Theorems · Theorem · group theory
Subgroup.le_normalizer_of_normal
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G} [H.Normal], K ≤ Subgroup.normalizer ↑H- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 3 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Subgroup.normalizerstatement · cited by 108
- Subgroup.subset_normalizer_of_normalproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- QuotientGroup.quotientInfEquivProdNormalQuotientproof · cited by 1
- Subgroup.normal_mulproof · cited by 1
- Subgroup.normalizer_le_normalizer_sup_normalproof · cited by 0
- Subgroup.mul_normalproof · cited by 0