Theorems · Theorem · number theory
PadicInt.norm_le_pow_iff_le_valuation
∀ {p : ℕ} [hp : Fact (Nat.Prime p)] (x : ℤ_[p]), x ≠ 0 → ∀ (n : ℕ), ‖x‖ ≤ ↑p ^ (-↑n) ↔ n ≤ x.valuation- Cited by
- 1 results in Mathlib
- Foundations
- Depth 182 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Norm.normstatement · cited by 5,413
- Factstatement and proof · cited by 2,726
- Nat.cast_oneproof · cited by 2,501
- Nat.Primestatement and proof · cited by 2,059
- Fact.outproof · cited by 328
- PadicIntstatement and proof · cited by 179
- Nat.cast_leproof · cited by 159
- Nat.Prime.one_ltproof · cited by 118
- neg_le_neg_iffproof · cited by 57
- PadicInt.valuationstatement and proof · cited by 19
- zpow_le_zpow_iff_right₀proof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- PadicInt.norm_le_pow_iff_mem_span_powproof · cited by 7