Theorems · Theorem · field theory
Valued.integer.exists_nnnorm_lt_one
∀ (K : Type u_1) [inst : NontriviallyNormedField K] [inst_1 : IsUltrametricDist K], ∃ x, 0 < ‖x‖₊ ∧ ‖x‖₊ < 1
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- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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
- Subringstatement · cited by 602
- IsUltrametricDiststatement and proof · cited by 177
- Valued.integerstatement · cited by 22
- NormedField.toValuedstatement · cited by 14
- Valued.integer.exists_norm_coe_lt_oneproof · cited by 2
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