Theorems · Theorem · order theory
monotone_dual_iff
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
Monotone (⇑OrderDual.toDual ∘ f ∘ ⇑OrderDual.ofDual) ↔ Monotone f- Defined in
- Mathlib.Order.Monotone.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, 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
- Equivstatement · cited by 8,337
- Preorderstatement and proof · cited by 7,952
- Monotonestatement and proof · cited by 1,397
- OrderDualstatement · cited by 927
- OrderDual.toDualstatement · cited by 481
- OrderDual.ofDualstatement · cited by 400
- monotone_toDual_comp_iffproof · cited by 3
- antitone_comp_ofDual_iffproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Monotone.dualproof · cited by 39
- Topology.IsLowerSet.monotone_iff_continuousproof · cited by 0