Theorems · Theorem · number theory
Int.padicValuation_lt_one_iff
∀ {p : ℕ} [inst : Fact (Nat.Prime p)] {x : ℤ}, (Int.padicValuation p) x < 1 ↔ ↑p ∣ x- Defined in
- Mathlib.NumberTheory.Padics.PadicNumbers
- Cited by
- 1 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Multiplicativestatement · cited by 875
- Valuationstatement · cited by 823
- WithZerostatement · cited by 586
- Int.padicValuationstatement · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Rat.padicValuation_le_one_iffproof · cited by 1