Theorems · Theorem · order theory
upperBounds_countableSupClosure
∀ {α : Type u_2} [inst : Preorder α] (s : Set α), upperBounds (countableSupClosure s) = upperBounds s- Defined in
- Mathlib.Order.CountableSupClosed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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
- Preorderstatement and proof · cited by 7,952
- Set.Nonemptyproof · cited by 2,627
- Set.Countableproof · cited by 545
- LE.le.antisymmproof · cited by 507
- ClosureOperatorstatement · cited by 371
- IsLUBproof · cited by 280
- upperBoundsstatement and proof · cited by 263
- isLUB_le_iffproof · cited by 24
- countableSupClosurestatement and proof · cited by 21
- upperBounds_mono_setproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- isLUB_countableSupClosureproof · cited by 0