Theorems · Theorem · group theory
AddSubgroup.mem_map_equiv
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] {f : G ≃+ N} {K : AddSubgroup G} {x : N},
x ∈ AddSubgroup.map f.toAddMonoidHom K ↔ f.symm x ∈ K- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddEquivstatement and proof · cited by 1,087
- AddEquiv.symmstatement · cited by 530
- AddSubgroup.mapstatement · cited by 189
- AddEquiv.toAddMonoidHomstatement · cited by 101
- Set.mem_image_equivproof · cited by 22
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.map_equiv_normalizer_eqproof · cited by 1
- AddAction.stabilizer_vadd_eq_stabilizer_map_addConjproof · cited by 1