@@ -49,17 +49,20 @@ theorem isUnit_of_eventually_isUnit {x : Πʳ i, [R i, B i]_[𝓕]} (hx : ∀ i,
4949 simp [← Units.eq_inv_of_mul_eq_one_left hu])
5050 simp [RestrictedProduct.ext_iff]
5151
52- theorem eventualy_isUnit_of_isUnit {x : Πʳ i, [R i, B i]_[𝓕]} (hx : IsUnit x) :
52+ theorem eventually_isUnit_of_isUnit {x : Πʳ i, [R i, B i]_[𝓕]} (hx : IsUnit x) :
5353 (∀ i, IsUnit (x i)) ∧ ∀ᶠ i in 𝓕, ∃ (h : x i ∈ B i), IsUnit (⟨x i, h⟩ : B i) := by
5454 simp only [isUnit_iff_exists, RestrictedProduct.ext_iff, ← forall_and] at hx
5555 simp only [isUnit_iff_exists]
5656 choose b hb using hx
5757 exact ⟨Classical.skolem.symm.1 ⟨b, hb⟩, by filter_upwards [x.2 , b.2 ] using
5858 fun i hx hb ↦ ⟨hx, ⟨b i, hb⟩, by simp_all [← SetLike.coe_eq_coe]⟩⟩
5959
60+ @ [deprecated (since := "2026-04-06" )]
61+ alias eventualy_isUnit_of_isUnit := eventually_isUnit_of_isUnit
62+
6063theorem isUnit_iff {x : Πʳ i, [R i, B i]_[𝓕]} :
6164 IsUnit x ↔ (∀ i, IsUnit (x i)) ∧ ∀ᶠ i in 𝓕, ∃ (h : x i ∈ B i), IsUnit (⟨x i, h⟩ : B i) :=
62- ⟨eventualy_isUnit_of_isUnit , fun h ↦ isUnit_of_eventually_isUnit h.1 h.2 ⟩
65+ ⟨eventually_isUnit_of_isUnit , fun h ↦ isUnit_of_eventually_isUnit h.1 h.2 ⟩
6366
6467/-- The homomorphism from the units of a restricted product to the regular product of unit. -/
6568def coeUnits : Πʳ i, [R i, B i]_[𝓕]ˣ →* (i : ι) → (R i)ˣ :=
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