Theorems · Theorem · group theory
Subgroup.normalClosure_eq_self
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) [H.Normal], Subgroup.normalClosure ↑H = H- 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.
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- le_antisymmproof · cited by 2,068
- Subgroup.Normalstatement and proof · cited by 334
- Eq.subsetproof · cited by 124
- Subgroup.normalClosurestatement · cited by 35
- Subgroup.normalClosure_le_normalproof · cited by 10
- Subgroup.le_normalClosureproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.normalClosure_idempotentproof · cited by 0
- Subgroup.normalClosure_emptyproof · cited by 0