Theorems · Theorem · group theory
neg_one_zsmul
∀ {G : Type u_1} [inst : SubNegMonoid G] (x : G), -1 • x = -x- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- SubNegMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SubNegMonoidstatement and proof · cited by 79
- one_nsmulproof · cited by 63
- negSucc_zsmulproof · cited by 45
Cited by14
Results whose statement or proof uses this declaration.
- norm_le_norm_add_norm_neg_addproof · cited by 3
- controlled_sum_of_mem_closureproof · cited by 2
- FreeAddGroup.reduceCyclically.reduce_flatten_replicate_succproof · cited by 1
- SubAddAction.fixingAddSubgroup_map_addConj_eqproof · cited by 1
- MeasureTheory.Measure.IsEverywherePos.IsGdelta_of_isAddLeftInvariantproof · cited by 1
- AddSubgroup.closure_add_image_add_eq_topproof · cited by 1
- mpullback_addInvariantVectorFieldproof · cited by 1
- Nat.eleven_dvd_of_palindromeproof · cited by 0
- AddSubgroup.focalAddSubgroupOf.mk'_addConj_eqproof · cited by 0
- AddGroupExtension.IsAddConj.symmproof · cited by 0