Theorems · Theorem · field theory
NormedField.exists_nnnorm_lt_one
∀ (α : Type u_2) [inst : NontriviallyNormedField α], ∃ x, 0 < ‖x‖₊ ∧ ‖x‖₊ < 1
- Defined in
- Mathlib.Analysis.Normed.Field.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NontriviallyNormedField
Around this declaration
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Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- NNRealstatement · cited by 4,310
- NNNorm.nnnormstatement · cited by 952
- NormedField.exists_norm_lt_oneproof · cited by 6
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