Theorems · Theorem · number theory
PadicInt.zmodRepr_eq_zero_iff_dvd
∀ {p : ℕ} [hp_prime : Fact (Nat.Prime p)] {x : ℤ_[p]}, x.zmodRepr = 0 ↔ ↑p ∣ x- Defined in
- Mathlib.NumberTheory.Padics.RingHoms
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 198 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Norm.normproof · cited by 5,413
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Nat.cast_zeroproof · cited by 1,870
- sub_zeroproof · cited by 938
- PadicIntstatement and proof · cited by 179
- PadicInt.zmodReprstatement and proof · cited by 21
- PadicInt.norm_lt_one_iff_dvdproof · cited by 4
- PadicInt.norm_sub_zmodRepr_lt_oneproof · cited by 2
- PadicInt.zmodRepr_eq_zero_of_dvdproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- PadicInt.norm_natCast_zmodRepr_eq_one_iff_neproof · cited by 0
- PadicInt.zmodRepr_units_ne_zeroproof · cited by 0