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Theorems · Theorem · group theory

AddSubsemigroup.closure_eq

∀ {M : Type u_1} [inst : Add M] (S : AddSubsemigroup M), AddSubsemigroup.closure ↑S = S

Additive closure of an additive subsemigroup S equals S

Defined in
Mathlib.Algebra.Group.Subsemigroup.Basic
Cited by
3 results in Mathlib
Foundations
Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Add
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Around this declaration

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

AddSubsemigroup.mem_iSup_of_directed · cited by 3AddSubsemigroup.mem_iSup_…AddSubsemigroup.iSup_eq_closure · cited by 1AddSubsemigroup.iSup_eq_c…AddSubsemigroup.closure_univ · cited by 0AddSubsemigroup.closure_u…SetLike.coe · cited by 8199SetLike.coeAddSubsemigroup · cited by 262AddSubsemigroupGaloisInsertion.l_u_eq · cited by 37GaloisInsertion.l_u_eqAddSubsemigroup.closure · cited by 34AddSubsemigroup.closureAddSubsemigroup.gi · cited by 5AddSubsemigroup.giAddSubsemigroup.closure_eqCITED BYCITES

Cites5

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

Cited by3

Results whose statement or proof uses this declaration.