Theorems · Theorem · group theory
Subgroup.closure_singleton_inv
∀ {G : Type u_2} [inst : Group G] (x : G), Subgroup.closure {x⁻¹} = Subgroup.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
- Group
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
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Subgroup.closurestatement and proof · cited by 196
- Set.inv_singletonproof · cited by 9
- Subgroup.closure_invproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.isLeast_of_closure_iff_eq_mabsproof · cited by 0