Theorems · Theorem · group theory
Subgroup.eq_bot_iff_forall
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G), H = ⊥ ↔ ∀ x ∈ H, x = 1- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Bot.botstatement · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- Subgroup.toSubmonoidproof · cited by 114
- Submonoid.eq_bot_iff_forallproof · cited by 3
- Subgroup.toSubmonoid_injectiveproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- IsQuotientCoveringMap.isCoveringMapproof · cited by 15
- Subgroup.eq_bot_of_subsingletonproof · cited by 8
- Subgroup.nontrivial_iff_ne_botproof · cited by 7
- MulAction.IwasawaStructure.isSimpleGroupproof · cited by 1
- IsCancelSMul.stabilizer_eq_botproof · cited by 0
- ProfiniteGrp.toLimit_injectiveproof · cited by 0