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Theorems · Theorem · general topology

isMinOn_Ioi_of_anti_mono

∀ {α : Type u} {β : Type u_1} [inst : LinearOrder α] [inst_1 : Preorder β] {a b : α} {f : α → β},
  AntitoneOn f (Set.Ioc a b) → MonotoneOn f (Set.Ici b) → IsMinOn f (Set.Ioi a) b

If f is antitone on Ioc a b and monotone on Ici b, then the minimum of f on Ioi a is attained at b.

Defined in
Mathlib.Order.Filter.Extr
Cited by
1 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Quot.sound
Assumes
LinearOrderPreorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

isMinOn_Ioi_of_deriv · cited by 0isMinOn_Ioi_of_derivLinearOrder · cited by 8572LinearOrderPreorder · cited by 7952PreorderSet.Ioi · cited by 1463Set.IoiSet.Ici · cited by 1070Set.IciSet.Ioc · cited by 971Set.IocMonotoneOn · cited by 311MonotoneOnAntitoneOn · cited by 266AntitoneOnIsMinOn · cited by 96IsMinOnisMaxOn_Ioi_of_mono_anti · cited by 2isMaxOn_Ioi_of_mono_antiisMinOn_Ioi_of_anti_monoCITED BYCITES

Cites9

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Cited by1

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