Theorems · Theorem · group theory
AddSubgroup.eq_bot_iff_forall
∀ {G : Type u_1} [inst : AddGroup G] (H : AddSubgroup G), H = ⊥ ↔ ∀ x ∈ H, x = 0- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
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.
- Bot.botstatement · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.toAddSubmonoidproof · cited by 91
- AddSubmonoid.eq_bot_iff_forallproof · cited by 4
- AddSubgroup.toAddSubmonoid_injectiveproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- IsAddQuotientCoveringMap.isCoveringMapproof · cited by 16
- AddGroup.residuallyFinite_iff_forall_finiteIndexNormalAddSubgroupproof · cited by 4
- AddSubgroup.nontrivial_iff_ne_botproof · cited by 4
- AddSubgroup.eq_bot_of_subsingletonproof · cited by 4
- AddSubgroup.closure_singleton_zeroproof · cited by 2
- CategoryTheory.Abelian.Ext.postcomp_mk₀_injective_of_monoproof · cited by 1
- CategoryTheory.Abelian.Ext.precomp_mk₀_injective_of_epiproof · cited by 1
- IsCancelVAdd.stabilizer_eq_botproof · cited by 0
- AddSubgroup.nsmulAddMonoidHom_injective_of_isTorsionFreeproof · cited by 0
- ProfiniteAddGrp.toLimit_injectiveproof · cited by 0
- isCancelVAdd_iff_stabilizer_eq_botproof · cited by 0