Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.mem_idealSet

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] {x : NumberField.mixedEmbedding.mixedSpace K}
  {J : ↥(nonZeroDivisors (Ideal (NumberField.RingOfIntegers K)))},
  x ∈ NumberField.mixedEmbedding.fundamentalCone.idealSet K J ↔
    x ∈ NumberField.mixedEmbedding.fundamentalCone K ∧ ∃ a ∈ ↑↑J, (NumberField.mixedEmbedding K) ↑a = x

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone
Cited by: 1 results in Mathlib
Foundations: Depth 327 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites25

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

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Complexstatement · cited by 5,565
Idealstatement and proof · cited by 4,748
Algebra.algebraMapproof · cited by 4,706
Submonoidstatement · cited by 3,086
nonZeroDivisorsstatement and proof · cited by 895
NumberFieldstatement and proof · cited by 653

Cited by1

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NumberField.mixedEmbedding.fundamentalCone.preimage_of_IdealSetMapproof · cited by 0