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Theorems · Theorem · order theory

OrderEmbedding.preimage_Ioi

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] (e : α ↪o β) (x : α),
  ⇑e ⁻¹' Set.Ioi (e x) = Set.Ioi x
Defined in
Mathlib.Order.Interval.Set.OrderEmbedding
Cited by
3 results in Mathlib
Foundations
Depth 16 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_Ioi · cited by 1OrderEmbedding.image_IoiNNRat.preimage_cast_Ioi · cited by 0NNRat.preimage_cast_IoiRat.preimage_cast_Ioi · cited by 0Rat.preimage_cast_IoiDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetPreorder · cited by 7952PreorderSet.preimage · cited by 4946Set.preimageSet.ext · cited by 2266Set.extSet.Ioi · cited by 1463Set.IoiOrderEmbedding · cited by 619OrderEmbeddingOrderEmbedding.lt_iff_lt · cited by 23OrderEmbedding.lt_iff_ltOrderEmbedding.preimage_IoiCITED BYCITES

Cites8

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Cited by3

Results whose statement or proof uses this declaration.