Theorems · Theorem · number theory
PadicAlgCl.norm_extends
∀ (p : ℕ) [hp : Fact (Nat.Prime p)] (x : ℚ_[p]), ‖(algebraMap ℚ_[p] (PadicAlgCl p)) x‖ = ‖x‖
The norm on PadicAlgCl p extends the p-adic norm on ℚ_[p].
- Defined in
- Mathlib.NumberTheory.Padics.Complex
- Cited by
- 1 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
- Realstatement · cited by 25,697
- RingHomstatement · cited by 10,189
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapstatement · cited by 4,706
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Padicstatement and proof · cited by 151
- AlgebraicClosurestatement · cited by 53
- norm_algebraMap'proof · cited by 39
- PadicAlgClstatement and proof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- PadicAlgCl.valuation_pproof · cited by 1