Rat.den_le_and_le_num_le_of_sub_lt_one_div_den_sq

∀ {ξ q : ℚ}, |ξ - q| < 1 / ↑q.den ^ 2 → q.den ≤ ξ.den ∧ ⌈ξ * ↑q.den⌉ - 1 ≤ q.num ∧ q.num ≤ ⌊ξ * ↑q.den⌋ + 1

If ξ is rational, then the good rational approximations to ξ have bounded numerator and denominator.

Defined in: Mathlib.NumberTheory.DiophantineApproximation.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

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