Theorems · Theorem · group theory
AddSubgroup.index_eq_one
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G}, H.index = 1 ↔ H = ⊤- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 95 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.indexstatement and proof · cited by 104
- Nat.card_eq_one_iff_uniqueproof · cited by 15
- AddSubgroup.index_topproof · cited by 9
- QuotientAddGroup.addSubgroup_eq_top_of_subsingletonproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- AddSubgroup.relIndex_eq_oneproof · cited by 3
- AddSubgroup.index_dvd_two_iffproof · cited by 2
- Submodule.cardQuot_eq_one_iffproof · cited by 1
- AddSubgroup.one_lt_index_of_ne_topproof · cited by 0