Theorems · Theorem · order theory
bddAbove_lowerClosure
∀ {α : Type u_1} [inst : Preorder α] {s : Set α}, BddAbove ↑(lowerClosure s) ↔ BddAbove s- Defined in
- Mathlib.Order.UpperLower.Closure
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 61 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.
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
- SetLike.coestatement · cited by 8,199
- Preorderstatement and proof · cited by 7,952
- Set.Nonemptyproof · cited by 2,627
- BddAbovestatement · cited by 620
- upperBoundsproof · cited by 263
- LowerSetstatement · cited by 230
- lowerClosurestatement · cited by 83
- upperBounds_lowerClosureproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- BddAbove.of_lowerClosureproof · cited by 0
- BddAbove.lowerClosureproof · cited by 0
- lowerClosure_eq_top_iffproof · cited by 0