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[Merged by Bors] - feat(Order/Filter/Extr): local minimum and local maximum implies const #34032

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[Merged by Bors] - feat(Order/Filter/Extr): local minimum and local maximum implies const #34032

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feat(Order/Filter/Extr): local minimum and local maximum implies const
b-mehta Jan 16, 2026
d01d657
Merge remote-tracking branch 'upstream/master' into eq-of-min-filter
b-mehta Jan 16, 2026
b14c1d3
add doc
b-mehta Jan 16, 2026
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6 changes: 6 additions & 0 deletions Mathlib/Order/Filter/Extr.lean
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Expand Up @@ -195,6 +195,12 @@ theorem isMaxOn_const {b : β} : IsMaxOn (fun _ => b) s a :=
theorem isExtrOn_const {b : β} : IsExtrOn (fun _ => b) s a :=
isExtrFilter_const

/-- If `f` has a minimum and a maximum both given by `f a` along the filter `l`, then it is
eventually equal to `f a` along the filter. -/
lemma eventuallyEq_of_isMinFilter_of_isMaxFilter {β : Type*} [PartialOrder β] {f : α → β}
(h₁ : IsMinFilter f l a) (h₂ : IsMaxFilter f l a) : f =ᶠ[l] (fun _ ↦ f a) := by
filter_upwards [h₁, h₂] using by grind

/-! ### Order dual -/


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