Theorems · Theorem · number theory
UnitAddCircle.mem_approxAddOrderOf_iff
∀ {δ : ℝ} {x : UnitAddCircle} {n : ℕ},
0 < n → (x ∈ approxAddOrderOf UnitAddCircle n δ ↔ ∃ m < n, gcd m n = 1 ∧ ‖x - ↑(↑m / ↑n)‖ < δ)- Defined in
- Mathlib.NumberTheory.WellApproximable
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- LinearOrderproof · cited by 8,572
- Fieldproof · cited by 7,404
- Set.ofPredproof · cited by 6,101
- Norm.normstatement and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- Factproof · cited by 2,726
- IsStrictOrderedRingproof · cited by 2,490
- AddSubgroup.zmultiplesstatement · cited by 493
- QuotientAddGroup.mkstatement and proof · cited by 348
- AddCircleproof · cited by 189
Cited by1
Results whose statement or proof uses this declaration.
- UnitAddCircle.mem_addWellApproximable_iffproof · cited by 0