Theorems · Theorem · group theory
zpow_mem
∀ {M : Type u_3} {S : Type u_4} [inst : DivInvMonoid M] [inst_1 : SetLike S M] [hSM : SubgroupClass S M] {K : S}
{x : M}, x ∈ K → ∀ (n : ℤ), x ^ n ∈ K- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
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.
- SetLikestatement and proof · cited by 1,084
- zpow_natCastproof · cited by 271
- DivInvMonoidstatement and proof · cited by 103
- zpow_negSuccproof · cited by 92
- InvMemClass.inv_memproof · cited by 52
- pow_memproof · cited by 46
- SubgroupClassstatement and proof · cited by 34
Cited by8
Results whose statement or proof uses this declaration.
- Subgroup.strictPeriods_eq_zmultiples_one_of_T_memproof · cited by 4
- Subgroup.mem_closure_singletonproof · cited by 3
- Subgroup.zpow_memproof · cited by 2
- Subgroup.dense_of_not_isolated_oneproof · cited by 2
- Subgroup.mem_closure_range_iffproof · cited by 1
- Field.exists_primitive_element_of_finite_topproof · cited by 1
- IntermediateField.pow_memproof · cited by 0
- Subfield.zpow_memproof · cited by 0