ring_theory.ideal.idempotent_fgMathlib.RingTheory.Ideal.IdempotentFG

This file has been ported!

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.

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -27,7 +27,7 @@ theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h :
   · intro e
     obtain ⟨r, hr, hr'⟩ :=
       Submodule.exists_mem_and_smul_eq_self_of_fg_of_le_smul I I h (by rw [smul_eq_mul]; exact e.ge)
-    simp_rw [smul_eq_mul] at hr' 
+    simp_rw [smul_eq_mul] at hr'
     refine' ⟨r, hr' r hr, antisymm _ ((Submodule.span_singleton_le_iff_mem _ _).mpr hr)⟩
     intro x hx
     rw [← hr' x hx]
Diff
@@ -3,8 +3,8 @@ Copyright (c) 2018 Mario Carneiro, Kevin Buzzard. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Kevin Buzzard
 -/
-import Mathbin.Algebra.Ring.Idempotents
-import Mathbin.RingTheory.Finiteness
+import Algebra.Ring.Idempotents
+import RingTheory.Finiteness
 
 #align_import ring_theory.ideal.idempotent_fg from "leanprover-community/mathlib"@"290a7ba01fbcab1b64757bdaa270d28f4dcede35"
 
Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2018 Mario Carneiro, Kevin Buzzard. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Kevin Buzzard
-
-! This file was ported from Lean 3 source module ring_theory.ideal.idempotent_fg
-! leanprover-community/mathlib commit 290a7ba01fbcab1b64757bdaa270d28f4dcede35
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Ring.Idempotents
 import Mathbin.RingTheory.Finiteness
 
+#align_import ring_theory.ideal.idempotent_fg from "leanprover-community/mathlib"@"290a7ba01fbcab1b64757bdaa270d28f4dcede35"
+
 /-!
 ## Lemmas on idempotent finitely generated ideals
 
Diff
@@ -21,6 +21,7 @@ import Mathbin.RingTheory.Finiteness
 
 namespace Ideal
 
+#print Ideal.isIdempotentElem_iff_of_fg /-
 /-- A finitely generated idempotent ideal is generated by an idempotent element -/
 theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h : I.FG) :
     IsIdempotentElem I ↔ ∃ e : R, IsIdempotentElem e ∧ I = R ∙ e :=
@@ -37,7 +38,9 @@ theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h :
   · rintro ⟨e, he, rfl⟩
     simp [IsIdempotentElem, Ideal.span_singleton_mul_span_singleton, he.eq]
 #align ideal.is_idempotent_elem_iff_of_fg Ideal.isIdempotentElem_iff_of_fg
+-/
 
+#print Ideal.isIdempotentElem_iff_eq_bot_or_top /-
 theorem isIdempotentElem_iff_eq_bot_or_top {R : Type _} [CommRing R] [IsDomain R] (I : Ideal R)
     (h : I.FG) : IsIdempotentElem I ↔ I = ⊥ ∨ I = ⊤ :=
   by
@@ -50,6 +53,7 @@ theorem isIdempotentElem_iff_eq_bot_or_top {R : Type _} [CommRing R] [IsDomain R
     simp
   · rintro (rfl | rfl) <;> simp [IsIdempotentElem]
 #align ideal.is_idempotent_elem_iff_eq_bot_or_top Ideal.isIdempotentElem_iff_eq_bot_or_top
+-/
 
 end Ideal
 
Diff
@@ -29,7 +29,7 @@ theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h :
   · intro e
     obtain ⟨r, hr, hr'⟩ :=
       Submodule.exists_mem_and_smul_eq_self_of_fg_of_le_smul I I h (by rw [smul_eq_mul]; exact e.ge)
-    simp_rw [smul_eq_mul] at hr'
+    simp_rw [smul_eq_mul] at hr' 
     refine' ⟨r, hr' r hr, antisymm _ ((Submodule.span_singleton_le_iff_mem _ _).mpr hr)⟩
     intro x hx
     rw [← hr' x hx]
Diff
@@ -21,12 +21,6 @@ import Mathbin.RingTheory.Finiteness
 
 namespace Ideal
 
-/- warning: ideal.is_idempotent_elem_iff_of_fg -> Ideal.isIdempotentElem_iff_of_fg is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.FG.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasMul.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Exists.{succ u1} R (fun (e : R) => And (IsIdempotentElem.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) e) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Submodule.span.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.hasSingleton.{u1} R) e))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ideal.FG.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instMulIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Exists.{succ u1} R (fun (e : R) => And (IsIdempotentElem.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) e) (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) I (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.instSingletonSet.{u1} R) e))))))
-Case conversion may be inaccurate. Consider using '#align ideal.is_idempotent_elem_iff_of_fg Ideal.isIdempotentElem_iff_of_fgₓ'. -/
 /-- A finitely generated idempotent ideal is generated by an idempotent element -/
 theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h : I.FG) :
     IsIdempotentElem I ↔ ∃ e : R, IsIdempotentElem e ∧ I = R ∙ e :=
@@ -44,12 +38,6 @@ theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h :
     simp [IsIdempotentElem, Ideal.span_singleton_mul_span_singleton, he.eq]
 #align ideal.is_idempotent_elem_iff_of_fg Ideal.isIdempotentElem_iff_of_fg
 
