Theorems · Definition · number theory
PadicSeq.norm
{p : ℕ} → [Fact (Nat.Prime p)] → PadicSeq p → ℚSince the norm of the entries of a Cauchy sequence is eventually stationary, we can lift the norm to sequences.
- Defined in
- Mathlib.NumberTheory.Padics.PadicNumbers
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 89 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.
Cites5
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
- padicNormproof · cited by 83
- PadicSeqstatement and proof · cited by 30
- PadicSeq.stationaryPointproof · cited by 15
Cited by21
Results whose statement or proof uses this declaration.
- padicNormEproof · cited by 18
- PadicSeq.norm_equivstatement · cited by 4
- padicNormE.defnproof · cited by 3
- PadicSeq.norm_zero_iffstatement and proof · cited by 3
- Padic.rat_dense'proof · cited by 2
- PadicSeq.norm_eq_zpow_neg_valuationstatement · cited by 2
- PadicSeq.norm_nonnegstatement · cited by 2
- PadicSeq.norm_values_discretestatement and proof · cited by 2
- PadicSeq.add_eq_max_of_nestatement and proof · cited by 1
- PadicSeq.norm_conststatement · cited by 1
- PadicSeq.norm_eqstatement · cited by 1
- PadicSeq.norm_eq_norm_app_of_nonzerostatement and proof · cited by 1