Theorems · Theorem · group theory
Subgroup.normalClosure_subset_iff
∀ {G : Type u_1} [inst : Group G] {s : Set G} {N : Subgroup G} [N.Normal], s ⊆ ↑N ↔ Subgroup.normalClosure s ≤ N- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 3,593
- Subgroup.Normalstatement and proof · cited by 334
- Set.Subset.transproof · cited by 218
- Subgroup.normalClosurestatement · cited by 35
- Subgroup.normalClosure_le_normalproof · cited by 10
- Subgroup.subset_normalClosureproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.Normal.quotient_commutative_iff_commutator_leproof · cited by 2
- Subgroup.normalClosure_eq_bot_iffproof · cited by 0