Theorems · Theorem · number theory
padicNorm.eq_zpow_of_nonzero
∀ {p : ℕ} {q : ℚ}, q ≠ 0 → padicNorm p q = ↑p ^ (-padicValRat p q)Unfolds the definition of the p-adic norm of q when q ≠ 0.
- Defined in
- Mathlib.NumberTheory.Padics.PadicNorm
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- zpow_negproof · cited by 198
- padicNormstatement · cited by 83
- padicValRatstatement and proof · cited by 49
Cited by7
Results whose statement or proof uses this declaration.
- Padic.valuation_ratCastproof · cited by 3
- Padic.norm_rat_le_oneproof · cited by 2
- Rat.AbsoluteValue.equiv_padic_of_boundedproof · cited by 1
- padicNorm.nonzeroproof · cited by 1
- PadicSeq.norm_oneproof · cited by 0
- harmonic_not_intproof · cited by 0
- padicNorm_two_harmonicproof · cited by 0