Theorems · Theorem · group theory
AddSubgroup.mem_comap
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] {K : AddSubgroup N} {f : G →+ N} {x : G},
x ∈ AddSubgroup.comap f K ↔ f x ∈ K- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext
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.
- DFunLike.coestatement · 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
- AddSubgroup.comapstatement · cited by 123
Cited by11
Results whose statement or proof uses this declaration.
- AddSubgroup.comap_map_eqproof · cited by 8
- AddSubgroup.map_addCommutatorproof · cited by 6
- AddSubgroup.Normal.comapproof · cited by 2
- AddSubgroup.le_normalizer_comapproof · cited by 2
- QuotientAddGroup.comap_comap_centerproof · cited by 1
- AddSubgroup.top_prodproof · cited by 1
- AddSubgroup.upperCentralSeriesStep_eq_comap_centerproof · cited by 1
- AddSubgroup.addCommutator_pi_pi_of_finiteproof · cited by 1
- AddSubgroup.prod_topproof · cited by 0
- AddMonoidHom.comap_range_selfproof · cited by 0
- AddMonoidHom.closure_preimage_leproof · cited by 0