Theorems · Definition · number theory
Height.mulHeight
{K : Type u_1} → [inst : Field K] → [Height.AdmissibleAbsValues K] → {ι : Type u_2} → (ι → K) → ℝThe multiplicative height of a tuple of elements of K.
For the zero tuple we take the junk value 1.
- Defined in
- Mathlib.NumberTheory.Height.Basic
- Cited by
- 64 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.Elemproof · cited by 7,166
- iSupproof · cited by 2,415
- Multiset.mapproof · cited by 876
- Multiset.prodproof · cited by 528
- AbsoluteValueproof · cited by 363
- finprodproof · cited by 257
- Height.AdmissibleAbsValuesstatement and proof · cited by 110
- Height.AdmissibleAbsValues.nonarchAbsValproof · cited by 30
- Height.AdmissibleAbsValues.archAbsValproof · cited by 28
Cited by68
Results whose statement or proof uses this declaration.
- Height.logHeightproof · cited by 35
- Height.mulHeight_zerostatement · cited by 17
- Height.mulHeight_eqstatement · cited by 14
- Height.mulHeight_posstatement · cited by 13
- Height.one_le_mulHeightstatement · cited by 8
- Height.mulHeight_comp_equivstatement · cited by 7
- Height.mulHeight_eq_one_of_subsingletonstatement and proof · cited by 7
- Height.mulHeight_smul_eq_mulHeightstatement and proof · cited by 6
- Height.mulHeight₁_eq_mulHeightstatement · cited by 6
- Projectivization.mulHeightproof · cited by 5
- Height.mulHeight_onestatement and proof · cited by 4
- Height.mulHeight_cons_cons_zerostatement and proof · cited by 3