Theorems · Definition · number theory
Padic.withValUniformEquiv
{p : ℕ} → [inst : Fact (Nat.Prime p)] → (Rat.padicValuation p).Completion ≃ᵤ ℚ_[p]The p-adic numbers are isomorphic as uniform spaces to the completion of the rationals at
the p-adic valuation.
- Defined in
- Mathlib.NumberTheory.Padics.WithVal
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 170 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Multiplicativestatement · cited by 875
- WithZerostatement · cited by 586
- RingEquiv.symmproof · cited by 567
- Padicstatement · cited by 151
- WithValstatement · cited by 151
- RingEquiv.toEquivproof · cited by 101
- UniformEquivstatement · cited by 80
- Valuation.Completionstatement · cited by 33
- UniformEquiv.symmproof · cited by 28
- Rat.padicValuationstatement · cited by 18
Cited by5
Results whose statement or proof uses this declaration.
- Rat.HeightOneSpectrum.adicCompletion.padicEquivproof · cited by 5
- Padic.withValUniformEquiv_cast_applystatement and proof · cited by 1
- Padic.toEquiv_withValUniformEquiv_eq_toEquiv_withValRingEquivstatement · cited by 0
- Padic.withValUniformEquiv_norm_le_one_iffstatement and proof · cited by 0
- PadicInt.withValIntegersUniformEquivproof · cited by 0