cauchySeq_of_edist_le_geometric_two

English

If edist is bounded by a geometric progression, then a Cauchy sequence exists.

Русский

Если edist ограничена геометрической прогрессией, существует последовательность Коши.

LaTeX

$$$$\text{Cauchy sequence under geometric bound}.$$$$

Lean4

/-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then `f` is a Cauchy sequence. -/
theorem cauchySeq_of_edist_le_geometric_two : CauchySeq f :=
  by
  simp only [div_eq_mul_inv, ENNReal.inv_pow] at hu
  refine cauchySeq_of_edist_le_geometric 2⁻¹ C ?_ hC hu
  simp

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