Theorems · Theorem · group theory
Subgroup.toAddSubgroup_closure
∀ {G : Type u_1} [inst : Group G] (S : Set G),
Subgroup.toAddSubgroup (Subgroup.closure S) = AddSubgroup.closure (⇑Additive.toMul ⁻¹' S)- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Groupstatement and proof · cited by 6,238
- Set.preimagestatement and proof · cited by 4,946
- Subgroupstatement · cited by 3,593
- AddSubgroupstatement · cited by 3,232
- le_antisymmproof · cited by 2,068
- OrderIsostatement · cited by 874
- OrderIso.symmproof · cited by 475
- Additivestatement · cited by 356
- Subgroup.closurestatement and proof · cited by 196
Cited by3
Results whose statement or proof uses this declaration.
- NumberField.Units.isMaxRank_iff_closure_finiteIndexproof · cited by 1
- NumberField.Units.span_basisOfIsMaxRankproof · cited by 1
- AddSubgroup.toSubgroup_closureproof · cited by 0