Theorems · Theorem · group theory
AddSubgroup.map_normalClosure_le
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] (s : Set G) (f : G →+ N),
AddSubgroup.map f (AddSubgroup.normalClosure s) ≤ AddSubgroup.normalClosure (⇑f '' 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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Set.imagestatement · cited by 5,609
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- AddSubgroup.mapstatement · cited by 189
- AddSubgroup.normalClosurestatement · cited by 21
- AddSubgroup.map_le_iff_le_comapproof · cited by 10
- AddSubgroup.comap_normalClosure_image_geproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.map_normalClosureproof · cited by 3