Theorems · Theorem · order theory
Finset.Ioc_toDual
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α] (b a : α),
Finset.Ioc (OrderDual.toDual b) (OrderDual.toDual a) = Finset.map OrderDual.toDual.toEmbedding (Finset.Ico a b)- 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
- Assumes
- PreorderLocallyFiniteOrder
Around this declaration
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Cites12
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 · cited by 927
- Finset.mapstatement · cited by 747
- LocallyFiniteOrderstatement and proof · cited by 658
- OrderDual.toDualstatement · cited by 481
- Finset.Icostatement · cited by 450
- Finset.Iocstatement · cited by 301
- Equiv.toEmbeddingstatement · cited by 254
- Finset.map_reflproof · cited by 32
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