Theorems · Theorem · order theory
abs_nsmul
∀ {G : Type u_1} [inst : AddCommGroup G] [inst_1 : LinearOrder G] [IsOrderedAddMonoid G] (n : ℕ) (a : G),
|n • a| = n • |a|- Defined in
- Mathlib.Algebra.Order.Group.Abs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
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
- abs_of_nonnegproof · cited by 279
- abs_negproof · cited by 93
- neg_nonnegproof · cited by 60
- abs_of_nonposproof · cited by 53
- neg_nsmulproof · cited by 19
- nsmul_nonnegproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- abs_zsmulproof · cited by 1
- HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iffproof · cited by 1
- Polynomial.Chebyshev.abs_iterate_derivative_T_real_leproof · cited by 0