Theorems · Theorem · number theory
PadicInt.valuation_p_pow_mul
∀ {p : ℕ} [hp : Fact (Nat.Prime p)] (n : ℕ) (c : ℤ_[p]), c ≠ 0 → (↑p ^ n * c).valuation = n + c.valuation- Cited by
- 2 results in Mathlib
- Foundations
- Depth 183 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- PadicIntstatement and proof · cited by 179
- PadicInt.valuationstatement and proof · cited by 19
- PadicInt.valuation_mulproof · cited by 1
- PadicInt.valuation_pproof · cited by 1
- PadicInt.valuation_powproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- PadicInt.appr_specproof · cited by 4
- PadicInt.mem_span_pow_iff_le_valuationproof · cited by 1