Theorems · Theorem · number theory
NumberField.mixedEmbedding.exists_primitive_element_lt_of_isComplex
∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K] {w₀ : NumberField.InfinitePlace K},
w₀.IsComplex →
∀ {B : NNReal},
NumberField.mixedEmbedding.minkowskiBound K 1 < ↑(NumberField.mixedEmbedding.convexBodyLT'Factor K) * ↑B →
∃ a, ℚ⟮↑a⟯ = ⊤ ∧ ∀ (w : NumberField.InfinitePlace K), w ↑a < √(1 + ↑B ^ 2)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 313 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.
Cites66
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 · cited by 53,352
- Realstatement and proof · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Complexproof · cited by 5,565
- Norm.normproof · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- Finset.univproof · cited by 3,473
- one_mulproof · cited by 2,841
- Unitsstatement · cited by 2,804
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplexproof · cited by 1