Theorems · Theorem · group theory
zsmul_neg
∀ {α : Type u_1} [inst : SubtractionMonoid α] (a : α) (n : ℤ), n • -a = -(n • a)- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- SubtractionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SubtractionMonoidstatement and proof · cited by 208
- natCast_zsmulproof · cited by 118
- negSucc_zsmulproof · cited by 45
- neg_nsmulproof · cited by 19
Cited by6
Results whose statement or proof uses this declaration.
- zsmul_neg'proof · cited by 6
- zsmul_subproof · cited by 3
- denseRange_zsmul_iff_surjectiveproof · cited by 1
- vadd_eq_self_of_preimage_zsmul_eq_selfproof · cited by 1
- AddAction.period_negproof · cited by 0
- zsmul_zero_subproof · cited by 0