Theorems · Definition · order theory
OrderDual
Type u_2 → Type u_2
Type synonym to equip a type with the dual order: ≤ means ≥ and < means >. αᵒᵈ is
notation for OrderDual α.
- Defined in
- Mathlib.Order.OrderDual
- Cited by
- 927 results in Mathlib
- Foundations
- Depth 0 from the axioms, rests on 1 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by1,053
Results whose statement or proof uses this declaration.
- OrderDual.toDualstatement · cited by 481
- OrderDual.ofDualstatement and proof · cited by 400
- AddValuationproof · cited by 96
- OrderHom.dualstatement and proof · cited by 48
- Antitone.dual_rightstatement · cited by 42
- Monotone.dualstatement · cited by 39
- ConcaveOn.dualstatement · cited by 35
- Antitone.dual_leftstatement · cited by 33
- AntitoneOn.dual_rightstatement · cited by 29
- OrderIso.invstatement and proof · cited by 27
- OrderIso.negstatement and proof · cited by 27
- OrderIso.dualstatement and proof · cited by 24
Showing the 200 most cited of 1,053.