Theorems · Theorem · order theory
Finset.coe_Iio
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : LocallyFiniteOrderBot α] (a : α), ↑(Finset.Iio a) = Set.Iio a- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
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 · cited by 53,352
- Finsetstatement · cited by 13,712
- SetLike.coestatement · cited by 8,199
- Preorderstatement and proof · cited by 7,952
- Set.extproof · cited by 2,266
- Set.Iiostatement · cited by 1,166
- LocallyFiniteOrderBotstatement and proof · cited by 286
- Finset.Iiostatement · cited by 147
- Finset.mem_Iioproof · cited by 20
Cited by34
Results whose statement or proof uses this declaration.
- LinearMap.support_singularValuesproof · cited by 3
- Fin.map_castLEEmb_Iioproof · cited by 2
- Set.ncard_Iio_natproof · cited by 2
- MeasureTheory.stoppedProcess_eq''proof · cited by 1
- Fin.map_finCongr_Iioproof · cited by 1
- Fin.finsetImage_castLE_Iioproof · cited by 1
- PowerSeries.WithPiTopology.summable_prod_of_tendsto_order_atTop_nhds_topproof · cited by 1
- Fin.addRothNumber_eq_rothNumberNatproof · cited by 1
- Finset.Ico_subset_Iio_selfproof · cited by 1
- disjointed_of_isMinproof · cited by 1
- Finset.Iic_pred_eq_Iioproof · cited by 1