Theorems · Theorem · order theory
MonotoneOn.mem_upperBounds_image_self
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β} {t : Set α} {a : α},
MonotoneOn f t → a ∈ upperBounds t → a ∈ t → f a ∈ upperBounds (f '' t)- Defined in
- Mathlib.Order.Bounds.Image
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 57 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.
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.imagestatement · cited by 5,609
- MonotoneOnstatement and proof · cited by 311
- upperBoundsstatement · cited by 263
- subset_rflproof · cited by 77
- MonotoneOn.mem_upperBounds_imageproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- MonotoneOn.map_isGreatestproof · cited by 5
- AntitoneOn.mem_lowerBounds_image_selfproof · cited by 0