Theorems · Theorem · number theory
padicNorm.add_eq_max_of_ne
∀ {p : ℕ} [hp : Fact (Nat.Prime p)] {q r : ℚ},
padicNorm p q ≠ padicNorm p r → padicNorm p (q + r) = max (padicNorm p q) (padicNorm p r)If the p-adic norms of q and r are different, then the norm of q + r is equal to the max
of the norms of q and r.
- Defined in
- Mathlib.NumberTheory.Padics.PadicNorm
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 86 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
- padicNormstatement and proof · cited by 83
- padicNorm.nonarchimedeanproof · cited by 5
- IsNonarchimedean.add_eq_max_of_neproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- PadicSeq.add_eq_max_of_neproof · cited by 1
- PadicSeq.stationaryproof · cited by 1