Theorems · Theorem · group theory
AddSubgroup.subset_normalizer_of_normal
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G} {S : Set G} [hH : H.Normal], S ⊆ ↑(AddSubgroup.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
- AddGroupAddSubgroup.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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- le_topproof · cited by 411
- AddSubgroup.Normalstatement and proof · cited by 183
- AddSubgroup.normalizerstatement · cited by 59
- AddSubgroup.normalizer_eq_topproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.le_normalizer_of_normalproof · cited by 3
- AddSubgroup.set_add_normal_commproof · cited by 0