Theorems · Theorem · group theory
AddGroup.residuallyFinite_iff_forall_finiteIndex
∀ {G : Type u_1} [inst : AddGroup G],
AddGroup.ResiduallyFinite G ↔ ∀ (g : G), (∀ (H : AddSubgroup G) [H.FiniteIndex], g ∈ H) → g = 0- Defined in
- Mathlib.GroupTheory.ResiduallyFinite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.FiniteIndexstatement and proof · cited by 66
- FiniteIndexNormalAddSubgroupproof · cited by 26
- FiniteIndexNormalAddSubgroup.toAddSubgroupproof · cited by 15
- AddGroup.ResiduallyFinitestatement · cited by 12
- AddSubgroup.normalCoreproof · cited by 11
- AddSubgroup.normalCore_leproof · cited by 7
- AddGroup.residuallyFinite_iff_forall_finiteIndexNormalAddSubgroupproof · cited by 4
- FiniteIndexNormalAddSubgroup.ofAddSubgroupproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddGroup.residuallyFinite_iff_exists_finiteIndexproof · cited by 1