Theorems · Theorem · group theory
AddSubgroup.addSubgroupOf_eq_top
∀ {G : Type u_1} [inst : AddGroup G] {H K : AddSubgroup G}, H.addSubgroupOf K = ⊤ ↔ K ≤ H- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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.
- Top.topstatement · cited by 9,680
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.addSubgroupOfstatement and proof · cited by 87
- inf_eq_rightproof · cited by 64
- top_inf_eqproof · cited by 30
- AddSubgroup.addSubgroupOf_injproof · cited by 3
- AddSubgroup.top_addSubgroupOfproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- AddSubgroup.normal_addSubgroupOf_iff_le_normalizerproof · cited by 8
- AddSubgroup.relIndex_eq_oneproof · cited by 3
- AddSubgroup.isSimpleAddGroup_iffproof · cited by 0