algebra.algebraic_card | Mathlib porting status

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

40494fe7

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

38df578a

bump to nightly-2024-04-07-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

b03b8656

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Violeta Hernández Palacios
 -/
-import Data.Polynomial.Cardinal
+import Algebra.Polynomial.Cardinal
 import RingTheory.Algebraic
 
 #align_import algebra.algebraic_card from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"

38df578a

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) 2022 Violeta Hernández Palacios. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Violeta Hernández Palacios
 -/
-import Mathbin.Data.Polynomial.Cardinal
-import Mathbin.RingTheory.Algebraic
+import Data.Polynomial.Cardinal
+import RingTheory.Algebraic
 
 #align_import algebra.algebraic_card from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"

38df578a

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) 2022 Violeta Hernández Palacios. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Violeta Hernández Palacios
-
-! This file was ported from Lean 3 source module algebra.algebraic_card
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Polynomial.Cardinal
 import Mathbin.RingTheory.Algebraic
 
+#align_import algebra.algebraic_card from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
 /-!
 ### Cardinality of algebraic numbers

38df578a

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -33,21 +33,26 @@ open scoped Cardinal Polynomial
 
 namespace Algebraic
 
+#print Algebraic.infinite_of_charZero /-
 theorem infinite_of_charZero (R A : Type _) [CommRing R] [IsDomain R] [Ring A] [Algebra R A]
     [CharZero A] : {x : A | IsAlgebraic R x}.Infinite :=
   infinite_of_injective_forall_mem Nat.cast_injective isAlgebraic_nat
 #align algebraic.infinite_of_char_zero Algebraic.infinite_of_charZero
+-/
 
+#print Algebraic.aleph0_le_cardinal_mk_of_charZero /-
 theorem aleph0_le_cardinal_mk_of_charZero (R A : Type _) [CommRing R] [IsDomain R] [Ring A]
     [Algebra R A] [CharZero A] : ℵ₀ ≤ (#{ x : A // IsAlgebraic R x }) :=
   infinite_iff.1 (Set.infinite_coe_iff.2 <| infinite_of_charZero R A)
 #align algebraic.aleph_0_le_cardinal_mk_of_char_zero Algebraic.aleph0_le_cardinal_mk_of_charZero
+-/
 
 section lift
 
 variable (R : Type u) (A : Type v) [CommRing R] [CommRing A] [IsDomain A] [Algebra R A]
   [NoZeroSMulDivisors R A]
 
+#print Algebraic.cardinal_mk_lift_le_mul /-
 theorem cardinal_mk_lift_le_mul :
     Cardinal.lift.{u} (#{ x : A // IsAlgebraic R x }) ≤ Cardinal.lift.{v} (#R[X]) * ℵ₀ :=
   by
@@ -60,13 +65,17 @@ theorem cardinal_mk_lift_le_mul :
   rintro x (rfl : g x = f)
   exact mem_root_set.2 ⟨hg₁ x, hg₂ x⟩
 #align algebraic.cardinal_mk_lift_le_mul Algebraic.cardinal_mk_lift_le_mul
+-/
 
+#print Algebraic.cardinal_mk_lift_le_max /-
 theorem cardinal_mk_lift_le_max :
     Cardinal.lift.{u} (#{ x : A // IsAlgebraic R x }) ≤ max (Cardinal.lift.{v} (#R)) ℵ₀ :=
   (cardinal_mk_lift_le_mul R A).trans <|
     (mul_le_mul_right' (lift_le.2 cardinal_mk_le_max) _).trans <| by simp
 #align algebraic.cardinal_mk_lift_le_max Algebraic.cardinal_mk_lift_le_max
+-/
 
