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Theorems · Theorem · group theory

Submonoid.iSup_eq_closure

∀ {M : Type u_1} [inst : MulOneClass M] {ι : Sort u_4} (p : ι → Submonoid M), ⨆ i, p i = Submonoid.closure (⋃ i, ↑(p i))
Defined in
Mathlib.Algebra.Group.Submonoid.Basic
Cited by
1 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MulOneClass
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Around this declaration

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

Submonoid.iSup_induction · cited by 1Submonoid.iSup_inductionSetLike.coe · cited by 8199SetLike.coeSubmonoid · cited by 3086SubmonoidSet.iUnion · cited by 2483Set.iUnioniSup · cited by 2415iSupMulOneClass · cited by 1018MulOneClassSubmonoid.closure · cited by 167Submonoid.closureSubmonoid.closure_eq · cited by 13Submonoid.closure_eqSubmonoid.closure_iUnion · cited by 5Submonoid.closure_iUnionSubmonoid.iSup_eq_closureCITED BYCITES

Cites8

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Cited by1

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