 246
 247end NumberTheory
 248end IndisputableMonolith

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