Theorems · Theorem · number theory
NumberField.finite_setOfPred_mulHeight_nat_le
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] {n : ℕ},
n ≠ 0 → ∀ (B : ℝ), {a | Height.mulHeight ![↑a, ↑n] ≤ B}.FiniteThe set of a : 𝓞 K such that mulHeight₁ (a / n) = mulHeight ![a, n] is bounded
(for some given nonzero n : ℕ) is finite.
- Defined in
- Mathlib.NumberTheory.Height.NumberField
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 306 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.
Cites39
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- Set.ofPredstatement and proof · cited by 6,101
- Finset.univproof · cited by 3,473
- one_mulproof · cited by 2,841
- iSupproof · cited by 2,415
- Finset.prodproof · cited by 2,356
- mul_commproof · cited by 2,262
- le_reflproof · cited by 2,061
- Set.Finitestatement · cited by 1,814
- mul_assocproof · cited by 1,667
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.finite_setOf_mulHeight_nat_leproof · cited by 0