Theorems · Theorem · order theory
MonotoneOn.image_lowerBounds_subset_lowerBounds_image
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β} {s t : Set α},
MonotoneOn f t → s ⊆ t → f '' (lowerBounds s ∩ t) ⊆ lowerBounds (f '' s)- Defined in
- Mathlib.Order.Bounds.Image
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, 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
- MonotoneOnstatement and proof · cited by 311
- lowerBoundsstatement and proof · cited by 212
- MonotoneOn.mem_lowerBounds_imageproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AntitoneOn.image_lowerBounds_subset_upperBounds_imageproof · cited by 0