Theorems · Theorem · number theory
NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis
∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
(I : (FractionalIdeal (nonZeroDivisors (NumberField.RingOfIntegers K)) K)ˣ)
{x : NumberField.mixedEmbedding.mixedSpace K},
x ∈ Submodule.span ℤ (Set.range ⇑(NumberField.mixedEmbedding.fractionalIdealLatticeBasis K I)) ↔
x ∈ ⇑(NumberField.mixedEmbedding K) '' ↑↑I- Cited by
- 3 results in Mathlib
- Foundations
- Depth 310 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.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- RingHomstatement · cited by 10,189
- SetLike.coestatement and proof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Submodulestatement and proof · cited by 7,192
- Set.imagestatement and proof · cited by 5,609
- Complexstatement · cited by 5,565
- Set.rangestatement and proof · cited by 4,705
- Unitsstatement and proof · cited by 2,804
- Set.extproof · cited by 2,266
Cited by3
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_leproof · cited by 2
- NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_ltproof · cited by 1
- NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt'proof · cited by 1