Theorems · Theorem · number theory
mem_approx_add_orderOf_iff
∀ {A : Type u_1} [inst : SeminormedAddGroup A] {n : ℕ} {δ : ℝ} {a : A},
a ∈ approxAddOrderOf A n δ ↔ ∃ b, addOrderOf b = n ∧ a ∈ Metric.ball b δ- Defined in
- Mathlib.NumberTheory.WellApproximable
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Metric.ballstatement and proof · cited by 735
- SeminormedAddGroupstatement and proof · cited by 331
- addOrderOfstatement and proof · cited by 208
- Set.mem_iUnion₂proof · cited by 70
- approxAddOrderOfstatement · cited by 9
- Metric.thickening_eq_biUnion_ballproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- approxAddOrderOf.image_nsmul_subsetproof · cited by 1
- approxAddOrderOf.image_nsmul_subset_of_coprimeproof · cited by 1