Theorems · Theorem · number theory
PadicInt.mem_span_pow_iff_le_valuation
∀ {p : ℕ} [hp : Fact (Nat.Prime p)] (x : ℤ_[p]), x ≠ 0 → ∀ (n : ℕ), x ∈ Ideal.span {↑p ^ n} ↔ n ≤ x.valuation- Cited by
- 1 results in Mathlib
- Foundations
- Depth 186 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Idealstatement · cited by 4,748
- Factstatement and proof · cited by 2,726
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.Primestatement and proof · cited by 2,059
- Ideal.spanstatement · cited by 948
- PadicIntstatement and proof · cited by 179
- Ideal.mem_span_singletonproof · cited by 69
- le_self_addproof · cited by 68
- pow_dvd_powproof · cited by 56
- PadicInt.valuationstatement and proof · cited by 19
- PadicInt.unitCoeffproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- PadicInt.norm_le_pow_iff_mem_span_powproof · cited by 7