Theorems · Theorem · number theory
Rat.iSup_finitePlace_apply_eq_one_of_gcd_eq_one
∀ {ι : Type u_1} [inst : Fintype ι] [Nonempty ι] {x : ι → ℤ} (v : NumberField.FinitePlace ℚ),
Finset.univ.gcd x = 1 → ⨆ i, v ↑(x i) = 1The term corresponding to a finite place in the definition of the multiplicative height
of a tuple of rational numbers equals 1 if the tuple consists of coprime integers.
- Defined in
- Mathlib.NumberTheory.Height.NumberField
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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
- Fintypestatement and proof · cited by 7,736
- Finset.sumproof · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- LE.le.transproof · cited by 3,151
- iSupstatement and proof · cited by 2,415
- Finset.sum_congrproof · cited by 2,323
- le_antisymmproof · cited by 2,068
- map_mulproof · cited by 1,137
- map_oneproof · cited by 861
- DFunLikeproof · cited by 576
Cited by1
Results whose statement or proof uses this declaration.
- Rat.mulHeight_eq_max_abs_of_gcd_eq_oneproof · cited by 2