Theorems · Theorem · number theory
ZMod.natAbs_valMinAbs_le
∀ {n : ℕ} [NeZero n] (x : ZMod n), x.valMinAbs.natAbs ≤ n / 2- Defined in
- Mathlib.Data.ZMod.ValMinAbs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.leproof · cited by 2,189
- ZModstatement and proof · cited by 1,024
- neg_mulproof · cited by 654
- neg_le_neg_iffproof · cited by 57
- ZMod.valMinAbsstatement and proof · cited by 28
- ZMod.valMinAbs_mem_Iocproof · cited by 3
- Nat.le_div_two_iff_mul_two_leproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Nat.sq_add_sq_zmodEqproof · cited by 2
- Nat.Prime.sum_four_squaresproof · cited by 1
- ZMod.Ico_map_valMinAbs_natAbs_eq_Ico_map_idproof · cited by 0
- ZMod.valMinAbs_natCast_eq_selfproof · cited by 0
- ZMod.natAbs_valMinAbs_add_leproof · cited by 0