Theorems · Theorem · order theory
Iio_orderDual_def
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : LocallyFiniteOrderTop α] (a : αᵒᵈ),
Finset.Iio a = Finset.map OrderDual.toDual.toEmbedding (Finset.Ioi (OrderDual.ofDual a))- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Finsetstatement · cited by 13,712
- Equivstatement · cited by 8,337
- Preorderstatement and proof · cited by 7,952
- OrderDualstatement and proof · cited by 927
- Finset.mapstatement · cited by 747
- OrderDual.toDualstatement · cited by 481
- OrderDual.ofDualstatement · cited by 400
- Equiv.toEmbeddingstatement · cited by 254
- Finset.Iiostatement · cited by 147
- LocallyFiniteOrderTopstatement and proof · cited by 114
- Finset.Ioistatement · cited by 106
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