-/- warning: ideal.is_idempotent_elem_iff_eq_bot_or_top -> Ideal.isIdempotentElem_iff_eq_bot_or_top is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.FG.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasMul.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Or (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{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] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ideal.FG.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instMulIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Or (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) I (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) I (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))
-Case conversion may be inaccurate. Consider using '#align ideal.is_idempotent_elem_iff_eq_bot_or_top Ideal.isIdempotentElem_iff_eq_bot_or_topₓ'. -/
 theorem isIdempotentElem_iff_eq_bot_or_top {R : Type _} [CommRing R] [IsDomain R] (I : Ideal R)
     (h : I.FG) : IsIdempotentElem I ↔ I = ⊥ ∨ I = ⊤ :=
   by
Diff
@@ -34,10 +34,7 @@ theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h :
   constructor
   · intro e
     obtain ⟨r, hr, hr'⟩ :=
-      Submodule.exists_mem_and_smul_eq_self_of_fg_of_le_smul I I h
-        (by
-          rw [smul_eq_mul]
-          exact e.ge)
+      Submodule.exists_mem_and_smul_eq_self_of_fg_of_le_smul I I h (by rw [smul_eq_mul]; exact e.ge)
     simp_rw [smul_eq_mul] at hr'
     refine' ⟨r, hr' r hr, antisymm _ ((Submodule.span_singleton_le_iff_mem _ _).mpr hr)⟩
     intro x hx
Diff
@@ -23,12 +23,12 @@ namespace Ideal
 
 /- warning: ideal.is_idempotent_elem_iff_of_fg -> Ideal.isIdempotentElem_iff_of_fg is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.Fg.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasMul.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Exists.{succ u1} R (fun (e : R) => And (IsIdempotentElem.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) e) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Submodule.span.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.hasSingleton.{u1} R) e))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.FG.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasMul.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Exists.{succ u1} R (fun (e : R) => And (IsIdempotentElem.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) e) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Submodule.span.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.hasSingleton.{u1} R) e))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ideal.Fg.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instMulIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Exists.{succ u1} R (fun (e : R) => And (IsIdempotentElem.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) e) (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) I (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.instSingletonSet.{u1} R) e))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ideal.FG.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instMulIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Exists.{succ u1} R (fun (e : R) => And (IsIdempotentElem.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) e) (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) I (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.instSingletonSet.{u1} R) e))))))
 Case conversion may be inaccurate. Consider using '#align ideal.is_idempotent_elem_iff_of_fg Ideal.isIdempotentElem_iff_of_fgₓ'. -/
 /-- A finitely generated idempotent ideal is generated by an idempotent element -/
-theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h : I.Fg) :
+theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h : I.FG) :
     IsIdempotentElem I ↔ ∃ e : R, IsIdempotentElem e ∧ I = R ∙ e :=
   by
   constructor
@@ -49,12 +49,12 @@ theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h :
 
