Theorems · Theorem · number theory
NumberField.finite_setOfPred_prod_infinitePlace_iSup_le
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] {n : ℕ},
n ≠ 0 → ∀ (B : ℝ), {x | ∏ v, (⨆ i, v (![↑x, ↑n] i)) ^ v.mult ≤ B}.Finite- Defined in
- Mathlib.NumberTheory.Height.NumberField
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 305 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.
Cites31
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
- Realstatement and proof · cited by 25,697
- RingHomproof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Set.ofPredstatement and proof · cited by 6,101
- Complexproof · cited by 5,565
- Norm.normproof · cited by 5,413
- Finset.univstatement and proof · cited by 3,473
- iSupstatement and proof · cited by 2,415
- Finset.prodstatement and proof · cited by 2,356
- Set.Finitestatement · cited by 1,814
- Matrix.vecConsstatement and proof · cited by 852
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.finite_setOfPred_mulHeight_nat_leproof · cited by 1
- NumberField.finite_setOf_prod_infinitePlace_iSup_leproof · cited by 0