Theorems · Theorem · order theory
Monotone.image_upperBounds_subset_upperBounds_image
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
Monotone f → ∀ {s : Set α}, f '' upperBounds s ⊆ upperBounds (f '' s)- Defined in
- Mathlib.Order.Bounds.Image
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.imagestatement and proof · cited by 5,609
- Monotonestatement and proof · cited by 1,397
- upperBoundsstatement and proof · cited by 263
- Monotone.mem_upperBounds_imageproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- OrderIso.upperBounds_imageproof · cited by 3
- Antitone.image_upperBounds_subset_lowerBounds_imageproof · cited by 1
- smul_upperBounds_subset_upperBounds_smul_of_nonnegproof · cited by 0