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rename iota to iso
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Mathlib/CategoryTheory/Closed/PowerObjects.lean

Lines changed: 2 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -157,12 +157,12 @@ noncomputable instance singleton_is_mono : Mono (singleton hPB) :=
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let PeqP' : P = P' := by
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unfold P P'
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rw[pullback_diag_eq_singleton hPB b, eq, ← pullback_diag_eq_singleton hPB b']
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let ι : X ≅ Subobject.underlying.obj P :=
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let iso : X ≅ Subobject.underlying.obj P :=
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IsPullback.isoIsPullback_congr
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(Subobject.underlyingIso (cmdiag B)).symm (Iso.refl _) (Iso.refl _)
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(by simpa using Subobject.underlyingIso_hom_comp_eq_mk (cmdiag B)) (by simp)
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(pullback_of_diag b) (Subobject.isPullback (B ◁ b) B_sub)
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let eq₁ : (lift b (𝟙 X)) = ι.hom ≫ P.arrow := by unfold P ι; simp
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let eq₁ : (lift b (𝟙 X)) = iso.hom ≫ P.arrow := by unfold P iso; simp
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let eq₂ := Eq.symm (Subobject.arrow_congr P P' PeqP')
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let eq₃ := Eq.symm (Subobject.isPullback (B ◁ b') B_sub).w
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let eq₄ := Eq.symm (Subobject.underlyingIso_hom_comp_eq_mk (cmdiag B))

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