Theorems · Theorem · number theory
PadicComplex.valuation_extends
∀ (p : ℕ) [hp : Fact (Nat.Prime p)] (x : PadicAlgCl p), Valued.v ↑x = Valued.v x
The valuation on ℂ_[p] extends the valuation on PadicAlgCl p.
- Defined in
- Mathlib.NumberTheory.Padics.Complex
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 239 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- NNRealstatement · cited by 4,310
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Valuationstatement · cited by 823
- UniformSpace.Completionstatement · cited by 192
- Valued.vstatement · cited by 163
- Padicstatement · cited by 151
- UniformSpace.Completion.coe'statement · cited by 144
- PadicAlgClstatement and proof · cited by 21
- Valued.extensionValuation_apply_coeproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- PadicComplex.norm_eq_norm'proof · cited by 1
- PadicComplex.valuation_pproof · cited by 0