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chore(Topology/Sheaves/SheafCondition/PairwiseIntersections): remove an erw #38508

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chore(Topology/Sheaves/SheafCondition/PairwiseIntersections): remove an erw #38508

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8 changes: 4 additions & 4 deletions Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -371,7 +371,7 @@ def interUnionPullbackConeLift : s.pt ⟶ F.1.obj (op (U ⊔ V)) := by
set_option backward.isDefEq.respectTransparency false in
theorem interUnionPullbackConeLift_left :
interUnionPullbackConeLift F U V s ≫ F.1.map (homOfLE le_sup_left).op = s.fst := by
erw [Category.assoc]
rw [interUnionPullbackConeLift, Category.assoc]
simp_rw [← F.1.map_comp]
exact
(F.presheaf.isSheaf_iff_isSheafPairwiseIntersections.mp F.2 _).some.fac _ <|
Expand All @@ -380,7 +380,7 @@ theorem interUnionPullbackConeLift_left :
set_option backward.isDefEq.respectTransparency false in
theorem interUnionPullbackConeLift_right :
interUnionPullbackConeLift F U V s ≫ F.1.map (homOfLE le_sup_right).op = s.snd := by
erw [Category.assoc]
rw [interUnionPullbackConeLift, Category.assoc]
simp_rw [← F.1.map_comp]
exact
(F.presheaf.isSheaf_iff_isSheafPairwiseIntersections.mp F.2 _).some.fac _ <|
Expand Down Expand Up @@ -409,10 +409,10 @@ def isLimitPullbackCone : IsLimit (interUnionPullbackCone F U V) := by
apply (F.presheaf.isSheaf_iff_isSheafPairwiseIntersections.mp F.2 ι).some.hom_ext
rintro ((_ | _) | (_ | _)) <;>
rw [Category.assoc, Category.assoc]
· erw [← F.1.map_comp]
· rw [Functor.mapCone_π_app, ← F.1.map_comp]
convert h₁
apply interUnionPullbackConeLift_left
· erw [← F.1.map_comp]
· rw [Functor.mapCone_π_app, ← F.1.map_comp]
convert h₂
apply interUnionPullbackConeLift_right
all_goals
Expand Down
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