Theorems · Theorem · number theory
PadicAlgCl.valuation_coe
∀ (p : ℕ) [hp : Fact (Nat.Prime p)] (x : PadicAlgCl p), ↑(Valued.v x) = ‖x‖
The coercion of the valuation of x : PadicAlgCl p to ℝ agrees with its norm.
- Defined in
- Mathlib.NumberTheory.Padics.Complex
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 237 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
- Norm.normstatement · cited by 5,413
- NNRealstatement · cited by 4,310
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- NNReal.toRealstatement · cited by 1,260
- Valuationstatement · cited by 823
- Valued.vstatement · cited by 163
- Padicstatement · cited by 151
- PadicAlgClstatement and proof · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- PadicComplex.norm_eq_norm'proof · cited by 1
- PadicAlgCl.valuation_pproof · cited by 1