Theorems · Theorem · order theory
OrderIso.preimage_Iio
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] (e : α ≃o β) (b : β),
⇑e ⁻¹' Set.Iio b = Set.Iio (e.symm b)- Defined in
- Mathlib.Order.Interval.Set.OrderIso
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.preimagestatement · cited by 4,946
- Set.extproof · cited by 2,266
- Set.Iiostatement · cited by 1,166
- OrderIsostatement and proof · cited by 874
- OrderIso.symmstatement and proof · cited by 475
- OrderIso.apply_symm_applyproof · cited by 45
- OrderIso.lt_iff_ltproof · cited by 16
Cited by5
Results whose statement or proof uses this declaration.
- OrderIso.continuousproof · cited by 6
- OrderIso.image_Iioproof · cited by 4
- Set.preimage_mul_const_Iio₀proof · cited by 2
- OrderIso.preimage_Icoproof · cited by 1
- OrderIso.preimage_Iooproof · cited by 1