Theorems · Definition · number theory
NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv
(K : Type u_1) →
[inst : Field K] →
[inst_1 : NumberField K] →
(J : ↥(nonZeroDivisors (Ideal (NumberField.RingOfIntegers K)))) →
↑(NumberField.mixedEmbedding.fundamentalCone.idealSet K J) ≃
↑{a | ↑(NumberField.mixedEmbedding.fundamentalCone.preimageOfMemIntegerSet a) ∈ ↑↑J}The map idealSetMap is actually an equiv between idealSet K J and the elements of
integerSet K whose preimage lies in J.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 338 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Equivstatement · cited by 8,337
- SetLike.coestatement · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Set.Elemstatement and proof · cited by 7,166
- Set.ofPredstatement · cited by 6,101
- Idealstatement and proof · cited by 4,748
- Submonoidstatement · cited by 3,086
- nonZeroDivisorsstatement and proof · cited by 895
- NumberFieldstatement and proof · cited by 653
- NumberField.RingOfIntegersstatement and proof · cited by 413
- NumberField.mixedEmbedding.mixedSpacestatement · cited by 239
Cited by5
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_applystatement · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.idealSetEquivNormproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_symm_applystatement and proof · cited by 0
- NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_applystatement and proof · cited by 0
- NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_leproof · cited by 0