Theorems · Theorem · group theory
Submonoid.closure_iUnion
∀ {M : Type u_1} [inst : MulOneClass M] {ι : Sort u_4} (s : ι → Set M),
Submonoid.closure (⋃ i, s i) = ⨆ i, Submonoid.closure (s i)- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Submonoidstatement · cited by 3,086
- Set.iUnionstatement · cited by 2,483
- iSupstatement · cited by 2,415
- MulOneClassstatement and proof · cited by 1,018
- Submonoid.closurestatement · cited by 167
- GaloisInsertion.gcproof · cited by 137
- GaloisConnection.l_iSupproof · cited by 78
- Submonoid.giproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Submonoid.mem_iSup_of_directedproof · cited by 3
- Monoid.CoprodI.mrange_eq_iSupproof · cited by 1
- Monoid.CoprodI.mclosure_iUnion_range_ofproof · cited by 1
- Submonoid.FG.piproof · cited by 1
- Submonoid.iSup_eq_closureproof · cited by 1