Theorems · Theorem · group theory
AddSubgroup.mem_map_of_mem
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] (f : G →+ N) {K : AddSubgroup G} {x : G},
x ∈ K → f x ∈ AddSubgroup.map f K- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- Set.mem_image_of_memproof · cited by 371
- AddSubgroup.mapstatement · cited by 189
Cited by6
Results whose statement or proof uses this declaration.
- AddSubgroup.map_addCommutatorproof · cited by 6
- CongruenceSubgroup.strictPeriods_Gammaproof · cited by 2
- AddSubgroup.upperCentralSeries.mapproof · cited by 2
- TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure_absorbingproof · cited by 2
- AddGroup.fg_of_descentproof · cited by 1
- AddSubgroup.apply_coe_mem_mapproof · cited by 0