Theorems · Theorem · group theory
AddSubmonoid.closure_iUnion
∀ {M : Type u_1} [inst : AddZeroClass M] {ι : Sort u_4} (s : ι → Set M),
AddSubmonoid.closure (⋃ i, s i) = ⨆ i, AddSubmonoid.closure (s i)- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddZeroClass
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
- Set.iUnionstatement · cited by 2,483
- iSupstatement · cited by 2,415
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement · cited by 1,178
- AddSubmonoid.closurestatement · cited by 224
- GaloisInsertion.gcproof · cited by 137
- GaloisConnection.l_iSupproof · cited by 78
- AddSubmonoid.giproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- AddSubmonoid.mem_iSup_of_directedproof · cited by 3
- AddSubmonoid.iSup_eq_closureproof · cited by 2
- AddSubmonoid.FG.piproof · cited by 1