Theorems · Theorem · order theory
abs_zsmul
∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α] (n : ℤ) (a : α),
|n • a| = |n| • |a|- Defined in
- Mathlib.Algebra.Order.Ring.Abs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- absstatement and proof · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- le_totalproof · cited by 294
- natCast_zsmulproof · cited by 118
- abs_negproof · cited by 93
- neg_nonnegproof · cited by 60
- neg_zsmulproof · cited by 41
- Nat.abs_castproof · cited by 36
- abs_nsmulproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.Units.abs_det_eq_abs_detproof · cited by 1