Theorems · Theorem · number theory
Height.mulHeight_smul_eq_mulHeight
∀ {K : Type u_1} [inst : Field K] [inst_1 : Height.AdmissibleAbsValues K] {ι : Type u_2} [Finite ι] (x : ι → K) {c : K},
c ≠ 0 → Height.mulHeight (c • x) = Height.mulHeight xThe multiplicative height of a tuple does not change under scaling.
- Defined in
- Mathlib.NumberTheory.Height.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- Semiringproof · cited by 13,802
- Fieldstatement and proof · cited by 7,404
- Set.Elemproof · cited by 7,166
- Finitestatement and proof · cited by 3,029
- one_mulproof · cited by 2,841
- iSupproof · cited by 2,415
- map_mulproof · cited by 1,137
- eq_or_neproof · cited by 1,117
- Multiset.mapproof · cited by 876
- smul_zeroproof · cited by 665
Cited by6
Results whose statement or proof uses this declaration.
- Height.one_le_mulHeightproof · cited by 8
- Height.mulHeight_eq_one_of_subsingletonproof · cited by 7
- Height.mulHeight₁_div_eq_mulHeightproof · cited by 2
- Height.mulHeight₁_invproof · cited by 2
- Rat.mulHeight_self_one_eq_mulHeight_num_denproof · cited by 1
- Height.logHeight_smul_eq_logHeightproof · cited by 0