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[Merged by Bors] - feat(Data/Set): a function surjective on univ is surjective #32655

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[Merged by Bors] - feat(Data/Set): a function surjective on univ is surjective #32655

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3 changes: 3 additions & 0 deletions Mathlib/Data/Set/Function.lean
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Expand Up @@ -539,6 +539,9 @@ lemma surjOn_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) : Su
protected lemma _root_.Function.Surjective.surjOn (hf : Surjective f) : SurjOn f univ t :=
(surjOn_univ.2 hf).mono .rfl (subset_univ _)

lemma SurjOn.surjective (hf : SurjOn f s .univ) : f.Surjective :=
surjOn_univ.1 <| hf.mono s.subset_univ .rfl

@[deprecated surjOn_univ (since := "2025-10-31")]
theorem surjective_iff_surjOn_univ : Surjective f ↔ SurjOn f univ univ := surjOn_univ.symm

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