Theorems · Theorem · order theory
Order.Ioc_pred_left_eq_insert
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : PredOrder α] {a b : α} [NoMinOrder α],
b ≤ a → 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 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Iocstatement · cited by 971
- PredOrderstatement and proof · cited by 334
- Order.predstatement · cited by 273
- NoMinOrderstatement and proof · cited by 247
- not_isMinproof · cited by 42
- Order.Ioc_pred_left_eq_insert_of_not_isMinproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Order.Ico_pred_right_eq_insertproof · cited by 0