Theorems · Theorem · group theory
AddSubgroup.normalClosure_closure_eq_normalClosure
∀ {G : Type u_1} [inst : AddGroup G] {s : Set G},
AddSubgroup.normalClosure ↑(AddSubgroup.closure s) = AddSubgroup.normalClosure s- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 · cited by 3,232
- le_antisymmproof · cited by 2,068
- AddSubgroup.closurestatement · cited by 156
- AddSubgroup.subset_closureproof · cited by 49
- AddSubgroup.normalClosurestatement · cited by 21
- AddSubgroup.normalClosure_le_normalproof · cited by 9
- AddSubgroup.closure_le_normalClosureproof · cited by 3
- AddSubgroup.normalClosure_monoproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.normalClosure_emptyproof · cited by 0