Theorems · Theorem · order theory
Set.insert_Ioc_left_eq_Ioc_pred_of_not_isMin
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : PredOrder α] {a b : α},
a ≤ b → ¬IsMin a → insert a (Set.Ioc a b) = Set.Ioc (Order.pred a) b- Defined in
- Mathlib.Order.Interval.Set.SuccPred
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 60 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.
Cites9
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.Iccproof · cited by 1,702
- Set.Iocstatement and proof · cited by 971
- PredOrderstatement and proof · cited by 334
- IsMinstatement and proof · cited by 277
- Order.predstatement · cited by 273
- Set.Ioc_insert_leftproof · cited by 6
- Order.Ioc_pred_left_of_not_isMinproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Set.insert_Ioc_left_eq_Ioc_predproof · cited by 2
- Finset.insert_Ioc_left_eq_Ioc_pred_of_not_isMinproof · cited by 1
- Set.insert_Ioc_left_eq_Ioc_sub_one_of_not_isMinproof · cited by 0