Theorems · Theorem · field theory
NormedField.exists_lt_nnnorm_lt
∀ (α : Type u_2) [inst : DenselyNormedField α] {r₁ r₂ : NNReal}, r₁ < r₂ → ∃ x, r₁ < ‖x‖₊ ∧ ‖x‖₊ < r₂- Defined in
- Mathlib.Analysis.Normed.Field.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DenselyNormedField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement and proof · cited by 4,310
- NNNorm.nnnormstatement and proof · cited by 952
- Subtype.propproof · cited by 505
- DenselyNormedFieldstatement and proof · cited by 14
- NormedField.exists_lt_norm_ltproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.exists_lt_apply_of_lt_opNNNormproof · cited by 3
- NormedField.denseRange_nnnormproof · cited by 0