Theorems · Definition · order theory
Antitone
{α : Type u} → {β : Type v} → [Preorder α] → [Preorder β] → (α → β) → PropA function f is antitone if a ≤ b implies f b ≤ f a.
- Defined in
- Mathlib.Order.Monotone.Defs
- Cited by
- 563 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 5 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
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
Cited by570
Results whose statement or proof uses this declaration.
- List.SortedGEproof · cited by 54
- Antitone.dual_rightstatement · cited by 42
- Antitone.dual_leftstatement · cited by 33
- antitone_nat_of_succ_lestatement · cited by 21
- Antitone.antitoneOnstatement and proof · cited by 21
- Monotone.comp_antitonestatement and proof · cited by 16
- StrictAnti.antitonestatement · cited by 15
- Filter.HasAntitoneBasis.antitonestatement · cited by 12
- MeasureTheory.tendsto_measure_iInter_atTopstatement and proof · cited by 12
- Antitone.compstatement and proof · cited by 10
- Antitone.comp_monotonestatement and proof · cited by 9
- Antitone.dualstatement · cited by 8
Showing the 200 most cited of 570.