Theorems · Theorem · number theory
ZMod.natCast_natAbs_valMinAbs
∀ {n : ℕ} [NeZero n] (a : ZMod n), ↑a.valMinAbs.natAbs = if a.val ≤ n / 2 then a else -a- Defined in
- Mathlib.Data.ZMod.ValMinAbs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Quot.sound
- Assumes
- NeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ZModstatement and proof · cited by 1,024
- sub_zeroproof · cited by 938
- Int.cast_natCastproof · cited by 393
- Int.cast_negproof · cited by 224
- ZMod.valstatement and proof · cited by 159
- Int.cast_subproof · cited by 78
- sub_nonposproof · cited by 29
- ZMod.natCast_zmod_valproof · cited by 29
- ZMod.valMinAbsstatement · cited by 28
- ZMod.natCast_selfproof · cited by 15
- ZMod.valMinAbs_def_posproof · cited by 10
- ZMod.val_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ZMod.Ico_map_valMinAbs_natAbs_eq_Ico_map_idproof · cited by 0