Theorems · Theorem · order theory
IsLUB.nonempty
∀ {α : Type u_1} [inst : Preorder α] {s : Set α} {a : α} [NoBotOrder α], IsLUB s a → s.Nonempty- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderNoBotOrder
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Cites10
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
- Preorderstatement and proof · cited by 7,952
- Set.Nonemptystatement · cited by 2,627
- Set.mem_univproof · cited by 416
- IsLUBstatement and proof · cited by 280
- upperBoundsproof · cited by 263
- Set.nonempty_iff_ne_emptyproof · cited by 96
- NoBotOrderstatement and proof · cited by 43
- not_isBotproof · cited by 4
- upperBounds_emptyproof · cited by 3
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