Theorems · Theorem · number theory
GenContFract.of_correctness_of_terminates
∀ {K : Type u_1} [inst : Field K] [inst_1 : LinearOrder K] {v : K} [inst_2 : FloorRing K],
(GenContFract.of v).Terminates → ∃ n, v = (GenContFract.of v).convs nIf GenContFract.of v terminates, then there is n : ℕ such that the nth convergent is
exactly v.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldLinearOrderFloorRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- FloorRingstatement and proof · cited by 405
- GenContFract.sproof · cited by 57
- GenContFract.ofstatement and proof · cited by 53
- Stream'.Seq.TerminatedAtproof · cited by 26
- GenContFract.convsstatement · cited by 22
- GenContFract.Terminatesstatement and proof · cited by 6
- GenContFract.of_correctness_of_terminatedAtproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- GenContFract.exists_rat_eq_of_terminatesproof · cited by 1