Theorems · Theorem · functional analysis
eventually_norm_sub_lt
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] (x₀ : E) {ε : ℝ}, 0 < ε → ∀ᶠ (x : E) in nhds x₀, ‖x - x₀‖ < ε- Defined in
- Mathlib.Analysis.Normed.Group.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Set.ofPredproof · cited by 6,101
- nhdsstatement · cited by 5,554
- Norm.normstatement and proof · cited by 5,413
- Filter.Eventuallystatement · cited by 3,134
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- sub_selfproof · cited by 996
- norm_zeroproof · cited by 366
- continuousAt_constproof · cited by 59
- gt_mem_nhdsproof · cited by 37
- continuousAt_idproof · cited by 28
- ContinuousAt.normproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Complex.log_sub_logTaylor_isBigOproof · cited by 1