Theorems · Definition · number theory
Height.AdmissibleAbsValues.nonarchAbsVal
{K : Type u_1} → {inst : Field K} → [self : Height.AdmissibleAbsValues K] → Set (AbsoluteValue K ℝ)The nonarchimedean absolute values as a set of ℝ-valued absolute values on K.
- Defined in
- Mathlib.NumberTheory.Height.Basic
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Height.AdmissibleAbsValues
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- AbsoluteValuestatement · cited by 363
- Height.AdmissibleAbsValuesstatement and proof · cited by 110
Cited by33
Results whose statement or proof uses this declaration.
- Height.mulHeightproof · cited by 64
- Height.mulHeight₁proof · cited by 35
- Height.mulHeight_zeroproof · cited by 17
- Height.mulHeight_eqstatement and proof · cited by 14
- Height.mulHeightBoundproof · cited by 10
- Height.one_le_mulHeightproof · cited by 8
- Height.mulHeight_comp_equivproof · cited by 7
- Height.mulHeight_smul_eq_mulHeightproof · cited by 6
- Height.mulHeight₁_eq_mulHeightproof · cited by 6
- Height.mulHeight_oneproof · cited by 4
- Height.AdmissibleAbsValues.isNonarchimedeanstatement · cited by 3
- Height.mulHeight_eval_leproof · cited by 3