Theorems · Theorem · order theory
Set.Ico_succ_left_eq_Ioo
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : SuccOrder α] (a b : α), Set.Ico (Order.succ a) b = Set.Ioo a b- Defined in
- Mathlib.Order.Interval.Set.SuccPred
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 25 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.extproof · cited by 2,266
- Set.Ioostatement and proof · cited by 1,214
- Set.Icostatement · cited by 799
- Order.succstatement and proof · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsMaxproof · cited by 372
- Order.le_succproof · cited by 96
- Set.mem_Iooproof · cited by 29
- Set.Ioo_eq_emptyproof · cited by 24
- Set.Ico_eq_emptyproof · cited by 24
Cited by4
Results whose statement or proof uses this declaration.
- Set.Ico_succ_succ_eq_Ioc_of_not_isMaxproof · cited by 3
- Set.Icc_succ_pred_eq_Iooproof · cited by 2
- Finset.Ico_succ_left_eq_Iooproof · cited by 1
- Set.Ico_add_one_left_eq_Iooproof · cited by 0