Theorems · Theorem · order theory
Antitone.set_prod
∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : Preorder α] {f : α → Set β} {g : α → Set γ},
Antitone f → Antitone g → Antitone fun x => f x ×ˢ g x- Defined in
- Mathlib.Data.Set.Prod
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- SProd.sprodstatement · cited by 1,750
- Antitonestatement and proof · cited by 563
- Set.prod_monoproof · cited by 52
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.tendsto_integral_density_of_antitoneproof · cited by 2
- Filter.HasAntitoneBasis.prodproof · cited by 1