 /- warning: ideal.is_idempotent_elem_iff_eq_bot_or_top -> Ideal.isIdempotentElem_iff_eq_bot_or_top is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.Fg.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasMul.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Or (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.FG.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasMul.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Or (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{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] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ideal.Fg.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instMulIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Or (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) I (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) I (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ideal.FG.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instMulIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Or (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) I (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) I (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align ideal.is_idempotent_elem_iff_eq_bot_or_top Ideal.isIdempotentElem_iff_eq_bot_or_topₓ'. -/
 theorem isIdempotentElem_iff_eq_bot_or_top {R : Type _} [CommRing R] [IsDomain R] (I : Ideal R)
-    (h : I.Fg) : IsIdempotentElem I ↔ I = ⊥ ∨ I = ⊤ :=
+    (h : I.FG) : IsIdempotentElem I ↔ I = ⊥ ∨ I = ⊤ :=
   by
   constructor
   · intro H
Diff
@@ -25,7 +25,7 @@ namespace Ideal
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.Fg.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasMul.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Exists.{succ u1} R (fun (e : R) => And (IsIdempotentElem.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) e) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Submodule.span.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.hasSingleton.{u1} R) e))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.Fg.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instMulIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Exists.{succ u1} R (fun (e : R) => And (IsIdempotentElem.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) e) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Submodule.span.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.instSingletonSet.{u1} R) e))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ideal.Fg.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instMulIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Exists.{succ u1} R (fun (e : R) => And (IsIdempotentElem.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) e) (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) I (Submodule.span.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.instSingletonSet.{u1} R) e))))))
 Case conversion may be inaccurate. Consider using '#align ideal.is_idempotent_elem_iff_of_fg Ideal.isIdempotentElem_iff_of_fgₓ'. -/
 /-- A finitely generated idempotent ideal is generated by an idempotent element -/
 theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h : I.Fg) :
@@ -51,7 +51,7 @@ theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.Fg.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasMul.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Or (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{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] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.Fg.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instMulIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Or (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.instBotSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ideal.Fg.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instMulIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Or (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) I (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) I (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align ideal.is_idempotent_elem_iff_eq_bot_or_top Ideal.isIdempotentElem_iff_eq_bot_or_topₓ'. -/
 theorem isIdempotentElem_iff_eq_bot_or_top {R : Type _} [CommRing R] [IsDomain R] (I : Ideal R)
     (h : I.Fg) : IsIdempotentElem I ↔ I = ⊥ ∨ I = ⊤ :=
Diff
@@ -25,7 +25,7 @@ namespace Ideal
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.Fg.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasMul.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Exists.{succ u1} R (fun (e : R) => And (IsIdempotentElem.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) e) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Submodule.span.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.hasSingleton.{u1} R) e))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.Fg.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instMulIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Exists.{succ u1} R (fun (e : R) => And (IsIdempotentElem.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) e) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Submodule.span.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_1 (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.instSingletonSet.{u1} R) e))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.Fg.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instMulIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Exists.{succ u1} R (fun (e : R) => And (IsIdempotentElem.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) e) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Submodule.span.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.instSingletonSet.{u1} R) e))))))
 Case conversion may be inaccurate. Consider using '#align ideal.is_idempotent_elem_iff_of_fg Ideal.isIdempotentElem_iff_of_fgₓ'. -/
 /-- A finitely generated idempotent ideal is generated by an idempotent element -/
 theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h : I.Fg) :
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Kevin Buzzard
 
 ! This file was ported from Lean 3 source module ring_theory.ideal.idempotent_fg
-! leanprover-community/mathlib commit 25cf7631da8ddc2d5f957c388bf5e4b25a77d8dc
+! leanprover-community/mathlib commit 290a7ba01fbcab1b64757bdaa270d28f4dcede35
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.RingTheory.Finiteness
 
 /-!
 ## Lemmas on idempotent finitely generated ideals
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 -/
 
 
Diff
@@ -18,6 +18,12 @@ import Mathbin.RingTheory.Finiteness
 
 namespace Ideal
 
+/- warning: ideal.is_idempotent_elem_iff_of_fg -> Ideal.isIdempotentElem_iff_of_fg is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.Fg.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasMul.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Exists.{succ u1} R (fun (e : R) => And (IsIdempotentElem.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) e) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Submodule.span.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.hasSingleton.{u1} R) e))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.Fg.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instMulIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Exists.{succ u1} R (fun (e : R) => And (IsIdempotentElem.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) e) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Submodule.span.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_1 (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.instSingletonSet.{u1} R) e))))))
+Case conversion may be inaccurate. Consider using '#align ideal.is_idempotent_elem_iff_of_fg Ideal.isIdempotentElem_iff_of_fgₓ'. -/
 /-- A finitely generated idempotent ideal is generated by an idempotent element -/
 theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h : I.Fg) :
     IsIdempotentElem I ↔ ∃ e : R, IsIdempotentElem e ∧ I = R ∙ e :=
@@ -38,6 +44,12 @@ theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h :
     simp [IsIdempotentElem, Ideal.span_singleton_mul_span_singleton, he.eq]
 #align ideal.is_idempotent_elem_iff_of_fg Ideal.isIdempotentElem_iff_of_fg
 
+/- warning: ideal.is_idempotent_elem_iff_eq_bot_or_top -> Ideal.isIdempotentElem_iff_eq_bot_or_top is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.Fg.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasMul.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Or (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{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] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ideal.Fg.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I) -> (Iff (IsIdempotentElem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instMulIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) I) (Or (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.instBotSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))
+Case conversion may be inaccurate. Consider using '#align ideal.is_idempotent_elem_iff_eq_bot_or_top Ideal.isIdempotentElem_iff_eq_bot_or_topₓ'. -/
 theorem isIdempotentElem_iff_eq_bot_or_top {R : Type _} [CommRing R] [IsDomain R] (I : Ideal R)
     (h : I.Fg) : IsIdempotentElem I ↔ I = ⊥ ∨ I = ⊤ :=
   by

Changes in mathlib4

mathlib3
mathlib4
chore: reduce imports (#9830)

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

Diff
@@ -5,6 +5,7 @@ Authors: Mario Carneiro, Kevin Buzzard
 -/
 import Mathlib.Algebra.Ring.Idempotents
 import Mathlib.RingTheory.Finiteness
+import Mathlib.Order.Basic
 
 #align_import ring_theory.ideal.idempotent_fg from "leanprover-community/mathlib"@"25cf7631da8ddc2d5f957c388bf5e4b25a77d8dc"
 
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.

