leanprover-community / mathlib4

The math library of Lean 4

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Porting note: change `rw` to `erw`

pitmonticone opened this issue · comments

Classifies porting notes claiming:

change rw to erw

Examples

/-- The first projection from the glued scheme into `X`. -/
def p1 : (gluing 𝒰 f g).glued ⟶ X := by
fapply Multicoequalizer.desc
exact fun i => pullback.fst ≫ 𝒰.map i
rintro ⟨i, j⟩
change pullback.fst ≫ _ ≫ 𝒰.map i = (_ ≫ _) ≫ _ ≫ 𝒰.map j
-- Porting note: change `rw` to `erw`
erw [pullback.condition]
rw [← Category.assoc]
congr 1
rw [Category.assoc]
exact (t_fst_fst _ _ _ _ _).symm
#align algebraic_geometry.Scheme.pullback.p1 AlgebraicGeometry.Scheme.Pullback.p1

theorem imageBasicOpen_image_open :
IsOpen ((coequalizer.π f.1 g.1).base '' (imageBasicOpen f g U s).1) := by
rw [← (TopCat.homeoOfIso (PreservesCoequalizer.iso (SheafedSpace.forget _) f.1
g.1)).isOpen_preimage, TopCat.coequalizer_isOpen_iff, ← Set.preimage_comp]
erw [← coe_comp]
rw [PreservesCoequalizer.iso_hom, ι_comp_coequalizerComparison]
dsimp only [SheafedSpace.forget]
-- Porting note: change `rw` to `erw`
erw [imageBasicOpen_image_preimage]
exact (imageBasicOpen f g U s).2
#align algebraic_geometry.LocallyRingedSpace.has_coequalizer.image_basic_open_image_open AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.imageBasicOpen_image_open