Theorems · Theorem · order theory
monotone_toDual_comp_iff
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
Monotone (⇑OrderDual.toDual ∘ f) ↔ Antitone f- Defined in
- Mathlib.Order.Monotone.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses Quot.sound
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.
- DFunLike.coestatement · cited by 62,936
- Equivstatement · cited by 8,337
- Preorderstatement and proof · cited by 7,952
- Monotonestatement · cited by 1,397
- OrderDualstatement · cited by 927
- Antitonestatement · cited by 563
- OrderDual.toDualstatement · cited by 481
Cited by3
Results whose statement or proof uses this declaration.
- Antitone.dual_rightproof · cited by 42
- monotone_dual_iffproof · cited by 2
- antitone_iff_map_nonposproof · cited by 1