Theorems · Theorem · order theory
OrderIso.image_Ioi
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] (e : α ≃o β) (a : α),
⇑e '' Set.Ioi a = Set.Ioi (e a)- Defined in
- Mathlib.Order.Interval.Set.OrderIso
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 27 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 and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.imagestatement · cited by 5,609
- Set.Ioistatement and proof · cited by 1,463
- OrderIsostatement and proof · cited by 874
- OrderIso.symmproof · cited by 475
- OrderIso.symm_symmproof · cited by 15
- OrderIso.image_eq_preimage_symmproof · cited by 13
- OrderIso.preimage_Ioiproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Set.image_mul_left_Ioiproof · cited by 2
- UpperSet.map_Ioiproof · cited by 0
- LinearOrderedField.smul_Ioiproof · cited by 0