Theorems · Theorem · number theory
PadicComplex.norm_eq_norm
∀ (p : ℕ) [hp : Fact (Nat.Prime p)] (x : ℂ_[p]), ‖x‖ = Valued.v.norm x
The norm on ℂ_[p] is compatible with the valuation.
- Defined in
- Mathlib.NumberTheory.Padics.Complex
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 246 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- NNRealstatement · cited by 4,310
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Valued.vstatement and proof · cited by 163
- Padicstatement · cited by 151
- PadicAlgClstatement · cited by 21
- PadicComplexstatement and proof · cited by 8
- Valuation.normstatement and proof · cited by 7
- PadicComplex.norm_eq_norm'proof · cited by 1
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