Theorems · Theorem · number theory
Padic.valuation_mul
∀ {p : ℕ} [hp : Fact (Nat.Prime p)] {x y : ℚ_[p]}, x ≠ 0 → y ≠ 0 → (x * y).valuation = x.valuation + y.valuation- Defined in
- Mathlib.NumberTheory.Padics.PadicNumbers
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 165 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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- Norm.normproof · 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
- Nat.cast_zeroproof · cited by 1,870
- LT.lt.ne'proof · cited by 1,417
- Fact.outproof · cited by 328
- mul_ne_zeroproof · cited by 178
- norm_mulproof · cited by 171
- Padicstatement and proof · cited by 151
- neg_injproof · cited by 85
Cited by2
Results whose statement or proof uses this declaration.
- PadicInt.valuation_mulproof · cited by 1
- Padic.AddValuation.map_mulproof · cited by 0