Theorems · Theorem · order theory
upperBounds_supClosure
∀ {α : Type u_3} [inst : SemilatticeSup α] (s : Set α), upperBounds (supClosure s) = upperBounds s- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Finset.Nonemptyproof · cited by 1,001
- SemilatticeSupstatement and proof · cited by 785
- LE.le.antisymmproof · cited by 507
- ClosureOperatorstatement · cited by 371
- upperBoundsstatement and proof · cited by 263
- Finset.sup'proof · cited by 174
- supClosurestatement and proof · cited by 33
- Finset.sup'_leproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- isLUB_supClosureproof · cited by 0