Theorems · Theorem · order theory
AntitoneOn.dual_left
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β} {s : Set α},
AntitoneOn f s → MonotoneOn (f ∘ ⇑OrderDual.ofDual) sAlias of the reverse direction of monotoneOn_comp_ofDual_iff.
- Defined in
- Mathlib.Order.Monotone.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Preorderstatement and proof · cited by 7,952
- OrderDualstatement · cited by 927
- OrderDual.ofDualstatement · cited by 400
- MonotoneOnstatement · cited by 311
- AntitoneOnstatement · cited by 266
- monotoneOn_comp_ofDual_iffproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Function.antitoneOn_of_rightInvOn_of_mapsToproof · cited by 1
- Filter.HasBasis.prod_same_index_antiproof · cited by 1
- AntitoneOn.sInf_image_Iccproof · cited by 0
- AntitoneOn.sSup_image_Iccproof · cited by 0