Theorems · Theorem · order theory
isLUB_supClosure
∀ {α : Type u_3} [inst : SemilatticeSup α] {s : Set α} {a : α}, IsLUB (supClosure s) a ↔ IsLUB s a- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 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.
Cites9
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
- IsLUBstatement · cited by 280
- upperBoundsproof · cited by 263
- IsLeastproof · cited by 122
- supClosurestatement · cited by 33
- upperBounds_supClosureproof · cited by 1
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