Theorems · Theorem · order theory
Order.Iio_succ
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : SuccOrder α] [NoMaxOrder α] (a : α),
Set.Iio (Order.succ a) = Set.Iic a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.Iiostatement · cited by 1,166
- Set.Iicstatement · cited by 1,111
- Order.succstatement · cited by 633
- SuccOrderstatement and proof · cited by 574
- NoMaxOrderstatement and proof · cited by 340
- not_isMaxproof · cited by 46
- Order.Iio_succ_of_not_isMaxproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Cardinal.preBeth_add_oneproof · cited by 6
- SuccOrder.isOpen_singleton_iffproof · cited by 3
- Finset.Iio_succ_eq_Iicproof · cited by 1
- Field.Emb.Cardinal.filtration_succproof · cited by 0