Theorems · Theorem · order theory
Set.Ico_eq_singleton_iff
∀ {α : Type u_1} [inst : PartialOrder α] {a b c : α}, Set.Ico a b = {c} ↔ a = c ∧ a ⋖ b- Defined in
- Mathlib.Order.Cover
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrder
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- LT.lt.neproof · cited by 872
- Set.Icostatement and proof · cited by 799
- LE.le.trans_ltproof · cited by 795
- CovBystatement and proof · cited by 290
- CovBy.Ico_eqproof · cited by 3
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