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Theorems · Theorem · general topology

IsMaxOn.comp_antitone

∀ {α : Type u} {β : Type v} {γ : Type w} [inst : Preorder β] [inst_1 : Preorder γ] {f : α → β} {s : Set α} {a : α},
  IsMaxOn f s a → ∀ {g : β → γ}, Antitone g → IsMinOn (g ∘ f) s a
Defined in
Mathlib.Order.Filter.Extr
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses Quot.sound
Assumes
PreorderPreorder
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Around this declaration

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

IsMaxOn.neg · cited by 2IsMaxOn.negSet · cited by 53352SetPreorder · cited by 7952PreorderAntitone · cited by 563AntitoneIsMaxOn · cited by 114IsMaxOnIsMinOn · cited by 96IsMinOnIsMaxFilter.comp_antitone · cited by 4IsMaxFilter.comp_antitoneIsMaxOn.comp_antitoneCITED BYCITES

Cites6

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Cited by1

Results whose statement or proof uses this declaration.