Theorems · Definition · number theory
Int.padicValuation
(p : ℕ) → [Fact (Nat.Prime p)] → Valuation ℤ (WithZero (Multiplicative ℤ))
The p-adic valuation on integers, sending p to (exp (-1) : ℤᵐ⁰)
- Defined in
- Mathlib.NumberTheory.Padics.PadicNumbers
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 162 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.
- 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.castRingHomproof · cited by 254
- Rat.padicValuationproof · cited by 18
- Valuation.comapproof · cited by 15
Cited by9
Results whose statement or proof uses this declaration.
- Int.padicValuation_eq_one_iffstatement · cited by 1
- Int.padicValuation_le_onestatement · cited by 1
- Int.padicValuation_lt_one_iffstatement · cited by 1
- Rat.padicValuation_caststatement · cited by 1
- Rat.padicValuation_le_one_iffproof · cited by 1
- Int.padicValuation_eq_zero_iffstatement · cited by 0
- Int.padicValuation_selfstatement · cited by 0
- Padic.comap_mulValuation_eq_int_padicValuationstatement · cited by 0
- Int.padicValuation.congr_simpstatement and proof · cited by 0