Theorems · Theorem · number theory
Padic.norm_le_pow_iff_norm_lt_pow_add_one
∀ {p : ℕ} [hp : Fact (Nat.Prime p)] (x : ℚ_[p]) (n : ℤ), ‖x‖ ≤ ↑p ^ n ↔ ‖x‖ < ↑p ^ (n + 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.
Cites19
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
- le_of_ltproof · cited by 1,175
- StrictMonoproof · cited by 706
- norm_zeroproof · cited by 366
- Fact.outproof · cited by 328
- Padicstatement and proof · cited by 151
- Nat.Prime.one_ltproof · cited by 118
Cited by2
Results whose statement or proof uses this declaration.
- PadicInt.norm_le_pow_iff_norm_lt_pow_add_oneproof · cited by 2
- Padic.norm_lt_pow_iff_norm_le_pow_sub_oneproof · cited by 0