+#print Algebraic.cardinal_mk_lift_of_infinite /-
 @[simp]
 theorem cardinal_mk_lift_of_infinite [Infinite R] :
     Cardinal.lift.{u} (#{ x : A // IsAlgebraic R x }) = Cardinal.lift.{v} (#R) :=
@@ -75,9 +84,11 @@ theorem cardinal_mk_lift_of_infinite [Infinite R] :
       ⟨⟨fun x => ⟨algebraMap R A x, isAlgebraic_algebraMap _⟩, fun x y h =>
           NoZeroSMulDivisors.algebraMap_injective R A (Subtype.ext_iff.1 h)⟩⟩
 #align algebraic.cardinal_mk_lift_of_infinite Algebraic.cardinal_mk_lift_of_infinite
+-/
 
 variable [Countable R]
 
+#print Algebraic.countable /-
 @[simp]
 protected theorem countable : Set.Countable {x : A | IsAlgebraic R x} :=
   by
@@ -85,12 +96,15 @@ protected theorem countable : Set.Countable {x : A | IsAlgebraic R x} :=
   apply (cardinal_mk_lift_le_max R A).trans
   simp
 #align algebraic.countable Algebraic.countable
+-/
 
+#print Algebraic.cardinal_mk_of_countable_of_charZero /-
 @[simp]
 theorem cardinal_mk_of_countable_of_charZero [CharZero A] [IsDomain R] :
     (#{ x : A // IsAlgebraic R x }) = ℵ₀ :=
   (Algebraic.countable R A).le_aleph0.antisymm (aleph0_le_cardinal_mk_of_charZero R A)
 #align algebraic.cardinal_mk_of_countble_of_char_zero Algebraic.cardinal_mk_of_countable_of_charZero
+-/
 
 end lift
 
@@ -99,18 +113,24 @@ section NonLift
 variable (R A : Type u) [CommRing R] [CommRing A] [IsDomain A] [Algebra R A]
   [NoZeroSMulDivisors R A]
 
+#print Algebraic.cardinal_mk_le_mul /-
 theorem cardinal_mk_le_mul : (#{ x : A // IsAlgebraic R x }) ≤ (#R[X]) * ℵ₀ := by
   rw [← lift_id (#_), ← lift_id (#R[X])]; exact cardinal_mk_lift_le_mul R A
 #align algebraic.cardinal_mk_le_mul Algebraic.cardinal_mk_le_mul
+-/
 
+#print Algebraic.cardinal_mk_le_max /-
 theorem cardinal_mk_le_max : (#{ x : A // IsAlgebraic R x }) ≤ max (#R) ℵ₀ := by
   rw [← lift_id (#_), ← lift_id (#R)]; exact cardinal_mk_lift_le_max R A
 #align algebraic.cardinal_mk_le_max Algebraic.cardinal_mk_le_max
+-/
 
+#print Algebraic.cardinal_mk_of_infinite /-
 @[simp]
 theorem cardinal_mk_of_infinite [Infinite R] : (#{ x : A // IsAlgebraic R x }) = (#R) :=
   lift_inj.1 <| cardinal_mk_lift_of_infinite R A
 #align algebraic.cardinal_mk_of_infinite Algebraic.cardinal_mk_of_infinite
+-/
 
 end NonLift

38df578a

bump to nightly-2023-06-08-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

d3cfe2e3

Diff

@@ -87,10 +87,10 @@ protected theorem countable : Set.Countable {x : A | IsAlgebraic R x} :=
 #align algebraic.countable Algebraic.countable
 
