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chore(Topology): fix typo in theorem name (leanprover-community#37726)
Rename the theorem `eventualy_isUnit_of_isUnit` to `eventually_isUnit_of_isUnit`. Co-authored-by: int-y1 <jason_yuen2007@hotmail.com>
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  • Mathlib/Topology/Algebra/RestrictedProduct

Mathlib/Topology/Algebra/RestrictedProduct/Units.lean

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@@ -49,17 +49,20 @@ theorem isUnit_of_eventually_isUnit {x : Πʳ i, [R i, B i]_[𝓕]} (hx : ∀ i,
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simp [← Units.eq_inv_of_mul_eq_one_left hu])
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simp [RestrictedProduct.ext_iff]
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theorem eventualy_isUnit_of_isUnit {x : Πʳ i, [R i, B i]_[𝓕]} (hx : IsUnit x) :
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theorem eventually_isUnit_of_isUnit {x : Πʳ i, [R i, B i]_[𝓕]} (hx : IsUnit x) :
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(∀ i, IsUnit (x i)) ∧ ∀ᶠ i in 𝓕, ∃ (h : x i ∈ B i), IsUnit (⟨x i, h⟩ : B i) := by
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simp only [isUnit_iff_exists, RestrictedProduct.ext_iff, ← forall_and] at hx
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simp only [isUnit_iff_exists]
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choose b hb using hx
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exact ⟨Classical.skolem.symm.1 ⟨b, hb⟩, by filter_upwards [x.2, b.2] using
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fun i hx hb ↦ ⟨hx, ⟨b i, hb⟩, by simp_all [← SetLike.coe_eq_coe]⟩⟩
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@[deprecated (since := "2026-04-06")]
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alias eventualy_isUnit_of_isUnit := eventually_isUnit_of_isUnit
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theorem isUnit_iff {x : Πʳ i, [R i, B i]_[𝓕]} :
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IsUnit x ↔ (∀ i, IsUnit (x i)) ∧ ∀ᶠ i in 𝓕, ∃ (h : x i ∈ B i), IsUnit (⟨x i, h⟩ : B i) :=
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eventualy_isUnit_of_isUnit, fun h ↦ isUnit_of_eventually_isUnit h.1 h.2
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eventually_isUnit_of_isUnit, fun h ↦ isUnit_of_eventually_isUnit h.1 h.2
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/-- The homomorphism from the units of a restricted product to the regular product of unit. -/
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def coeUnits : Πʳ i, [R i, B i]_[𝓕]ˣ →* (i : ι) → (R i)ˣ :=

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