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tweak counterexample docstring
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Mathlib/Order/ConditionallyCompleteLattice/Indexed.lean

Lines changed: 2 additions & 2 deletions
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@@ -360,8 +360,8 @@ lemma ciInf_image {ι ι' : Type*} {s : Set ι} {f : ι → ι'} {g : ι' → α
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⨅ i ∈ (f '' s), g i = ⨅ x ∈ s, g (f x) :=
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ciSup_image (α := αᵒᵈ) hf hg'
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/-- Note that equality doesn't always hold, for example for `ι := , p := (· = 0), f := fun _ ↦ -1`
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the LHS is `-1` but the RHS is `-1 ⊔ sSup ∅ = -1 ⊔ 0 = 0`. -/
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/-- Note that equality need not hold: consider `ι := Bool, p := (·), α := ℤ, f := fun _ ↦ -1`,
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then the LHS is `-1` but the RHS is `-1 ⊔ sSup ∅ = -1 ⊔ 0 = 0`. -/
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theorem ciSup_exists_le {p : ι → Prop} {f : Exists p → α} : ⨆ ih, f ih ≤ ⨆ (i) (h), f ⟨i, h⟩ := by
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by_cases! h : Exists p
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· have : Nonempty <| Exists p := ⟨h⟩

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