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Theorems · Theorem · general topology

IsMinOn.dual

∀ {α : Type u} {β : Type v} [inst : Preorder β] {f : α → β} {s : Set α} {a : α},
  IsMinOn f s a → IsMaxOn (⇑OrderDual.toDual ∘ f) s a

Alias of the reverse direction of isMaxOn_dual_iff.

Defined in
Mathlib.Order.Filter.Extr
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses Quot.sound
Assumes
Preorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsMinOn.closure · cited by 1IsMinOn.closureinf_eq_of_isMinOn · cited by 0inf_eq_of_isMinOnDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetEquiv · cited by 8337EquivPreorder · cited by 7952PreorderOrderDual · cited by 927OrderDualOrderDual.toDual · cited by 481OrderDual.toDualIsMaxOn · cited by 114IsMaxOnIsMinOn · cited by 96IsMinOnisMaxOn_dual_iff · cited by 2isMaxOn_dual_iffIsMinOn.dualCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.