algebraic_geometry.prime_spectrum.is_open_comap_C

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

052f6013

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

a87d2257

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 -/
-import Mathbin.AlgebraicGeometry.PrimeSpectrum.Basic
-import Mathbin.RingTheory.Polynomial.Basic
+import AlgebraicGeometry.PrimeSpectrum.Basic
+import RingTheory.Polynomial.Basic
 
 #align_import algebraic_geometry.prime_spectrum.is_open_comap_C from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"

a87d2257

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
-
-! This file was ported from Lean 3 source module algebraic_geometry.prime_spectrum.is_open_comap_C
-! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicGeometry.PrimeSpectrum.Basic
 import Mathbin.RingTheory.Polynomial.Basic
 
+#align_import algebraic_geometry.prime_spectrum.is_open_comap_C from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
+
 /-!
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
 > Any changes to this file require a corresponding PR to mathlib4.

a87d2257

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -51,6 +51,7 @@ theorem isOpen_imageOfDf : IsOpen (imageOfDf f) :=
 #align algebraic_geometry.polynomial.is_open_image_of_Df AlgebraicGeometry.Polynomial.isOpen_imageOfDf
 -/
 
+#print AlgebraicGeometry.Polynomial.comap_C_mem_imageOfDf /-
 /-- If a point of `Spec R[x]` is not contained in the vanishing set of `f`, then its image in
 `Spec R` is contained in the open set where at least one of the coefficients of `f` is non-zero.
 This lemma is a reformulation of `exists_C_coeff_not_mem`. -/
@@ -59,7 +60,9 @@ theorem comap_C_mem_imageOfDf {I : PrimeSpectrum R[X]}
     PrimeSpectrum.comap (Polynomial.C : R →+* R[X]) I ∈ imageOfDf f :=
   exists_C_coeff_not_mem (mem_compl_zeroLocus_iff_not_mem.mp H)
 #align algebraic_geometry.polynomial.comap_C_mem_image_of_Df AlgebraicGeometry.Polynomial.comap_C_mem_imageOfDf
+-/
 
+#print AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocus /-
 /-- The open set `image_of_Df f` coincides with the image of `basic_open f` under the
 morphism `C⁺ : Spec R[x] → Spec R`. -/
 theorem imageOfDf_eq_comap_C_compl_zeroLocus :
@@ -77,7 +80,9 @@ theorem imageOfDf_eq_comap_C_compl_zeroLocus :
   · rintro ⟨xli, complement, rfl⟩
     exact comap_C_mem_image_of_Df complement
 #align algebraic_geometry.polynomial.image_of_Df_eq_comap_C_compl_zero_locus AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocus
+-/
 
+#print AlgebraicGeometry.Polynomial.isOpenMap_comap_C /-
 /-- The morphism `C⁺ : Spec R[x] → Spec R` is open.
 Stacks Project "Lemma 00FB", first part.
 
@@ -90,6 +95,7 @@ theorem isOpenMap_comap_C : IsOpenMap (PrimeSpectrum.comap (C : R →+* R[X])) :
   simp_rw [← image_of_Df_eq_comap_C_compl_zero_locus]
   exact isOpen_iUnion fun f => is_open_image_of_Df
 #align algebraic_geometry.polynomial.is_open_map_comap_C AlgebraicGeometry.Polynomial.isOpenMap_comap_C
+-/
 
 end Polynomial

a87d2257

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -39,7 +39,7 @@ of the coefficients of `f` does not vanish.  Lemma `image_of_Df_eq_comap_C_compl
 proves that `image_of_Df` is the image of `(zero_locus {f})ᶜ` under the morphism
 `comap C : Spec R[x] → Spec R`. -/
 def imageOfDf (f) : Set (PrimeSpectrum R) :=
-  { p : PrimeSpectrum R | ∃ i : ℕ, coeff f i ∉ p.asIdeal }
+  {p : PrimeSpectrum R | ∃ i : ℕ, coeff f i ∉ p.asIdeal}
 #align algebraic_geometry.polynomial.image_of_Df AlgebraicGeometry.Polynomial.imageOfDf
 -/

a87d2257

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -25,7 +25,7 @@ https://stacks.math.columbia.edu/tag/00FB
 
