Theorems · Theorem · order theory
Order.Ioi_pred_eq_insert_of_not_isMin
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : PredOrder α] {a : α},
¬IsMin a → Set.Ioi (Order.pred a) = insert a (Set.Ioi a)- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 3 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.
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.extproof · cited by 2,266
- Set.Ioistatement · cited by 1,463
- PredOrderstatement and proof · cited by 334
- IsMinstatement and proof · cited by 277
- Order.predstatement · cited by 273
- Order.pred_lt_iff_eq_or_lt_of_not_isMinproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Order.Ioc_pred_left_eq_insert_of_not_isMinproof · cited by 1
- Order.Ioo_pred_left_eq_insert_of_not_isMinproof · cited by 1
- Order.Ioi_pred_eq_insertproof · cited by 0