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Theorems · Theorem · group theory

Subsemigroup.closure_iUnion

∀ {M : Type u_1} [inst : Mul M] {ι : Sort u_3} (s : ι → Set M),
  Subsemigroup.closure (⋃ i, s i) = ⨆ i, Subsemigroup.closure (s i)
Defined in
Mathlib.Algebra.Group.Subsemigroup.Basic
Cited by
2 results in Mathlib
Foundations
Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Mul
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Around this declaration

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

Subsemigroup.mem_iSup_of_directed · cited by 3Subsemigroup.mem_iSup_of_…Subsemigroup.iSup_eq_closure · cited by 1Subsemigroup.iSup_eq_clos…Set · cited by 53352SetSet.iUnion · cited by 2483Set.iUnioniSup · cited by 2415iSupSubsemigroup · cited by 323SubsemigroupGaloisInsertion.gc · cited by 137GaloisInsertion.gcGaloisConnection.l_iSup · cited by 78GaloisConnection.l_iSupSubsemigroup.closure · cited by 43Subsemigroup.closureSubsemigroup.gi · cited by 5Subsemigroup.giSubsemigroup.closure_iUnionCITED BYCITES

Cites8

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

Cited by2

Results whose statement or proof uses this declaration.