 open Ideal Polynomial PrimeSpectrum Set
 
-open Polynomial
+open scoped Polynomial
 
 namespace AlgebraicGeometry

a87d2257

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -51,12 +51,6 @@ theorem isOpen_imageOfDf : IsOpen (imageOfDf f) :=
 #align algebraic_geometry.polynomial.is_open_image_of_Df AlgebraicGeometry.Polynomial.isOpen_imageOfDf
 -/
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.polynomial.comap_C_mem_image_of_Df AlgebraicGeometry.Polynomial.comap_C_mem_imageOfDfₓ'. -/
 /-- If a point of `Spec R[x]` is not contained in the vanishing set of `f`, then its image in
 `Spec R` is contained in the open set where at least one of the coefficients of `f` is non-zero.
 This lemma is a reformulation of `exists_C_coeff_not_mem`. -/
@@ -66,12 +60,6 @@ theorem comap_C_mem_imageOfDf {I : PrimeSpectrum R[X]}
   exists_C_coeff_not_mem (mem_compl_zeroLocus_iff_not_mem.mp H)
 #align algebraic_geometry.polynomial.comap_C_mem_image_of_Df AlgebraicGeometry.Polynomial.comap_C_mem_imageOfDf
 
-/- warning: algebraic_geometry.polynomial.image_of_Df_eq_comap_C_compl_zero_locus -> AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocus is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.polynomial.image_of_Df_eq_comap_C_compl_zero_locus AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocusₓ'. -/
 /-- The open set `image_of_Df f` coincides with the image of `basic_open f` under the
 morphism `C⁺ : Spec R[x] → Spec R`. -/
 theorem imageOfDf_eq_comap_C_compl_zeroLocus :
@@ -90,12 +78,6 @@ theorem imageOfDf_eq_comap_C_compl_zeroLocus :
     exact comap_C_mem_image_of_Df complement
 #align algebraic_geometry.polynomial.image_of_Df_eq_comap_C_compl_zero_locus AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocus
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.polynomial.is_open_map_comap_C AlgebraicGeometry.Polynomial.isOpenMap_comap_Cₓ'. -/
 /-- The morphism `C⁺ : Spec R[x] → Spec R` is open.
 Stacks Project "Lemma 00FB", first part.

a87d2257

bump to nightly-2023-05-28-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6c6011cf

Diff

@@ -90,24 +90,24 @@ theorem imageOfDf_eq_comap_C_compl_zeroLocus :
     exact comap_C_mem_image_of_Df complement
 #align algebraic_geometry.polynomial.image_of_Df_eq_comap_C_compl_zero_locus AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocus
 
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   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], IsOpenMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (fun (_x : ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) => (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) -> (PrimeSpectrum.{u1} R _inst_1)) (ContinuousMap.hasCoeToFun.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (PrimeSpectrum.comap.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _inst_1 (Polynomial.commRing.{u1} R _inst_1) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], IsOpenMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (fun (_x : PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) => PrimeSpectrum.{u1} R _inst_1) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1))) (PrimeSpectrum.comap.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.commRing.{u1} R _inst_1) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.polynomial.is_open_map_comap_C AlgebraicGeometry.Polynomial.isOpenMap_comap_cₓ'. -/
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.polynomial.is_open_map_comap_C AlgebraicGeometry.Polynomial.isOpenMap_comap_Cₓ'. -/
 /-- The morphism `C⁺ : Spec R[x] → Spec R` is open.
 Stacks Project "Lemma 00FB", first part.
 
 https://stacks.math.columbia.edu/tag/00FB
 -/
-theorem isOpenMap_comap_c : IsOpenMap (PrimeSpectrum.comap (C : R →+* R[X])) :=
+theorem isOpenMap_comap_C : IsOpenMap (PrimeSpectrum.comap (C : R →+* R[X])) :=
   by
   rintro U ⟨s, z⟩
   rw [← compl_compl U, ← z, ← Union_of_singleton_coe s, zero_locus_Union, compl_Inter, image_Union]
   simp_rw [← image_of_Df_eq_comap_C_compl_zero_locus]
   exact isOpen_iUnion fun f => is_open_image_of_Df
-#align algebraic_geometry.polynomial.is_open_map_comap_C AlgebraicGeometry.Polynomial.isOpenMap_comap_c
+#align algebraic_geometry.polynomial.is_open_map_comap_C AlgebraicGeometry.Polynomial.isOpenMap_comap_C
 
 end Polynomial

a87d2257

bump to nightly-2023-05-26-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c

d59ee359

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 
 ! This file was ported from Lean 3 source module algebraic_geometry.prime_spectrum.is_open_comap_C
-! leanprover-community/mathlib commit 052f6013363326d50cb99c6939814a4b8eb7b301
+! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -12,6 +12,9 @@ import Mathbin.AlgebraicGeometry.PrimeSpectrum.Basic
 import Mathbin.RingTheory.Polynomial.Basic
 
