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Theorems · Theorem · order theory

Set.Icc_eq_empty_iff

∀ {α : Type u_1} [inst : Preorder α] {a b : α}, Set.Icc a b = ∅ ↔ ¬a ≤ b
Defined in
Mathlib.Order.Interval.Set.Basic
Cited by
4 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Preorder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.Iic_disjoint_Ici · cited by 2Set.Iic_disjoint_IciFinset.Icc_eq_empty_iff · cited by 2Finset.Icc_eq_empty_iffSet.Icc_eq_Icc_iff · cited by 1Set.Icc_eq_Icc_iffSet.Ici_disjoint_Iic · cited by 1Set.Ici_disjoint_IicSet · cited by 53352SetPreorder · cited by 7952PreorderSet.Icc · cited by 1702Set.IccSet.nonempty_Icc · cited by 21Set.nonempty_IccSet.Icc_eq_empty_iffCITED BYCITES

Cites4

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Cited by4

Results whose statement or proof uses this declaration.