Theorems · Theorem · order theory
Antitone.map_bddBelow
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
Antitone f → ∀ {s : Set α}, BddBelow s → BddAbove (f '' s)The image under an antitone function of a set which is bounded below is bounded above.
- 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
- BddAbovestatement · cited by 620
- Antitonestatement and proof · cited by 563
- BddBelowstatement · cited by 401
- Antitone.dual_rightproof · cited by 42
- Monotone.map_bddBelowproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- BddBelow.smul_of_nonposproof · cited by 0