Mathlib Map

Theorems · Definition · number theory

Height.mulHeight

{K : Type u_1} → [inst : Field K] → [Height.AdmissibleAbsValues K] → {ι : Type u_2} → (ι → K) → ℝ

The 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
Assumes
FieldHeight.AdmissibleAbsValues

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Height.logHeight · cited by 35Height.logHeightHeight.mulHeight_zero · cited by 17Height.mulHeight_zeroHeight.mulHeight_eq · cited by 14Height.mulHeight_eqHeight.mulHeight_pos · cited by 13Height.mulHeight_posHeight.one_le_mulHeight · cited by 8Height.one_le_mulHeightHeight.mulHeight_comp_equiv · cited by 7Height.mulHeight_comp_equ…Height.mulHeight_eq_one_of_subsingleton · cited by 7Height.mulHeight_eq_one_o…Height.mulHeight_smul_eq_mulHeight · cited by 6Height.mulHeight_smul_eq_…Height.mulHeight₁_eq_mulHeight · cited by 6Height.mulHeight₁_eq_mulH…Projectivization.mulHeight · cited by 5Projectivization.mulHeightHeight.mulHeight_one · cited by 4Height.mulHeight_oneHeight.mulHeight_cons_cons_zero · cited by 3Height.mulHeight_cons_con…Height.mulHeight_eval_le · cited by 3Height.mulHeight_eval_leHeight.mulHeight_fun_mul_eq · cited by 3Height.mulHeight_fun_mul_…Height.mulHeight_pow · cited by 3Height.mulHeight_powDFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealField · cited by 7404FieldSet.Elem · cited by 7166Set.ElemiSup · cited by 2415iSupMultiset.map · cited by 876Multiset.mapMultiset.prod · cited by 528Multiset.prodAbsoluteValue · cited by 363AbsoluteValuefinprod · cited by 257finprodHeight.AdmissibleAbsValues · cited by 110Height.AdmissibleAbsValuesHeight.AdmissibleAbsValues.nonarchAbsVal · cited by 30AdmissibleAbsValues.nonar…Height.AdmissibleAbsValues.archAbsVal · cited by 28AdmissibleAbsValues.archA…Height.mulHeightCITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by68

Results whose statement or proof uses this declaration.