Theorems · Theorem · order theory
StrictAntiOn.antitoneOn
∀ {α : Type u} {β : Type v} [inst : PartialOrder α] [inst_1 : Preorder β] {f : α → β} {s : Set α},
StrictAntiOn f s → AntitoneOn f s- Defined in
- Mathlib.Order.Monotone.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderPreorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- PartialOrderstatement and proof · cited by 6,410
- LT.lt.leproof · cited by 2,189
- AntitoneOnstatement · cited by 266
- StrictAntiOnstatement and proof · cited by 120
- antitoneOn_iff_forall_ltproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- StrictAntiOn.mapsTo_Icoproof · cited by 2
- StrictAntiOn.mapsTo_Iocproof · cited by 2
- Continuous.strictMonoOn_of_inj_rigidityproof · cited by 1
- Real.exists_isMinOn_Gamma_Ioiproof · cited by 0
- antitoneOn_inv_posproof · cited by 0
- Real.antitoneOn_cosproof · cited by 0