Theorems · Theorem · group theory
neg_zsmul
∀ {α : Type u_1} [inst : SubtractionMonoid α] (a : α) (n : ℤ), -n • a = -(n • a)- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- SubtractionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- neg_negproof · cited by 960
- neg_zeroproof · cited by 542
- SubtractionMonoidstatement and proof · cited by 208
- zero_nsmulproof · cited by 137
- natCast_zsmulproof · cited by 118
- negSucc_zsmulproof · cited by 45
- ofNat_zsmulproof · cited by 24
- SubNegMonoid.zsmul_neg'proof · cited by 2
Cited by41
Results whose statement or proof uses this declaration.
- add_one_zsmulproof · cited by 19
- mul_zsmul'proof · cited by 16
- sub_zsmulproof · cited by 12
- AddSubgroup.mem_closure_singletonproof · cited by 6
- zsmul_neg'proof · cited by 6
- neg_one_zsmul_addproof · cited by 5
- AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eqproof · cited by 4
- Function.Antiperiodic.add_zsmul_eqproof · cited by 3
- existsUnique_add_zsmul_mem_Icoproof · cited by 3
- existsUnique_sub_zsmul_mem_Iocproof · cited by 3
- existsUnique_zsmul_near_of_posproof · cited by 3
- addOrderOf_dvd_iff_zsmul_eq_zeroproof · cited by 3