Theorems · Theorem · number theory
Real.convs_eq_convergent
∀ (ξ : ℝ) (n : ℕ), (GenContFract.of ξ).convs n = ↑(ξ.convergent n)
The nth convergent of the GenContFract.of ξ agrees with ξ.convergent n.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- one_divproof · cited by 624
- Int.floorproof · cited by 225
- Int.fractproof · cited by 114
- Rat.cast_intCastproof · cited by 74
- GenContFract.ofstatement and proof · cited by 53
- GenContFract.convsstatement and proof · cited by 22
- Real.convergentstatement and proof · cited by 9
- Real.convergent_succproof · cited by 2
- GenContFract.zeroth_conv_eq_hproof · cited by 2
- GenContFract.convs_succproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Real.exists_convs_eq_ratproof · cited by 0