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theorem proved term proof

scale_step_ratio

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formal statement (Lean)

  44theorem scale_step_ratio (S : GeometricScaleSequence) (k : ℕ) :
  45    S.scale (k + 1) / S.scale k = S.ratio := by

proof body

Term-mode proof.

  46  unfold GeometricScaleSequence.scale
  47  rw [pow_succ]
  48  have hr : S.ratio ≠ 0 := ne_of_gt S.ratio_pos
  49  have hk : S.ratio ^ k ≠ 0 := pow_ne_zero k hr
  50  simpa using (mul_div_cancel_left₀ S.ratio hk)
  51
  52/-- The realized orbit has constant adjacent ratio. -/

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