Theorems · Theorem · group theory
Subgroup.subset_normalizer_of_normal
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {S : Set G} [hH : H.Normal], S ⊆ ↑(Subgroup.normalizer ↑H)- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 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.
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 and proof · cited by 3,593
- le_topproof · cited by 411
- Subgroup.Normalstatement and proof · cited by 334
- Subgroup.normalizerstatement · cited by 108
- Subgroup.normalizer_eq_topproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.le_normalizer_of_normalproof · cited by 3
- Subgroup.set_mul_normal_commproof · cited by 0