Theorems · Theorem · number theory
Rat.padicValuation_le_one_iff
∀ {p : ℕ} [inst : Fact (Nat.Prime p)] {x : ℚ}, (Rat.padicValuation p) x ≤ 1 ↔ ¬p ∣ x.den- Defined in
- Mathlib.NumberTheory.Padics.PadicNumbers
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 166 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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Multiplicativestatement and proof · cited by 875
- LT.lt.neproof · cited by 872
- Valuationstatement · cited by 823
- WithZerostatement and proof · cited by 586
- Int.cast_natCastproof · cited by 393
- Fact.outproof · cited by 328
- LE.le.eq_or_ltproof · cited by 220
- Nat.Prime.one_ltproof · cited by 118
- map_div₀proof · cited by 98
Cited by1
Results whose statement or proof uses this declaration.
- Padic.norm_rat_le_one_iff_padicValuation_le_oneproof · cited by 1