Theorems · Definition · number theory
Rat.AbsoluteValue.padic
(p : ℕ) → [Fact (Nat.Prime p)] → AbsoluteValue ℚ ℝ
The real-valued AbsoluteValue corresponding to the p-adic norm on ℚ.
- Defined in
- Mathlib.NumberTheory.Ostrowski
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
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.
- Realstatement · cited by 25,697
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- AbsoluteValuestatement · cited by 363
- padicNormproof · cited by 83
Cited by6
Results whose statement or proof uses this declaration.
- Rat.AbsoluteValue.equiv_padic_of_boundedstatement and proof · cited by 1
- Rat.AbsoluteValue.padic_le_onestatement · cited by 1
- Rat.AbsoluteValue.equiv_real_or_padicstatement · cited by 0
- Rat.AbsoluteValue.not_real_isEquiv_padicstatement and proof · cited by 0
- Rat.AbsoluteValue.padic_eq_padicNormstatement · cited by 0
- Rat.AbsoluteValue.padic.congr_simpstatement and proof · cited by 0