 @[simp]
-theorem cardinal_mk_of_countble_of_charZero [CharZero A] [IsDomain R] :
+theorem cardinal_mk_of_countable_of_charZero [CharZero A] [IsDomain R] :
     (#{ x : A // IsAlgebraic R x }) = ℵ₀ :=
   (Algebraic.countable R A).le_aleph0.antisymm (aleph0_le_cardinal_mk_of_charZero R A)
-#align algebraic.cardinal_mk_of_countble_of_char_zero Algebraic.cardinal_mk_of_countble_of_charZero
+#align algebraic.cardinal_mk_of_countble_of_char_zero Algebraic.cardinal_mk_of_countable_of_charZero
 
 end lift

38df578a

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -34,7 +34,7 @@ open scoped Cardinal Polynomial
 namespace Algebraic
 
 theorem infinite_of_charZero (R A : Type _) [CommRing R] [IsDomain R] [Ring A] [Algebra R A]
-    [CharZero A] : { x : A | IsAlgebraic R x }.Infinite :=
+    [CharZero A] : {x : A | IsAlgebraic R x}.Infinite :=
   infinite_of_injective_forall_mem Nat.cast_injective isAlgebraic_nat
 #align algebraic.infinite_of_char_zero Algebraic.infinite_of_charZero
 
@@ -52,7 +52,7 @@ theorem cardinal_mk_lift_le_mul :
     Cardinal.lift.{u} (#{ x : A // IsAlgebraic R x }) ≤ Cardinal.lift.{v} (#R[X]) * ℵ₀ :=
   by
   rw [← mk_ulift, ← mk_ulift]
-  choose g hg₁ hg₂ using fun x : { x : A | IsAlgebraic R x } => x.coe_prop
+  choose g hg₁ hg₂ using fun x : {x : A | IsAlgebraic R x} => x.coe_prop
   refine' lift_mk_le_lift_mk_mul_of_lift_mk_preimage_le g fun f => _
   rw [lift_le_aleph_0, le_aleph_0_iff_set_countable]
   suffices : maps_to coe (g ⁻¹' {f}) (f.root_set A)
@@ -79,7 +79,7 @@ theorem cardinal_mk_lift_of_infinite [Infinite R] :
 variable [Countable R]
 
 @[simp]
-protected theorem countable : Set.Countable { x : A | IsAlgebraic R x } :=
+protected theorem countable : Set.Countable {x : A | IsAlgebraic R x} :=
   by
   rw [← le_aleph_0_iff_set_countable, ← lift_le]
   apply (cardinal_mk_lift_le_max R A).trans

38df578a

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -29,7 +29,7 @@ universe u v
 
 open Cardinal Polynomial Set
 
-open Cardinal Polynomial
+open scoped Cardinal Polynomial
 
 namespace Algebraic

38df578a

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -33,23 +33,11 @@ open Cardinal Polynomial
 
 namespace Algebraic
 
-/- warning: algebraic.infinite_of_char_zero -> Algebraic.infinite_of_charZero is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] [_inst_5 : CharZero.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (AddCommGroupWithOne.toAddGroupWithOne.{u2} A (Ring.toAddCommGroupWithOne.{u2} A _inst_3)))], Set.Infinite.{u2} A (setOf.{u2} A (fun (x : A) => IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 x))
-but is expected to have type
-  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommRing.{u2} R] [_inst_2 : IsDomain.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))] [_inst_3 : Ring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A _inst_3)] [_inst_5 : CharZero.{u1} A (AddGroupWithOne.toAddMonoidWithOne.{u1} A (Ring.toAddGroupWithOne.{u1} A _inst_3))], Set.Infinite.{u1} A (setOf.{u1} A (fun (x : A) => IsAlgebraic.{u2, u1} R A _inst_1 _inst_3 _inst_4 x))
-Case conversion may be inaccurate. Consider using '#align algebraic.infinite_of_char_zero Algebraic.infinite_of_charZeroₓ'. -/
 theorem infinite_of_charZero (R A : Type _) [CommRing R] [IsDomain R] [Ring A] [Algebra R A]
     [CharZero A] : { x : A | IsAlgebraic R x }.Infinite :=
   infinite_of_injective_forall_mem Nat.cast_injective isAlgebraic_nat
 #align algebraic.infinite_of_char_zero Algebraic.infinite_of_charZero
 
