Theorems · Theorem · number theory
NumberField.hermiteTheorem.rank_le_rankOfDiscrBdd
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] {N : ℕ},
|NumberField.discr K| ≤ ↑N → Module.finrank ℚ K ≤ NumberField.hermiteTheorem.rankOfDiscrBdd NIf |discr K| ≤ N then the degree of K is at most rankOfDiscrBdd.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 316 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.
Cites53
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- mul_commproof · cited by 2,262
- le_reflproof · cited by 2,061
- Nat.cast_zeroproof · cited by 1,870
- absstatement and proof · cited by 1,814
- Real.piproof · cited by 1,774
- Module.finrankstatement and proof · cited by 1,770
- mul_assocproof · cited by 1,667
- le_of_ltproof · cited by 1,175
Cited by4
Results whose statement or proof uses this declaration.
- NumberField.hermiteTheorem.minkowskiBound_lt_boundOfDiscBddproof · cited by 2
- NumberField.hermiteTheorem.natDegree_le_rankOfDiscrBddproof · cited by 2
- NumberField.hermiteTheorem.finite_of_discr_bdd_of_isRealproof · cited by 1
- NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplexproof · cited by 1