Diff
@@ -16,7 +16,7 @@ import Mathlib.RingTheory.Finiteness
 namespace Ideal
 
 /-- A finitely generated idempotent ideal is generated by an idempotent element -/
-theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h : I.FG) :
+theorem isIdempotentElem_iff_of_fg {R : Type*} [CommRing R] (I : Ideal R) (h : I.FG) :
     IsIdempotentElem I ↔ ∃ e : R, IsIdempotentElem e ∧ I = R ∙ e := by
   constructor
   · intro e
@@ -34,7 +34,7 @@ theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h :
     simp [IsIdempotentElem, Ideal.span_singleton_mul_span_singleton, he.eq]
 #align ideal.is_idempotent_elem_iff_of_fg Ideal.isIdempotentElem_iff_of_fg
 
-theorem isIdempotentElem_iff_eq_bot_or_top {R : Type _} [CommRing R] [IsDomain R] (I : Ideal R)
+theorem isIdempotentElem_iff_eq_bot_or_top {R : Type*} [CommRing R] [IsDomain R] (I : Ideal R)
     (h : I.FG) : IsIdempotentElem I ↔ I = ⊥ ∨ I = ⊤ := by
   constructor
   · intro H
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

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

Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2018 Mario Carneiro, Kevin Buzzard. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Kevin Buzzard
-
-! This file was ported from Lean 3 source module ring_theory.ideal.idempotent_fg
-! leanprover-community/mathlib commit 25cf7631da8ddc2d5f957c388bf5e4b25a77d8dc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Ring.Idempotents
 import Mathlib.RingTheory.Finiteness
 
+#align_import ring_theory.ideal.idempotent_fg from "leanprover-community/mathlib"@"25cf7631da8ddc2d5f957c388bf5e4b25a77d8dc"
+
 /-!
 ## Lemmas on idempotent finitely generated ideals
 -/
chore: reenable eta, bump to nightly 2023-05-16 (#3414)

Now that leanprover/lean4#2210 has been merged, this PR:

  • removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
  • removes many but not quite all set_option maxHeartbeats commands
  • makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

Diff
@@ -18,7 +18,6 @@ import Mathlib.RingTheory.Finiteness
 
 namespace Ideal
 
-set_option synthInstance.etaExperiment true in
 /-- A finitely generated idempotent ideal is generated by an idempotent element -/
 theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h : I.FG) :
     IsIdempotentElem I ↔ ∃ e : R, IsIdempotentElem e ∧ I = R ∙ e := by
Diff
@@ -20,7 +20,7 @@ namespace Ideal
 
 set_option synthInstance.etaExperiment true in
 /-- A finitely generated idempotent ideal is generated by an idempotent element -/
-theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h : I.Fg) :
+theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h : I.FG) :
     IsIdempotentElem I ↔ ∃ e : R, IsIdempotentElem e ∧ I = R ∙ e := by
   constructor
   · intro e
@@ -39,7 +39,7 @@ theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h :
 #align ideal.is_idempotent_elem_iff_of_fg Ideal.isIdempotentElem_iff_of_fg
 
 theorem isIdempotentElem_iff_eq_bot_or_top {R : Type _} [CommRing R] [IsDomain R] (I : Ideal R)
-    (h : I.Fg) : IsIdempotentElem I ↔ I = ⊥ ∨ I = ⊤ := by
+    (h : I.FG) : IsIdempotentElem I ↔ I = ⊥ ∨ I = ⊤ := by
   constructor
   · intro H
     obtain ⟨e, he, rfl⟩ := (I.isIdempotentElem_iff_of_fg h).mp H
chore: use etaExperiment rather than hacking with instances (#3668)

This is to fix timeouts in https://github.com/leanprover-community/mathlib4/pull/3552.

See discussion at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/!4.233552.20.28LinearAlgebra.2EMatrix.2EToLin.29.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

Diff
@@ -18,6 +18,7 @@ import Mathlib.RingTheory.Finiteness
 
 namespace Ideal
 
+set_option synthInstance.etaExperiment true in
 /-- A finitely generated idempotent ideal is generated by an idempotent element -/
 theorem isIdempotentElem_iff_of_fg {R : Type _} [CommRing R] (I : Ideal R) (h : I.Fg) :
     IsIdempotentElem I ↔ ∃ e : R, IsIdempotentElem e ∧ I = R ∙ e := by
feat: port RingTheory.Ideal.IdempotentFg (#2980)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

Dependencies 8 + 461

462 files ported (98.3%)
190006 lines ported (98.4%)
Show graph

The unported dependencies are