Theorems · Theorem · general topology
isMaxOn_dual_iff
∀ {α : Type u} {β : Type v} [inst : Preorder β] {f : α → β} {s : Set α} {a : α},
IsMaxOn (⇑OrderDual.toDual ∘ f) s a ↔ IsMinOn f s a- Defined in
- Mathlib.Order.Filter.Extr
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.toDualstatement · cited by 481
- IsMaxOnstatement · cited by 114
- IsMinOnstatement · cited by 96
Cited by2
Results whose statement or proof uses this declaration.
- IsMinOn.dualproof · cited by 2
- IsMaxOn.undualproof · cited by 0