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Theorems · Theorem · order theory

OrderEmbedding.preimage_Ici

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] (e : α ↪o β) (x : α),
  ⇑e ⁻¹' Set.Ici (e x) = Set.Ici x
Defined in
Mathlib.Order.Interval.Set.OrderEmbedding
Cited by
3 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Quot.sound
Assumes
PreorderPreorder
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Around this declaration

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

OrderEmbedding.image_Ici · cited by 1OrderEmbedding.image_IciRat.preimage_cast_Ici · cited by 0Rat.preimage_cast_IciNNRat.preimage_cast_Ici · cited by 0NNRat.preimage_cast_IciDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetPreorder · cited by 7952PreorderSet.preimage · cited by 4946Set.preimageSet.ext · cited by 2266Set.extSet.Ici · cited by 1070Set.IciOrderEmbedding · cited by 619OrderEmbeddingOrderEmbedding.le_iff_le · cited by 32OrderEmbedding.le_iff_leOrderEmbedding.preimage_IciCITED BYCITES

Cites8

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Cited by3

Results whose statement or proof uses this declaration.