Theorems · Theorem · order theory
OrderIso.image_Ioc
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] (e : α ≃o β) (a b : α),
⇑e '' Set.Ioc a b = Set.Ioc (e a) (e b)- Defined in
- Mathlib.Order.Interval.Set.OrderIso
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 28 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.Iocstatement and proof · cited by 971
- 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_Iocproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Set.image_mul_left_Iocproof · cited by 1
- Set.image_mul_right_Iocproof · cited by 0
- LinearOrderedField.smul_Iocproof · cited by 0