Theorems · Theorem · order theory
Set.toFinset_Iio
∀ {α : Type u_3} [inst : Preorder α] [inst_1 : LocallyFiniteOrderBot α] (a : α) [inst_2 : Fintype ↑(Set.Iio a)],
(Set.Iio a).toFinset = Finset.Iio a- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 58 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
- Preorderstatement and proof · cited by 7,952
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Set.Iiostatement and proof · cited by 1,166
- Finset.extproof · cited by 565
- LocallyFiniteOrderBotstatement and proof · cited by 286
- Set.toFinsetstatement · cited by 217
- Finset.Iiostatement · cited by 147
- Set.mem_Iioproof · cited by 49
- Set.mem_toFinsetproof · cited by 47
- Finset.mem_Iioproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- IsOfFinAddOrder.natCard_multiples_le_addOrderOfproof · cited by 0
- IsOfFinOrder.natCard_powers_le_orderOfproof · cited by 0