Theorems · Theorem · order theory
Antitone.image_lowerBounds_subset_upperBounds_image
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
Antitone f → ∀ {s : Set α}, f '' lowerBounds s ⊆ upperBounds (f '' s)- Defined in
- Mathlib.Order.Bounds.Image
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 · cited by 5,609
- Antitonestatement and proof · cited by 563
- upperBoundsstatement · cited by 263
- lowerBoundsstatement · cited by 212
- Antitone.dual_rightproof · cited by 42
- Monotone.image_lowerBounds_subset_lowerBounds_imageproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- smul_lowerBounds_subset_upperBounds_smulproof · cited by 0