Theorems · Theorem · group theory
AddSubgroup.closure_singleton_neg
∀ {G : Type u_2} [inst : AddGroup G] (x : G), AddSubgroup.closure {-x} = AddSubgroup.closure {x}- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.closurestatement and proof · cited by 156
- Set.neg_singletonproof · cited by 14
- AddSubgroup.closure_negproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.isLeast_of_closure_iff_eq_absproof · cited by 0