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Theorems · Theorem · group theory

AddSubmonoid.iSup_eq_closure

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

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

AddSubmonoid.iSup_induction · cited by 5AddSubmonoid.iSup_inducti…Submodule.iSup_toAddSubmonoid · cited by 2Submodule.iSup_toAddSubmo…SetLike.coe · cited by 8199SetLike.coeSet.iUnion · cited by 2483Set.iUnioniSup · cited by 2415iSupAddZeroClass · cited by 1237AddZeroClassAddSubmonoid · cited by 1178AddSubmonoidAddSubmonoid.closure · cited by 224AddSubmonoid.closureAddSubmonoid.closure_eq · cited by 10AddSubmonoid.closure_eqAddSubmonoid.closure_iUnion · cited by 3AddSubmonoid.closure_iUni…AddSubmonoid.iSup_eq_closureCITED BYCITES

Cites8

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Cited by2

Results whose statement or proof uses this declaration.