Theorems · Theorem · order theory
Antitone.directed_le
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [IsCodirectedOrder α] [inst_2 : Preorder β] {f : α → β},
Antitone f → Directed (fun x1 x2 => x1 ≤ x2) f- Defined in
- Mathlib.Order.Directed
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
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.
- Preorderstatement and proof · cited by 7,952
- Antitonestatement and proof · cited by 563
- Directedstatement · cited by 213
- IsCodirectedOrderstatement and proof · cited by 95
- directed_of_isDirected_geproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.indep_limsup_atBot_selfproof · cited by 3
- ProbabilityTheory.Kernel.indep_iSup_of_antitoneproof · cited by 2