Theorems · Theorem · number theory

NumberField.mixedEmbedding.norm_ne_zero_iff

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] {x : NumberField.mixedEmbedding.mixedSpace K},
  NumberField.mixedEmbedding.norm x ≠ 0 ↔
    ∀ (w : NumberField.InfinitePlace K), (NumberField.mixedEmbedding.normAtPlace w) x ≠ 0

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 300 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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NumberField.mixedEmbedding.mixedSpacestatement and proof · cited by 239
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NumberField.mixedEmbedding.normstatement · cited by 46

Cited by2

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.logMap_mulproof · cited by 2
NumberField.mixedEmbedding.fundamentalCone.normAtPlace_pos_of_memproof · cited by 1