Theorems · Theorem · order theory
Finset.Iic_pred_eq_Iio_of_not_isMin
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : LocallyFiniteOrderBot α] [inst_2 : PredOrder α] {b : α},
¬IsMin b → Finset.Iic (Order.pred b) = Finset.Iio b- Defined in
- Mathlib.Order.Interval.Finset.SuccPred
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Finsetstatement · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- PredOrderstatement and proof · cited by 334
- LocallyFiniteOrderBotstatement and proof · cited by 286
- Finset.Iicstatement and proof · cited by 280
- IsMinstatement and proof · cited by 277
- Order.predstatement and proof · cited by 273
- Finset.Iiostatement and proof · cited by 147
- Finset.coe_injectiveproof · cited by 127
- Finset.coe_Iicproof · cited by 36
- Finset.coe_Iioproof · cited by 34
- Set.Iic_pred_eq_Iio_of_not_isMinproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Finset.Iic_sub_one_eq_Iio_of_not_isMinproof · cited by 0