 /-!
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The morphism `Spec R[x] --> Spec R` induced by the natural inclusion `R --> R[x]` is an open map.
 
 The main result is the first part of the statement of Lemma 00FB in the Stacks Project.

052f6013

bump to nightly-2023-05-25-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

cab2c307

Diff

@@ -30,6 +30,7 @@ namespace Polynomial
 
 variable {R : Type _} [CommRing R] {f : R[X]}
 
+#print AlgebraicGeometry.Polynomial.imageOfDf /-
 /-- Given a polynomial `f ∈ R[x]`, `image_of_Df` is the subset of `Spec R` where at least one
 of the coefficients of `f` does not vanish.  Lemma `image_of_Df_eq_comap_C_compl_zero_locus`
 proves that `image_of_Df` is the image of `(zero_locus {f})ᶜ` under the morphism
@@ -37,25 +38,40 @@ proves that `image_of_Df` is the image of `(zero_locus {f})ᶜ` under the morphi
 def imageOfDf (f) : Set (PrimeSpectrum R) :=
   { p : PrimeSpectrum R | ∃ i : ℕ, coeff f i ∉ p.asIdeal }
 #align algebraic_geometry.polynomial.image_of_Df AlgebraicGeometry.Polynomial.imageOfDf
+-/
 
+#print AlgebraicGeometry.Polynomial.isOpen_imageOfDf /-
 theorem isOpen_imageOfDf : IsOpen (imageOfDf f) :=
   by
   rw [image_of_Df, set_of_exists fun i (x : PrimeSpectrum R) => coeff f i ∉ x.asIdeal]
   exact isOpen_iUnion fun i => is_open_basic_open
 #align algebraic_geometry.polynomial.is_open_image_of_Df AlgebraicGeometry.Polynomial.isOpen_imageOfDf
+-/
 
