Theorems · Theorem · group theory
AddSubgroup.mem_top
∀ {G : Type u_1} [inst : AddGroup G] (x : G), x ∈ ⊤- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- AddGroup
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- Set.mem_univproof · cited by 416
Cited by29
Results whose statement or proof uses this declaration.
- AddMonoidHom.range_eq_mapproof · cited by 15
- AddSubgroup.eq_top_iff'proof · cited by 11
- AddSubgroup.normalizer_eq_top_iffproof · cited by 6
- AddSubgroup.subsingleton_iffproof · cited by 3
- mem_zmultiples_of_prime_cardproof · cited by 2
- AddMonoidHom.ker_eq_top_iffproof · cited by 2
- AddSubgroup.pi_topproof · cited by 2
- AddSubgroup.index_dvd_two_iffproof · cited by 2
- AddSubgroup.lowerCentralSeries_isDescendingCentralSeriesproof · cited by 2
- IsSimpleAddGroup.prime_cardproof · cited by 2
- AddSubgroup.is_ascending_rev_series_of_is_descendingproof · cited by 2
- addCommutator_eq_closureproof · cited by 1