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chore(Geometry/RingedSpace/PresheafedSpace/HasColimits): remove an erw (#38506)
- rewrites the `TopCat.comp_app` step in `colimitPresheafObjIsoComponentwiseLimit` with `simp only [colimitCocone, colimit, ← TopCat.comp_app]` - folds `colimitCocone_ι_app_c`, `limitObjIsoLimitCompEvaluation_inv_π_app_assoc`, and `limMap_π_assoc` into a single `rw` chain in `colimitPresheafObjIsoComponentwiseLimit_inv_ι_app` Extracted from #38415 [![Open in Gitpod](https://gitpod.io/button/open-in-gitpod.svg)](https://gitpod.io/from-referrer/)
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Mathlib/Geometry/RingedSpace/PresheafedSpace/HasColimits.lean

Lines changed: 3 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -304,7 +304,7 @@ def colimitPresheafObjIsoComponentwiseLimit (F : J ⥤ PresheafedSpace.{_, _, v}
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simp only [Functor.op_obj, op_inj_iff, Opens.map_coe, SetLike.ext'_iff,
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Set.preimage_preimage]
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refine congr_arg (Set.preimage · U.1) (funext fun x => ?_)
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erw [← TopCat.comp_app]
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simp only [colimitCocone, colimit, ← TopCat.comp_app]
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congr
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exact ι_preservesColimitIso_inv (forget C) F (unop X)
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· intro X Y f
@@ -327,9 +327,8 @@ theorem colimitPresheafObjIsoComponentwiseLimit_inv_ι_app (F : J ⥤ Presheafed
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congr_app (Iso.symm_inv _)]
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dsimp
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rw [map_id, comp_id, assoc, assoc, assoc, NatTrans.naturality,
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← comp_c_app_assoc,
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congr_app (colimit.isoColimitCocone_ι_hom _ _), assoc]
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erw [limitObjIsoLimitCompEvaluation_inv_π_app_assoc, limMap_π_assoc]
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← comp_c_app_assoc, congr_app (colimit.isoColimitCocone_ι_hom _ _), assoc,
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colimitCocone_ι_app_c, limitObjIsoLimitCompEvaluation_inv_π_app_assoc, limMap_π_assoc]
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simp
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set_option backward.isDefEq.respectTransparency false in

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