Theorems · Theorem · order theory
OrderIso.preimage_Iic
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] (e : α ≃o β) (b : β),
⇑e ⁻¹' Set.Iic b = Set.Iic (e.symm b)- Defined in
- Mathlib.Order.Interval.Set.OrderIso
- Cited by
- 4 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.Iicstatement · cited by 1,111
- OrderIsostatement and proof · cited by 874
- OrderIso.symmstatement and proof · cited by 475
- OrderIso.apply_symm_applyproof · cited by 45
- OrderIso.le_iff_leproof · cited by 29
Cited by4
Results whose statement or proof uses this declaration.
- OrderIso.image_Iicproof · cited by 4
- OrderIso.preimage_Iccproof · cited by 4
- Set.preimage_mul_const_Iic₀proof · cited by 2
- OrderIso.preimage_Iocproof · cited by 1