Theorems · Theorem · group theory
neg_one_zsmul_add
∀ {α : Type u_1} [inst : SubtractionMonoid α] (a b : α), -1 • (a + b) = -1 • b + -1 • a- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 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.
- neg_add_revproof · cited by 236
- SubtractionMonoidstatement and proof · cited by 208
- one_zsmulproof · cited by 59
- neg_zsmulproof · cited by 41
Cited by5
Results whose statement or proof uses this declaration.
- AddSubgroup.closure_add_image_add_eq_topproof · cited by 1
- AddSubgroup.focalAddSubgroupOf.mk'_addConj_eqproof · cited by 0
- AddGroupExtension.IsAddConj.transproof · cited by 0