+/- warning: algebraic_geometry.polynomial.comap_C_mem_image_of_Df -> AlgebraicGeometry.Polynomial.comap_C_mem_imageOfDf is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {I : PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)}, (Membership.Mem.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Set.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))) (Set.hasMem.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))) I (HasCompl.compl.{u1} (Set.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))) (Set.booleanAlgebra.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)))) (PrimeSpectrum.zeroLocus.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1) (Singleton.singleton.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.hasSingleton.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) f)))) -> (Membership.Mem.{u1, u1} (PrimeSpectrum.{u1} R _inst_1) (Set.{u1} (PrimeSpectrum.{u1} R _inst_1)) (Set.hasMem.{u1} (PrimeSpectrum.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (fun (_x : ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) => (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) -> (PrimeSpectrum.{u1} R _inst_1)) (ContinuousMap.hasCoeToFun.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (PrimeSpectrum.comap.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _inst_1 (Polynomial.commRing.{u1} R _inst_1) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) I) (AlgebraicGeometry.Polynomial.imageOfDf.{u1} R _inst_1 f))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {I : PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)}, (Membership.mem.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Set.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))) (Set.instMembershipSet.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))) I (HasCompl.compl.{u1} (Set.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))) (Set.instBooleanAlgebraSet.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)))) (PrimeSpectrum.zeroLocus.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1) (Singleton.singleton.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Set.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Set.instSingletonSet.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) f)))) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) => PrimeSpectrum.{u1} R _inst_1) I) (Set.{u1} (PrimeSpectrum.{u1} R _inst_1)) (Set.instMembershipSet.{u1} (PrimeSpectrum.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (fun (_x : PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) => PrimeSpectrum.{u1} R _inst_1) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1))) (PrimeSpectrum.comap.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.commRing.{u1} R _inst_1) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) I) (AlgebraicGeometry.Polynomial.imageOfDf.{u1} R _inst_1 f))
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.polynomial.comap_C_mem_image_of_Df AlgebraicGeometry.Polynomial.comap_C_mem_imageOfDfₓ'. -/
 /-- If a point of `Spec R[x]` is not contained in the vanishing set of `f`, then its image in
 `Spec R` is contained in the open set where at least one of the coefficients of `f` is non-zero.
 This lemma is a reformulation of `exists_C_coeff_not_mem`. -/
-theorem comap_c_mem_imageOfDf {I : PrimeSpectrum R[X]}
+theorem comap_C_mem_imageOfDf {I : PrimeSpectrum R[X]}
     (H : I ∈ (zeroLocus {f} : Set (PrimeSpectrum R[X]))ᶜ) :
     PrimeSpectrum.comap (Polynomial.C : R →+* R[X]) I ∈ imageOfDf f :=
   exists_C_coeff_not_mem (mem_compl_zeroLocus_iff_not_mem.mp H)
-#align algebraic_geometry.polynomial.comap_C_mem_image_of_Df AlgebraicGeometry.Polynomial.comap_c_mem_imageOfDf
-
+#align algebraic_geometry.polynomial.comap_C_mem_image_of_Df AlgebraicGeometry.Polynomial.comap_C_mem_imageOfDf
+
+/- warning: algebraic_geometry.polynomial.image_of_Df_eq_comap_C_compl_zero_locus -> AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocus is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Eq.{succ u1} (Set.{u1} (PrimeSpectrum.{u1} R _inst_1)) (AlgebraicGeometry.Polynomial.imageOfDf.{u1} R _inst_1 f) (Set.image.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (fun (_x : ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) => (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) -> (PrimeSpectrum.{u1} R _inst_1)) (ContinuousMap.hasCoeToFun.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (PrimeSpectrum.comap.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _inst_1 (Polynomial.commRing.{u1} R _inst_1) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HasCompl.compl.{u1} (Set.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))) (Set.booleanAlgebra.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)))) (PrimeSpectrum.zeroLocus.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1) (Singleton.singleton.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.hasSingleton.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) f))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Eq.{succ u1} (Set.{u1} (PrimeSpectrum.{u1} R _inst_1)) (AlgebraicGeometry.Polynomial.imageOfDf.{u1} R _inst_1 f) (Set.image.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (fun (_x : PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) => PrimeSpectrum.{u1} R _inst_1) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1))) (PrimeSpectrum.comap.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.commRing.{u1} R _inst_1) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HasCompl.compl.{u1} (Set.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))) (Set.instBooleanAlgebraSet.{u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)))) (PrimeSpectrum.zeroLocus.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1) (Singleton.singleton.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Set.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Set.instSingletonSet.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) f))))
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.polynomial.image_of_Df_eq_comap_C_compl_zero_locus AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocusₓ'. -/
 /-- The open set `image_of_Df f` coincides with the image of `basic_open f` under the
 morphism `C⁺ : Spec R[x] → Spec R`. -/
-theorem imageOfDf_eq_comap_c_compl_zeroLocus :
+theorem imageOfDf_eq_comap_C_compl_zeroLocus :
     imageOfDf f = PrimeSpectrum.comap (C : R →+* R[X]) '' zeroLocus {f}ᶜ :=
   by
   ext x
@@ -69,8 +85,14 @@ theorem imageOfDf_eq_comap_c_compl_zeroLocus :
     exact mem_map_C_iff.mp h 0
   · rintro ⟨xli, complement, rfl⟩
     exact comap_C_mem_image_of_Df complement
-#align algebraic_geometry.polynomial.image_of_Df_eq_comap_C_compl_zero_locus AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_c_compl_zeroLocus
-
+#align algebraic_geometry.polynomial.image_of_Df_eq_comap_C_compl_zero_locus AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocus
+
+/- warning: algebraic_geometry.polynomial.is_open_map_comap_C -> AlgebraicGeometry.Polynomial.isOpenMap_comap_c is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], IsOpenMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (fun (_x : ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) => (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) -> (PrimeSpectrum.{u1} R _inst_1)) (ContinuousMap.hasCoeToFun.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (PrimeSpectrum.comap.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _inst_1 (Polynomial.commRing.{u1} R _inst_1) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], IsOpenMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (fun (_x : PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) => PrimeSpectrum.{u1} R _inst_1) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1)) (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1) (ContinuousMap.instContinuousMapClassContinuousMap.{u1, u1} (PrimeSpectrum.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.{u1} R _inst_1) (PrimeSpectrum.zariskiTopology.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (PrimeSpectrum.zariskiTopology.{u1} R _inst_1))) (PrimeSpectrum.comap.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.commRing.{u1} R _inst_1) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.polynomial.is_open_map_comap_C AlgebraicGeometry.Polynomial.isOpenMap_comap_cₓ'. -/
 /-- The morphism `C⁺ : Spec R[x] → Spec R` is open.
 Stacks Project "Lemma 00FB", first part.

