Theorems · Theorem · group theory
Submonoid.powers_le_zpowers
∀ {G : Type u_2} [inst : Group G] (g : G), Submonoid.powers g ≤ (Subgroup.zpowers g).toSubmonoid- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Submonoidstatement and proof · cited by 3,086
- Submonoid.powersstatement and proof · cited by 408
- le_sup_leftproof · cited by 265
- Subgroup.zpowersstatement · cited by 204
- Subgroup.toSubmonoidstatement · cited by 114
- Subgroup.toSubmonoid_zpowersproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- orderOf_eq_card_of_forall_mem_powersproof · cited by 0