Theorems · Theorem · order theory
Order.Ioc_pred_left_eq_insert_of_not_isMin
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : PredOrder α] {a b : α},
b ≤ a → ¬IsMin b → Set.Ioc (Order.pred b) a = insert b (Set.Ioc b a)- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 20 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.
Cites12
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.Ioiproof · cited by 1,463
- 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.mem_Iicproof · cited by 37
- Set.Ioi_inter_Iicproof · cited by 13
- Set.insert_inter_of_memproof · cited by 5
- Order.Ioi_pred_eq_insert_of_not_isMinproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Order.Ioc_pred_left_eq_insertproof · cited by 1