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Theorems · Theorem · order theory

Order.Ioo_eq_empty_iff_le_succ

∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : SuccOrder α] {a b : α} [NoMaxOrder α],
  Set.Ioo a b = ∅ ↔ b ≤ Order.succ a
Defined in
Mathlib.Order.SuccPred.Basic
Cited by
0 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderSuccOrderNoMaxOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.ext · cited by 2266Set.extSet.Ioo · cited by 1214Set.IooOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderlt_of_le_of_lt · cited by 432lt_of_le_of_ltNoMaxOrder · cited by 340NoMaxOrdernot_isMax · cited by 46not_isMaxOrder.le_of_lt_succ · cited by 9Order.le_of_lt_succOrder.lt_succ_iff_not_isMax · cited by 3Order.lt_succ_iff_not_isM…Order.succ_strictMono · cited by 2Order.succ_strictMonoOrder.Ioo_eq_empty_iff_le_succCITED BYCITES

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