Theorems · Theorem · number theory
Rat.AbsoluteValue.eq_one_of_not_dvd
∀ {f : AbsoluteValue ℚ ℝ},
(∀ (n : ℕ), f ↑n ≤ 1) →
∀ {p : ℕ}, 0 < f ↑p → f ↑p < 1 → (∀ (m : ℕ), 0 < f ↑m ∧ f ↑m < 1 → p ≤ m) → ∀ {m : ℕ}, ¬p ∣ m → f ↑m = 1A natural number not divisible by p has absolute value 1.
- Defined in
- Mathlib.NumberTheory.Ostrowski
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites56
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- Nat.cast_zeroproof · cited by 1,870
- le_of_ltproof · cited by 1,175
- map_mulproof · cited by 1,137
- Real.logproof · cited by 939
- LT.lt.neproof · cited by 872
- map_oneproof · cited by 861
Cited by1
Results whose statement or proof uses this declaration.
- Rat.AbsoluteValue.equiv_padic_of_boundedproof · cited by 1