Theorems · Theorem · order theory
Order.Ioc_pred_left_of_not_isMin
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : PredOrder α] {a b : α},
¬IsMin b → Set.Ioc (Order.pred b) a = Set.Icc b a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 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.
Cites11
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.Iccstatement and proof · cited by 1,702
- Set.Iicproof · cited by 1,111
- Set.Iocstatement · cited by 971
- PredOrderstatement and proof · cited by 334
- IsMinstatement and proof · cited by 277
- Order.predstatement · cited by 273
- Set.Iic_inter_Iciproof · cited by 6
- Set.Iic_inter_Ioiproof · cited by 5
- Order.Ioi_pred_of_not_isMinproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Set.insert_Ioc_left_eq_Ioc_pred_of_not_isMinproof · cited by 3
- Order.Ioc_pred_leftproof · cited by 2