Theorems · Theorem · group theory
Subgroup.normalClosure_eq_iInf
∀ {G : Type u_1} [inst : Group G] {s : Set G}, Subgroup.normalClosure s = ⨅ N, ⨅ (_ : N.Normal), ⨅ (_ : s ⊆ ↑N), N- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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_antisymmproof · cited by 2,068
- iInfstatement · cited by 1,690
- le_rflproof · cited by 1,558
- Subgroup.Normalstatement and proof · cited by 334
- le_iInfproof · cited by 102
- iInf_le_of_leproof · cited by 62
- Subgroup.normalClosurestatement and proof · cited by 35
- Subgroup.normalClosure_le_normalproof · cited by 10
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.