Theorems · Theorem · order theory
lowerClosure_eq_top_iff
∀ {α : Type u_1} [inst : LinearOrder α] [NoMaxOrder α] {s : Set α}, lowerClosure s = ⊤ ↔ ¬BddAbove s- Defined in
- Mathlib.Order.UpperLower.Closure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderNoMaxOrder
Around this declaration
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Cites11
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
- Top.topstatement and proof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- SetLike.coeproof · cited by 8,199
- BddAbovestatement and proof · cited by 620
- NoMaxOrderstatement and proof · cited by 340
- LowerSetstatement · cited by 230
- lowerClosurestatement and proof · cited by 83
- bddAbove_lowerClosureproof · cited by 3
- not_bddAbove_univproof · cited by 3
- lowerClosure_eq_topproof · cited by 1
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