Theorems · Theorem · number theory
Rat.AbsoluteValue.equiv_padic_of_bounded
∀ {f : AbsoluteValue ℚ ℝ},
f.IsNontrivial → (∀ (n : ℕ), f ↑n ≤ 1) → ∃! p, ∃ (x : Fact (Nat.Prime p)), f.IsEquiv (Rat.AbsoluteValue.padic p)If f is bounded and not trivial, then it is equivalent to a p-adic absolute value.
- Defined in
- Mathlib.NumberTheory.Ostrowski
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites47
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- mul_oneproof · cited by 3,885
- Factstatement and proof · cited by 2,726
- mul_commproof · cited by 2,262
- Nat.Primestatement and proof · cited by 2,059
- LT.lt.ne'proof · cited by 1,417
- eq_or_neproof · cited by 1,117
- neg_mulproof · cited by 654
- AbsoluteValuestatement and proof · cited by 363
- CharP.cast_eq_zeroproof · cited by 357
- Nat.cast_mulproof · cited by 309
Cited by1
Results whose statement or proof uses this declaration.
- Rat.AbsoluteValue.equiv_real_or_padicproof · cited by 0