Theorems · Theorem · number theory
Rat.AbsoluteValue.is_prime_of_minimal_nat_zero_lt_and_lt_one
∀ {f : AbsoluteValue ℚ ℝ} {p : ℕ}, 0 < f ↑p → f ↑p < 1 → (∀ (m : ℕ), 0 < f ↑m ∧ f ↑m < 1 → p ≤ m) → Nat.Prime pThe minimal positive integer with absolute value smaller than 1 is a prime number.
- Defined in
- Mathlib.NumberTheory.Ostrowski
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- le_antisymmproof · cited by 2,068
- Nat.Primestatement · cited by 2,059
- Nat.cast_zeroproof · cited by 1,870
- map_mulproof · cited by 1,137
- AbsoluteValuestatement and proof · cited by 363
- Nat.cast_mulproof · cited by 309
- not_le_of_gtproof · cited by 97
- mul_ne_zero_iffproof · cited by 39
- one_le_mul_of_one_le_of_one_leproof · cited by 11
- map_pos_of_ne_zeroproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Rat.AbsoluteValue.eq_one_of_not_dvdproof · cited by 1
- Rat.AbsoluteValue.equiv_padic_of_boundedproof · cited by 1
- Rat.AbsoluteValue.exists_pos_eq_pow_negproof · cited by 1