Theorems · Theorem · number theory
Padic.norm_rat_le_one
∀ {p : ℕ} [hp : Fact (Nat.Prime p)] {q : ℚ}, ¬p ∣ q.den → ‖↑q‖ ≤ 1- Defined in
- Mathlib.NumberTheory.Padics.PadicNumbers
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 165 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.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Factstatement and proof · cited by 2,726
- Nat.cast_oneproof · cited by 2,501
- Nat.Primestatement and proof · cited by 2,059
- Nat.cast_zeroproof · cited by 1,870
- norm_zeroproof · cited by 366
- zero_subproof · cited by 335
- Fact.outproof · cited by 328
- neg_subproof · cited by 272
- zpow_natCastproof · cited by 271
- zpow_negproof · cited by 198
Cited by2
Results whose statement or proof uses this declaration.
- Padic.norm_rat_le_one_iff_padicValuation_le_oneproof · cited by 1
- Padic.norm_int_le_oneproof · cited by 1