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4 changes: 2 additions & 2 deletions Mathlib/CategoryTheory/Presentable/IsCardinalFiltered.lean
Original file line number Diff line number Diff line change
Expand Up @@ -197,11 +197,11 @@ lemma isCardinalFiltered_preorder (J : Type w) [Preorder J]
{ app a := homOfLE (hj a)
naturality _ _ _ := rfl }⟩

set_option backward.isDefEq.respectTransparency.types false in
instance (κ : Cardinal.{w}) [hκ : Fact κ.IsRegular] :
IsCardinalFiltered κ.ord.ToType κ :=
isCardinalFiltered_preorder _ _ (fun ι f hs ↦ by
have h : Function.Surjective (fun i ↦ (⟨f i, i, rfl⟩ : Set.range f)) := fun _ ↦ by aesop
have h : Function.Surjective (fun i ↦ (⟨f i, Set.mem_range_self i⟩ : Set.range f)) :=
fun _ ↦ by aesop
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contrapose! hs
rw [← hκ.out.cof_ord, ← Ordinal.cof_toType]
refine (Order.cof_le fun j ↦ ?_).trans (Cardinal.mk_le_of_surjective h)
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