052f6013

bump to nightly-2023-05-14-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

d31da313

Diff

@@ -41,7 +41,7 @@ def imageOfDf (f) : Set (PrimeSpectrum R) :=
 theorem isOpen_imageOfDf : IsOpen (imageOfDf f) :=
   by
   rw [image_of_Df, set_of_exists fun i (x : PrimeSpectrum R) => coeff f i ∉ x.asIdeal]
-  exact isOpen_unionᵢ fun i => is_open_basic_open
+  exact isOpen_iUnion fun i => is_open_basic_open
 #align algebraic_geometry.polynomial.is_open_image_of_Df AlgebraicGeometry.Polynomial.isOpen_imageOfDf
 
 /-- If a point of `Spec R[x]` is not contained in the vanishing set of `f`, then its image in
@@ -81,7 +81,7 @@ theorem isOpenMap_comap_c : IsOpenMap (PrimeSpectrum.comap (C : R →+* R[X])) :
   rintro U ⟨s, z⟩
   rw [← compl_compl U, ← z, ← Union_of_singleton_coe s, zero_locus_Union, compl_Inter, image_Union]
   simp_rw [← image_of_Df_eq_comap_C_compl_zero_locus]
-  exact isOpen_unionᵢ fun f => is_open_image_of_Df
+  exact isOpen_iUnion fun f => is_open_image_of_Df
 #align algebraic_geometry.polynomial.is_open_map_comap_C AlgebraicGeometry.Polynomial.isOpenMap_comap_c
 
 end Polynomial

052f6013

bump to nightly-2023-03-08-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

422cc012

Diff

@@ -49,14 +49,14 @@ theorem isOpen_imageOfDf : IsOpen (imageOfDf f) :=
 This lemma is a reformulation of `exists_C_coeff_not_mem`. -/
 theorem comap_c_mem_imageOfDf {I : PrimeSpectrum R[X]}
     (H : I ∈ (zeroLocus {f} : Set (PrimeSpectrum R[X]))ᶜ) :
-    PrimeSpectrum.comap (Polynomial.c : R →+* R[X]) I ∈ imageOfDf f :=
-  exists_c_coeff_not_mem (mem_compl_zeroLocus_iff_not_mem.mp H)
+    PrimeSpectrum.comap (Polynomial.C : R →+* R[X]) I ∈ imageOfDf f :=
+  exists_C_coeff_not_mem (mem_compl_zeroLocus_iff_not_mem.mp H)
 #align algebraic_geometry.polynomial.comap_C_mem_image_of_Df AlgebraicGeometry.Polynomial.comap_c_mem_imageOfDf
 
 /-- The open set `image_of_Df f` coincides with the image of `basic_open f` under the
 morphism `C⁺ : Spec R[x] → Spec R`. -/
 theorem imageOfDf_eq_comap_c_compl_zeroLocus :
-    imageOfDf f = PrimeSpectrum.comap (c : R →+* R[X]) '' zeroLocus {f}ᶜ :=
+    imageOfDf f = PrimeSpectrum.comap (C : R →+* R[X]) '' zeroLocus {f}ᶜ :=
   by
   ext x
   refine' ⟨fun hx => ⟨⟨map C x.as_ideal, is_prime_map_C_of_is_prime x.is_prime⟩, ⟨_, _⟩⟩, _⟩
@@ -76,7 +76,7 @@ Stacks Project "Lemma 00FB", first part.
 
