Theorems · Theorem · number theory
PadicInt.norm_eq_zpow_neg_valuation
∀ {p : ℕ} [hp : Fact (Nat.Prime p)] {x : ℤ_[p]}, x ≠ 0 → ‖x‖ = ↑p ^ (-↑x.valuation)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 181 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.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- zpow_natCastproof · cited by 271
- zpow_negproof · cited by 198
- PadicIntstatement and proof · cited by 179
- PadicInt.valuationstatement and proof · cited by 19
- Padic.norm_eq_zpow_neg_valuationproof · cited by 9
- PadicInt.coe_ne_zeroproof · cited by 4
- PadicInt.valuation_coeproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- PadicInt.appr_specproof · cited by 4
- PadicInt.norm_le_pow_iff_le_valuationproof · cited by 1