Theorems · Theorem · number theory
PadicInt.norm_sub_zmodRepr_lt_one
∀ {p : ℕ} [hp_prime : Fact (Nat.Prime p)] (x : ℤ_[p]), ‖x - ↑x.zmodRepr‖ < 1- Defined in
- Mathlib.NumberTheory.Padics.RingHoms
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 197 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- PadicIntstatement and proof · cited by 179
- PadicInt.zmodReprstatement and proof · cited by 21
- IsLocalRing.mem_maximalIdealproof · cited by 6
- PadicInt.sub_zmodRepr_memproof · cited by 3
- PadicInt.mem_nonunitsproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- PadicInt.zmodRepr_eq_zero_iff_dvdproof · cited by 2
- PadicInt.norm_natCast_zmodRepr_eq_one_iffproof · cited by 1