Theorems · Theorem · number theory
GenContFract.exists_rat_eq_nth_conv
∀ {K : Type u_1} [inst : Field K] [inst_1 : LinearOrder K] [inst_2 : FloorRing K] (v : K) (n : ℕ),
∃ q, (GenContFract.of v).convs n = ↑qEvery finite convergent corresponds to a rational number.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 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.
Cites10
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.ofstatement and proof · cited by 53
- Rat.cast_divproof · cited by 37
- GenContFract.convsstatement · cited by 22
- GenContFract.densproof · cited by 19
- GenContFract.numsproof · cited by 12
- GenContFract.exists_rat_eq_nth_denproof · cited by 1
- GenContFract.exists_rat_eq_nth_numproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- GenContFract.exists_rat_eq_of_terminatesproof · cited by 1