Theorems · Theorem · order theory
BddAbove.exists_isGreatest_of_nonempty
∀ {X : Type u_3} [inst : LinearOrder X] [inst_1 : SuccOrder X] [IsSuccArchimedean X] {S : Set X},
BddAbove S → S.Nonempty → ∃ x, IsGreatest S x- Defined in
- Mathlib.Order.SuccPred.Archimedean
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- LinearOrderstatement and proof · cited by 8,572
- Set.Nonemptystatement and proof · cited by 2,627
- Order.succproof · cited by 633
- BddAbovestatement and proof · cited by 620
- SuccOrderstatement and proof · cited by 574
- upperBoundsproof · cited by 263
- IsGreateststatement and proof · cited by 112
- IsSuccArchimedeanstatement and proof · cited by 88
- mem_upperBoundsproof · cited by 20
- Succ.recproof · cited by 10
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