Theorems · Theorem · group theory
AddSubgroup.map_top_of_surjective
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] (f : G →+ N),
Function.Surjective ⇑f → AddSubgroup.map f ⊤ = ⊤- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Top.topstatement and proof · cited by 9,680
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- eq_top_iffproof · cited by 236
- AddSubgroup.mapstatement · cited by 189
Cited by5
Results whose statement or proof uses this declaration.
- AddGroup.rank_le_of_surjectiveproof · cited by 3
- AddSubgroup.IsSubnormal.mapproof · cited by 1
- AddSubgroup.map_equiv_topproof · cited by 1
- AddSubgroup.codisjoint_mapproof · cited by 0
- AddCommGroup.smul_top_eq_top_of_divisibleBy_intproof · cited by 0