Theorems · Theorem · group theory
Subgroup.mem_top
∀ {G : Type u_1} [inst : Group G] (x : G), x ∈ ⊤- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Set.mem_univproof · cited by 416
Cited by20
Results whose statement or proof uses this declaration.
- Subgroup.eq_top_iff'proof · cited by 13
- Subgroup.normalizer_eq_top_iffproof · cited by 10
- Subgroup.is_ascending_rev_series_of_is_descendingproof · cited by 3
- Subgroup.strictPeriods_SL2Zproof · cited by 3
- Subgroup.lowerCentralSeries_isDescendingCentralSeriesproof · cited by 3
- orderOf_eq_card_of_zpowers_eq_topproof · cited by 2
- Equiv.Perm.not_isSolvable_fin_5proof · cited by 2
- Subgroup.subsingleton_iffproof · cited by 2
- Matrix.transvection_mem_commutator₀proof · cited by 1
- Matrix.transvection_mem_commutator₁proof · cited by 1
- Polynomial.Gal.galActionHom_bijective_of_prime_degreeproof · cited by 1
- IsGalois.of_card_aut_eq_finrankproof · cited by 1