Theorems · Theorem · order theory
Set.Ioo_succ_right_eq_Ioc_of_not_isMax
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : SuccOrder α] {b : α},
¬IsMax b → ∀ (a : α), Set.Ioo a (Order.succ b) = Set.Ioc a b- Defined in
- Mathlib.Order.Interval.Set.SuccPred
- Cited by
- 4 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.Ioostatement · cited by 1,214
- Set.Iocstatement and proof · cited by 971
- Order.succstatement and proof · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsMaxstatement and proof · cited by 372
- Set.mem_Iooproof · cited by 29
- Set.mem_Iocproof · cited by 20
- Order.lt_succ_iff_of_not_isMaxproof · cited by 17
Cited by4
Results whose statement or proof uses this declaration.
- Set.Ico_succ_succ_eq_Ioc_of_not_isMaxproof · cited by 3
- Finset.Ioo_succ_right_eq_Ioc_of_not_isMaxproof · cited by 1
- Set.Ioo_succ_right_eq_Iocproof · cited by 1
- Set.Ioo_add_one_right_eq_Ioc_of_not_isMaxproof · cited by 0