Theorems · Theorem · group theory
Subgroup.toSubmonoid_zpowers
∀ {G : Type u_2} [inst : Group G] (g : G), (Subgroup.zpowers g).toSubmonoid = Submonoid.powers g ⊔ Submonoid.powers g⁻¹- 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Subgroupproof · cited by 3,593
- Submonoidstatement and proof · cited by 3,086
- Submonoid.powersstatement and proof · cited by 408
- Subgroup.zpowersstatement · cited by 204
- Submonoid.closureproof · cited by 167
- Subgroup.toSubmonoidstatement and proof · cited by 114
- Submonoid.closure_unionproof · cited by 10
- Set.inv_singletonproof · cited by 9
- Subgroup.closure_toSubmonoidproof · cited by 9
- Submonoid.powers_eq_closureproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Submonoid.powers_le_zpowersproof · cited by 1