Theorems · Theorem · group theory
Subgroup.closure_le_normalClosure
∀ {G : Type u_1} [inst : Group G] {s : Set G}, Subgroup.closure s ≤ Subgroup.normalClosure s- 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
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Subgroup.closurestatement · cited by 196
- Subgroup.normalClosurestatement and proof · cited by 35
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.IsFinitelyNormallyGenerated.of_FGproof · cited by 1
- Subgroup.normalClosure_closure_eq_normalClosureproof · cited by 1
- Subgroup.commutator_def'proof · cited by 1