Theorems · Theorem · order theory
Set.Ioc_pred_right_eq_Ioo
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : PredOrder α] (a b : α), Set.Ioc a (Order.pred b) = Set.Ioo a b- Defined in
- Mathlib.Order.Interval.Set.SuccPred
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderPredOrder
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.Iocstatement · cited by 971
- PredOrderstatement and proof · cited by 334
- IsMinproof · cited by 277
- Order.predstatement and proof · cited by 273
- Set.Ioc_eq_emptyproof · cited by 38
- Set.mem_Iooproof · cited by 29
- Set.Ioo_eq_emptyproof · cited by 24
- Set.mem_Iocproof · cited by 20
Cited by3
Results whose statement or proof uses this declaration.
- Set.Ioc_pred_pred_eq_Ico_of_not_isMinproof · cited by 3
- Finset.Ioc_pred_right_eq_Iooproof · cited by 1
- Set.Ioc_sub_one_right_eq_Iooproof · cited by 0