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Theorems · Theorem · order theory

LowerSet.map_Iio

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] (f : α ≃o β) (a : α),
  (LowerSet.map f) (LowerSet.Iio a) = LowerSet.Iio (f a)
Defined in
Mathlib.Order.UpperLower.Principal
Cited by
0 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderPreorder
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Around this declaration

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DFunLike.coe · cited by 62936DFunLike.coePreorder · cited by 7952PreorderSet.ext · cited by 2266Set.extOrderIso · cited by 874OrderIsoLowerSet · cited by 230LowerSetSet.mem_Iio · cited by 49Set.mem_IioLowerSet.ext · cited by 29LowerSet.extLowerSet.map · cited by 12LowerSet.mapLowerSet.Iio · cited by 7LowerSet.IioOrderIso.image_Iio · cited by 4OrderIso.image_IioLowerSet.map_IioCITED BYCITES

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