Theorems · Theorem · order theory
IsUpperSet.eq_empty_or_Ici
∀ {α : Type u_1} [inst : LinearOrder α] {s : Set α} [WellFoundedLT α], IsUpperSet s → s = ∅ ∨ ∃ a, s = Set.Ici a- Defined in
- Mathlib.Order.UpperLower.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderWellFoundedLT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.extproof · cited by 2,266
- Set.Icistatement and proof · cited by 1,070
- WellFoundedLTstatement and proof · cited by 491
- IsUpperSetstatement and proof · cited by 148
- Set.nonempty_iff_ne_emptyproof · cited by 96
- WellFounded.minproof · cited by 33
- WellFounded.min_memproof · cited by 23
- wellFounded_ltproof · cited by 22
- WellFounded.min_leproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsLowerSet.eq_univ_or_Iioproof · cited by 2
- IsUpperSet.isClosedproof · cited by 1