Mathlib Map

Theorems · Definition · group theory

AddSubgroup.closure

{G : Type u_1} → [inst : AddGroup G] → Set G → AddSubgroup G

The AddSubgroup generated by a set

Defined in
Mathlib.Algebra.Group.Subgroup.Lattice
Cited by
156 results in Mathlib
Foundations
Depth 66 from the axioms, rests on 747 definitions · uses propext, Classical.choice, Quot.sound
Assumes
AddGroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddSubgroup.subset_closure · cited by 49AddSubgroup.subset_closureAddSubgroup.closure_le · cited by 30AddSubgroup.closure_leAddSubgroup.normalClosure · cited by 21AddSubgroup.normalClosureAddSubgroup.FG · cited by 21AddSubgroup.FGAddSubgroup.closure_induction · cited by 14AddSubgroup.closure_induc…AddSubgroup.zmultiples_eq_closure · cited by 9AddSubgroup.zmultiples_eq…AddSubgroup.normalClosure_le_normal · cited by 9AddSubgroup.normalClosure…AddMonoidHom.map_closure · cited by 8AddMonoidHom.map_closureAddSubgroup.closure_eq · cited by 7AddSubgroup.closure_eqAddSubgroup.closure_union · cited by 7AddSubgroup.closure_unionAddSubgroup.focalAddSubgroup · cited by 7AddSubgroup.focalAddSubgr…AddSubgroup.closure_toAddSubmonoid · cited by 6AddSubgroup.closure_toAdd…AddMonoidHom.map_zmultiples · cited by 6AddMonoidHom.map_zmultipl…AddSubgroup.mem_closure_singleton · cited by 6AddSubgroup.mem_closure_s…AddSubgroup.fg_iff_addSubmonoid_fg · cited by 6AddSubgroup.fg_iff_addSub…Set · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeSet.ofPred · cited by 6101Set.ofPredAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupInfSet.sInf · cited by 935InfSet.sInfAddSubgroup.closureCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by166

Results whose statement or proof uses this declaration.