Theorems · Theorem · order theory
Set.Ioc_pred_pred_eq_Ico_of_not_isMin
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : PredOrder α] {a : α},
¬IsMin a → ∀ (b : α), Set.Ioc (Order.pred a) (Order.pred b) = Set.Ico a b- Defined in
- Mathlib.Order.Interval.Set.SuccPred
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 26 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.Iocstatement · cited by 971
- Set.Icostatement and proof · cited by 799
- PredOrderstatement and proof · cited by 334
- IsMinstatement and proof · cited by 277
- Order.predstatement and proof · cited by 273
- Set.Ioo_pred_left_eq_Ioc_of_not_isMinproof · cited by 4
- Set.Ioc_pred_right_eq_Iooproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Finset.Ioc_pred_pred_eq_Ico_of_not_isMinproof · cited by 1
- Set.Ioc_pred_pred_eq_Icoproof · cited by 1
- Set.Ioc_sub_one_sub_one_eq_Ico_of_not_isMinproof · cited by 0