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CoolRmaljcommelin
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Update Mathlib/Topology/GDelta/Basic.lean
Co-authored-by: Johan Commelin <johan@commelin.net>
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Mathlib/Topology/GDelta/Basic.lean

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@@ -152,7 +152,7 @@ theorem IsGδ.iUnion [Finite ι'] {f : ι' → Set X} (h : ∀ i, IsGδ (f i)) :
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/- The preimage of a Gδ set under a continuous map is Gδ. -/
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theorem isGδ_induced [TopologicalSpace Y] {f : X → Y} {s : Set Y} (hf : Continuous f)
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(hs : IsGδ s) : IsGδ (f ⁻¹' s) := by
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obtain ⟨U, hU1, hU2⟩ := IsGδ.eq_iInter_nat hs
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obtain ⟨U, hU1, hU2⟩ := hs.eq_iInter_nat
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simp_all only [preimage_iInter]
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exact IsGδ.iInter_of_isOpen (fun i => hf.isOpen_preimage (U i) (hU1 i))
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