Theorems · Theorem · number theory
GenContFract.of_correctness_atTop_of_terminates
∀ {K : Type u_1} [inst : Field K] [inst_1 : LinearOrder K] {v : K} [inst_2 : FloorRing K],
(GenContFract.of v).Terminates → ∀ᶠ (n : ℕ) in Filter.atTop, v = (GenContFract.of v).convs nIf GenContFract.of v terminates, then its convergents will eventually always be v.
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- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldLinearOrderFloorRing
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Cites12
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
- Filter.Eventuallystatement · cited by 3,134
- Filter.atTopstatement · cited by 2,405
- FloorRingstatement and proof · cited by 405
- Filter.eventually_atTopproof · cited by 112
- GenContFract.ofstatement and proof · cited by 53
- GenContFract.TerminatedAtproof · cited by 30
- GenContFract.convsstatement · cited by 22
- GenContFract.Terminatesstatement and proof · cited by 6
- GenContFract.convs_stable_of_terminatedproof · cited by 4
- GenContFract.of_correctness_of_terminatedAtproof · cited by 3
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