Theorems · Theorem · order theory
OrderIso.image_preimage
∀ {α : Type u_1} {β : Type u_2} [inst : LE α] [inst_1 : LE β] (e : α ≃o β) (s : Set β), ⇑e '' ⇑e ⁻¹' s = s- Defined in
- Mathlib.Order.Hom.Set
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Set.imagestatement · cited by 5,609
- Set.preimagestatement · cited by 4,946
- OrderIsostatement and proof · cited by 874
- RelIso.toEquivproof · cited by 113
- Equiv.image_preimageproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- OrderIso.bddAbove_preimageproof · cited by 2
- OrderIso.bddBelow_preimageproof · cited by 2
- IsChain.preimage_iso_iffproof · cited by 0
- IsAntichain.preimage_iso_iffproof · cited by 0