theorem
proved
tactic proof
honestPhaseFamily_cost_bounded_iff_charge_zero
show as:
view Lean formalization →
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