Theorems · Theorem · group theory
Subgroup.subset_normalClosure
∀ {G : Type u_1} [inst : Group G] {s : Set G}, s ⊆ ↑(Subgroup.normalClosure s)- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 70 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Set.Subset.transproof · cited by 218
- Subgroup.normalClosurestatement · cited by 35
- Group.subset_conjugatesOfSetproof · cited by 1
- Subgroup.conjugatesOfSet_subset_normalClosureproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- CoxeterSystem.simple_mul_simple_selfproof · cited by 9
- PresentedGroup.one_of_memproof · cited by 3
- Subgroup.map_normalClosureproof · cited by 3
- Subgroup.le_normalClosureproof · cited by 2
- Subgroup.normalClosure_subset_iffproof · cited by 2
- CoxeterSystem.simple_mul_simple_powproof · cited by 1
- Subgroup.normalClosure_monoproof · cited by 1
- IsConj.normalClosure_eq_top_ofproof · cited by 0
- Subgroup.normalClosure_eq_iInfproof · cited by 0