Theorems · Theorem · order theory
Set.Iio_succ_eq_Iic_of_not_isMax
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : SuccOrder α] {b : α}, ¬IsMax b → Set.Iio (Order.succ b) = Set.Iic b- Defined in
- Mathlib.Order.Interval.Set.SuccPred
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderSuccOrder
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 · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.extproof · cited by 2,266
- Set.Iiostatement · cited by 1,166
- Set.Iicstatement and proof · cited by 1,111
- Order.succstatement and proof · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsMaxstatement and proof · cited by 372
- Set.mem_Iioproof · cited by 49
- Set.mem_Iicproof · cited by 37
- Order.lt_succ_iff_of_not_isMaxproof · cited by 17
Cited by3
Results whose statement or proof uses this declaration.
- Set.Iio_succ_eq_Iicproof · cited by 2
- Finset.Iio_succ_eq_Iic_of_not_isMaxproof · cited by 1
- Set.Iio_add_one_eq_Iic_of_not_isMaxproof · cited by 0