Theorems · Theorem · number theory
GenContFract.dens_recurrence
∀ {K : Type u_1} {g : GenContFract K} {n : ℕ} [inst : DivisionRing K] {gp : GenContFract.Pair K} {ppredB predB : K},
g.s.get? (n + 1) = some gp →
g.dens n = ppredB → g.dens (n + 1) = predB → g.dens (n + 2) = gp.b * predB + gp.a * ppredBShows that Bₙ = bₙ * Bₙ₋₁ + aₙ * Bₙ₋₂.
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- Foundations
- Depth 52 from the axioms · uses propext, Quot.sound
- Assumes
- DivisionRing
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DivisionRingstatement and proof · cited by 1,062
- Stream'.Seq.get?statement and proof · cited by 122
- GenContFract.Pairstatement and proof · cited by 85
- GenContFractstatement and proof · cited by 68
- GenContFract.sstatement and proof · cited by 57
- GenContFract.Pair.bstatement and proof · cited by 51
- GenContFract.Pair.astatement and proof · cited by 43
- GenContFract.densstatement and proof · cited by 19
- GenContFract.contsproof · cited by 18
- GenContFract.den_eq_conts_bproof · cited by 4
- GenContFract.conts_recurrenceproof · cited by 2
- GenContFract.exists_conts_b_of_denproof · cited by 1
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