Theorems · Theorem · order theory
supClosed_supClosure
∀ {α : Type u_3} [inst : SemilatticeSup α] {s : Set α}, SupClosed (supClosure s)- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- SemilatticeSupstatement and proof · cited by 785
- ClosureOperatorstatement · cited by 371
- SupClosedstatement · cited by 57
- supClosurestatement and proof · cited by 33
- ClosureOperator.isClosed_closureproof · cited by 15
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.IsSetSemiring.isSetRing_supClosureproof · cited by 3
- MeasureTheory.IsSetSemiring.mem_supClosure_iffproof · cited by 2
- supClosure_infClosureproof · cited by 2
- supClosure_prodproof · cited by 1
- finsetSup'_mem_supClosureproof · cited by 1
- MeasureTheory.addContent_le_sum_of_subset_sUnionproof · cited by 1
- infClosure_supClosureproof · cited by 0
- sup_mem_supClosureproof · cited by 0