Theorems · Theorem · order theory
Set.Iic_pred_eq_Iio_of_not_isMin
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : PredOrder α] {b : α}, ¬IsMin b → Set.Iic (Order.pred b) = Set.Iio b- Defined in
- Mathlib.Order.Interval.Set.SuccPred
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, 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 · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.extproof · cited by 2,266
- Set.Iiostatement and proof · cited by 1,166
- Set.Iicstatement · cited by 1,111
- PredOrderstatement and proof · cited by 334
- IsMinstatement and proof · cited by 277
- Order.predstatement and proof · cited by 273
- Set.mem_Iioproof · cited by 49
- Set.mem_Iicproof · cited by 37
- Order.le_pred_iff_of_not_isMinproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- Set.Iic_pred_eq_Iioproof · cited by 1
- Finset.Iic_pred_eq_Iio_of_not_isMinproof · cited by 1
- Set.Iic_sub_one_eq_Iio_of_not_isMinproof · cited by 0