`bandUpper_ratio`

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module: IndisputableMonolith.Unification.RecognitionBandGeometry
domain: Unification
line: 77 · github
papers citing: none yet

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IndisputableMonolith.Unification.RecognitionBandGeometry on GitHub at line 77.

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depends on

formal source

  74  field_simp [phi_ne_zero]
  75
  76/-- At the upper boundary, `ρ/(1-ρ) = φ`. -/
  77theorem bandUpper_ratio : rhoBandUpper / (1 - rhoBandUpper) = phi := by
  78  rw [one_sub_rhoBandUpper_eq_rhoBandLower]
  79  unfold rhoBandLower rhoBandUpper
  80  field_simp [phi_ne_zero]
  81
  82theorem bandBoundaries_product : rhoBandLower * rhoBandUpper = phi⁻¹ ^ 3 := by
  83  unfold rhoBandLower rhoBandUpper
  84  ring
  85
  86end
  87end RecognitionBandGeometry
  88end Unification
  89end IndisputableMonolith

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