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theorem proved term proof

zeroCompositionLaw_forces_eta_zero

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formal statement (Lean)

  72theorem zeroCompositionLaw_forces_eta_zero
  73    (zc : ZeroCompositionLaw) (ρ : ℂ) :
  74    zc.H (zeroDeviation ρ) = 1 ↔ OnCriticalLine ρ := by

proof body

Term-mode proof.

  75  constructor
  76  · intro h
  77    have hz : zeroDeviation ρ = 0 :=
  78      (zeroCompositionLaw_forces_unique_minimum zc (zeroDeviation ρ)).mp h
  79    exact (zeroDeviation_eq_zero_iff_on_critical_line ρ).mp hz
  80  · intro h
  81    have hz : zeroDeviation ρ = 0 :=
  82      (zeroDeviation_eq_zero_iff_on_critical_line ρ).mpr h
  83    exact (zeroCompositionLaw_forces_unique_minimum zc (zeroDeviation ρ)).mpr hz
  84
  85/-- A concrete Vector C witness at a specific complex point. -/

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