Theorems · Theorem · order theory
OrderIso.upperBounds_image
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] (f : α ≃o β) {s : Set α},
upperBounds (⇑f '' s) = ⇑f '' upperBounds s- Defined in
- Mathlib.Order.Bounds.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.
Cites13
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 and proof · cited by 5,609
- OrderIsostatement and proof · cited by 874
- OrderIso.symmproof · cited by 475
- Set.mem_image_of_memproof · cited by 371
- upperBoundsstatement and proof · cited by 263
- Set.Subset.antisymmproof · cited by 213
- OrderIso.apply_symm_applyproof · cited by 45
- OrderIso.monotoneproof · cited by 23
- OrderIso.le_symm_applyproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- OrderIso.lowerBounds_imageproof · cited by 2
- lowerBounds_smul_of_negproof · cited by 0
- upperBounds_smul_of_posproof · cited by 0