Theorems · Theorem · number theory
padicNorm.padicNorm_p
∀ {p : ℕ}, 1 < p → padicNorm p ↑p = (↑p)⁻¹The p-adic norm of p is p⁻¹ if p > 1.
See also padicNorm.padicNorm_p_of_prime for a version assuming p is prime.
- Defined in
- Mathlib.NumberTheory.Padics.PadicNorm
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.cast_oneproof · cited by 2,501
- LT.lt.ne'proof · cited by 1,417
- pow_oneproof · cited by 894
- zpow_negproof · cited by 198
- zpow_ofNatproof · cited by 144
- padicNormstatement · cited by 83
- padicValRatproof · cited by 49
- pos_of_gtproof · cited by 24
- padicValRat.of_natproof · cited by 9
- padicValNat.selfproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- padicNorm.padicNorm_p_of_primeproof · cited by 1
- padicNorm.padicNorm_p_lt_oneproof · cited by 1