Mathlib Map

Theorems · Definition · group theory

AddSubsemigroup.closure

{M : Type u_1} → [inst : Add M] → Set M → AddSubsemigroup M

The AddSubsemigroup generated by a set

Defined in
Mathlib.Algebra.Group.Subsemigroup.Basic
Cited by
34 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext, Quot.sound
Assumes
Add
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Around this declaration

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

AddSubsemigroup.subset_closure · cited by 12AddSubsemigroup.subset_cl…AddSubsemigroup.closure_le · cited by 11AddSubsemigroup.closure_leAddSubsemigroup.gi · cited by 5AddSubsemigroup.giAddSubsemigroup.closure_induction · cited by 5AddSubsemigroup.closure_i…AddSubsemigroup.closure_eq · cited by 3AddSubsemigroup.closure_eqAddSubsemigroup.mem_iSup_of_directed · cited by 3AddSubsemigroup.mem_iSup_…AddSubsemigroup.closure_iUnion · cited by 2AddSubsemigroup.closure_i…AddSubsemigroup.iSup_eq_closure · cited by 1AddSubsemigroup.iSup_eq_c…AddSubsemigroup.iSup_induction · cited by 1AddSubsemigroup.iSup_indu…AddSubsemigroup.mem_closure · cited by 1AddSubsemigroup.mem_closu…AddHom.eqOn_closure · cited by 1AddHom.eqOn_closureAddSubsemigroup.closure_eq_of_le · cited by 1AddSubsemigroup.closure_e…AddSubsemigroup.closure_le_centralizer_centralizer · cited by 1AddSubsemigroup.closure_l…AddSubsemigroup.closure_singleton_le_iff_mem · cited by 1AddSubsemigroup.closure_s…AddSubsemigroup.mem_closure_of_mem · cited by 1AddSubsemigroup.mem_closu…Set · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeSet.ofPred · cited by 6101Set.ofPredInfSet.sInf · cited by 935InfSet.sInfAddSubsemigroup · cited by 262AddSubsemigroupAddSubsemigroup.closureCITED BYCITES

Cites5

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

Cited by37

Results whose statement or proof uses this declaration.