theorem
proved
term proof
scale_step_ratio
show as:
view Lean formalization →
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. -/