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Theorems · Theorem · order theory

List.sortedGT_map_toDual

∀ {α : Type u_1} [inst : Preorder α] {l : List αᵒᵈ}, (List.map (⇑OrderDual.toDual) l).SortedGT ↔ l.SortedLT
Defined in
Mathlib.Data.List.Sort
Cited by
2 results in Mathlib
Foundations
Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Preorder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

List.SortedGT.map_toDual · cited by 0SortedGT.map_toDualList.SortedLT.of_map_toDual · cited by 0SortedLT.of_map_toDualDFunLike.coe · cited by 62936DFunLike.coeEquiv · cited by 8337EquivPreorder · cited by 7952PreorderOrderDual · cited by 927OrderDualOrderDual.toDual · cited by 481OrderDual.toDualList.SortedLT · cited by 66List.SortedLTList.SortedGT · cited by 54List.SortedGTList.sortedGT_map_toDualCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.