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chore(AlgebraicGeometry/Restrict): restore two lemmas that were deleted by toolchain bump (leanprover-community#40189)
These two lemmas were originally added in leanprover-community#39442. Then the toolchain bump leanprover-community#39980 mysteriously deleted them two days later without replacement.
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Mathlib/AlgebraicGeometry/Restrict.lean

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@@ -652,6 +652,20 @@ theorem morphismRestrict_appLE {X Y : Scheme.{u}} (f : X ⟶ Y) (U : Y.Opens) (V
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rw [Scheme.Hom.appLE, morphismRestrict_app', Scheme.Opens.toScheme_presheaf_map,
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Scheme.Hom.appLE_map]
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@[reassoc]
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theorem morphismRestrict_homOfLE_isoImage_ι_hom
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{X : Scheme.{u}} {U V : X.Opens} (e : U ≤ V) (W : Opens V) :
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X.homOfLE e ∣_ W ≫ (V.ι.isoImage W).hom =
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(U.ι.isoImage (X.homOfLE e ⁻¹ᵁ W)).hom ≫ X.homOfLE (X.ι_image_homOfLE_le_ι_image e W) := by
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simp [← cancel_mono (V.ι ''ᵁ W).ι]
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@[reassoc]
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theorem isoImage_ι_inv_morphismRestrict_homOfLE {X : Scheme.{u}} {U V : X.Opens}
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(e : U ≤ V) (W : Opens V) :
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(U.ι.isoImage (X.homOfLE e ⁻¹ᵁ W)).inv ≫ X.homOfLE e ∣_ W =
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X.homOfLE (X.ι_image_homOfLE_le_ι_image e W) ≫ (V.ι.isoImage W).inv := by
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simp [← cancel_mono (V.ι.isoImage W).hom, morphismRestrict_homOfLE_isoImage_ι_hom]
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set_option backward.defeqAttrib.useBackward true in
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set_option backward.isDefEq.respectTransparency false in
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/-- Restricting a morphism onto the image of an open immersion is isomorphic to the base change

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