 https://stacks.math.columbia.edu/tag/00FB
 -/
-theorem isOpenMap_comap_c : IsOpenMap (PrimeSpectrum.comap (c : R →+* R[X])) :=
+theorem isOpenMap_comap_c : IsOpenMap (PrimeSpectrum.comap (C : R →+* R[X])) :=
   by
   rintro U ⟨s, z⟩
   rw [← compl_compl U, ← z, ← Union_of_singleton_coe s, zero_locus_Union, compl_Inter, image_Union]

052f6013

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

052f6013

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -23,7 +23,7 @@ namespace AlgebraicGeometry
 
 namespace Polynomial
 
-variable {R : Type _} [CommRing R] {f : R[X]}
+variable {R : Type*} [CommRing R] {f : R[X]}
 
 set_option linter.uppercaseLean3 false

052f6013

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
-
-! This file was ported from Lean 3 source module algebraic_geometry.prime_spectrum.is_open_comap_C
-! leanprover-community/mathlib commit 052f6013363326d50cb99c6939814a4b8eb7b301
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic
 import Mathlib.RingTheory.Polynomial.Basic
 
+#align_import algebraic_geometry.prime_spectrum.is_open_comap_C from "leanprover-community/mathlib"@"052f6013363326d50cb99c6939814a4b8eb7b301"
+
 /-!
 The morphism `Spec R[x] --> Spec R` induced by the natural inclusion `R --> R[x]` is an open map.

052f6013

fix: change compl precedence (#5586)

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

4d4f0f25

Diff

@@ -55,7 +55,7 @@ theorem comap_C_mem_imageOfDf {I : PrimeSpectrum R[X]}
 /-- The open set `imageOfDf f` coincides with the image of `basicOpen f` under the
 morphism `C⁺ : Spec R[x] → Spec R`. -/
 theorem imageOfDf_eq_comap_C_compl_zeroLocus :
-    imageOfDf f = PrimeSpectrum.comap (C : R →+* R[X]) '' zeroLocus {f}ᶜ := by
+    imageOfDf f = PrimeSpectrum.comap (C : R →+* R[X]) '' (zeroLocus {f})ᶜ := by
   ext x
   refine' ⟨fun hx => ⟨⟨map C x.asIdeal, isPrime_map_C_of_isPrime x.IsPrime⟩, ⟨_, _⟩⟩, _⟩
   · rw [mem_compl_iff, mem_zeroLocus, singleton_subset_iff]

052f6013

chore: tidy various files (#4423)

9f94180e

Diff

@@ -22,8 +22,6 @@ https://stacks.math.columbia.edu/tag/00FB
 
 open Ideal Polynomial PrimeSpectrum Set
 
-open Polynomial
-
 namespace AlgebraicGeometry
 
 namespace Polynomial
@@ -76,13 +74,13 @@ Stacks Project "Lemma 00FB", first part.
 
 https://stacks.math.columbia.edu/tag/00FB
 -/
-theorem isOpenMap_comap_c : IsOpenMap (PrimeSpectrum.comap (C : R →+* R[X])) := by
+theorem isOpenMap_comap_C : IsOpenMap (PrimeSpectrum.comap (C : R →+* R[X])) := by
   rintro U ⟨s, z⟩
   rw [← compl_compl U, ← z, ← iUnion_of_singleton_coe s, zeroLocus_iUnion, compl_iInter,
     image_iUnion]
   simp_rw [← imageOfDf_eq_comap_C_compl_zeroLocus]
   exact isOpen_iUnion fun f => isOpen_imageOfDf
-#align algebraic_geometry.polynomial.is_open_map_comap_C AlgebraicGeometry.Polynomial.isOpenMap_comap_c
+#align algebraic_geometry.polynomial.is_open_map_comap_C AlgebraicGeometry.Polynomial.isOpenMap_comap_C
 
 end Polynomial

052f6013

feat: port AlgebraicGeometry.PrimeSpectrum.IsOpenComapC (#4302)

52d71ad9

`algebraic_geometry.prime_spectrum.is_open_comap_C` ⟷ `Mathlib.AlgebraicGeometry.PrimeSpectrum.IsOpenComapC`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11 + 676

algebraic_geometry.prime_spectrum.is_open_comap_C ⟷ Mathlib.AlgebraicGeometry.PrimeSpectrum.IsOpenComapC

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11 + 676

`algebraic_geometry.prime_spectrum.is_open_comap_C` ⟷ `Mathlib.AlgebraicGeometry.PrimeSpectrum.IsOpenComapC`