-/- warning: algebraic.aleph_0_le_cardinal_mk_of_char_zero -> Algebraic.aleph0_le_cardinal_mk_of_charZero is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] [_inst_5 : CharZero.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (AddCommGroupWithOne.toAddGroupWithOne.{u2} A (Ring.toAddCommGroupWithOne.{u2} A _inst_3)))], LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} Cardinal.aleph0.{u2} (Cardinal.mk.{u2} (Subtype.{succ u2} A (fun (x : A) => IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 x)))
-but is expected to have type
-  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommRing.{u2} R] [_inst_2 : IsDomain.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))] [_inst_3 : Ring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A _inst_3)] [_inst_5 : CharZero.{u1} A (AddGroupWithOne.toAddMonoidWithOne.{u1} A (Ring.toAddGroupWithOne.{u1} A _inst_3))], LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} A (fun (x : A) => IsAlgebraic.{u2, u1} R A _inst_1 _inst_3 _inst_4 x)))
-Case conversion may be inaccurate. Consider using '#align algebraic.aleph_0_le_cardinal_mk_of_char_zero Algebraic.aleph0_le_cardinal_mk_of_charZeroₓ'. -/
 theorem aleph0_le_cardinal_mk_of_charZero (R A : Type _) [CommRing R] [IsDomain R] [Ring A]
     [Algebra R A] [CharZero A] : ℵ₀ ≤ (#{ x : A // IsAlgebraic R x }) :=
   infinite_iff.1 (Set.infinite_coe_iff.2 <| infinite_of_charZero R A)
@@ -60,12 +48,6 @@ section lift
 variable (R : Type u) (A : Type v) [CommRing R] [CommRing A] [IsDomain A] [Algebra R A]
   [NoZeroSMulDivisors R A]
 
-/- warning: algebraic.cardinal_mk_lift_le_mul -> Algebraic.cardinal_mk_lift_le_mul is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_4)))))], LE.le.{succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.hasLe.{max u2 u1} (Cardinal.lift.{u1, u2} (Cardinal.mk.{u2} (Subtype.{succ u2} A (fun (x : A) => IsAlgebraic.{u1, u2} R A _inst_1 (CommRing.toRing.{u2} A _inst_2) _inst_4 x)))) (HMul.hMul.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.{max u2 u1} Cardinal.{max u2 u1} (instHMul.{succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.hasMul.{max u2 u1}) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) Cardinal.aleph0.{max u2 u1})
-but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) _inst_3))) (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_4)], LE.le.{max (succ u1) (succ u2)} Cardinal.{max u2 u1} Cardinal.instLECardinal.{max u1 u2} (Cardinal.lift.{u1, u2} (Cardinal.mk.{u2} (Subtype.{succ u2} A (fun (x : A) => IsAlgebraic.{u1, u2} R A _inst_1 (CommRing.toRing.{u2} A _inst_2) _inst_4 x)))) (HMul.hMul.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.{max u1 u2} Cardinal.{max u1 u2} (instHMul.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instMulCardinal.{max u1 u2}) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) Cardinal.aleph0.{max u1 u2})
-Case conversion may be inaccurate. Consider using '#align algebraic.cardinal_mk_lift_le_mul Algebraic.cardinal_mk_lift_le_mulₓ'. -/
 theorem cardinal_mk_lift_le_mul :
     Cardinal.lift.{u} (#{ x : A // IsAlgebraic R x }) ≤ Cardinal.lift.{v} (#R[X]) * ℵ₀ :=
   by
@@ -79,24 +61,12 @@ theorem cardinal_mk_lift_le_mul :
   exact mem_root_set.2 ⟨hg₁ x, hg₂ x⟩
 #align algebraic.cardinal_mk_lift_le_mul Algebraic.cardinal_mk_lift_le_mul
 
-/- warning: algebraic.cardinal_mk_lift_le_max -> Algebraic.cardinal_mk_lift_le_max is a dubious translation:
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 theorem cardinal_mk_lift_le_max :
     Cardinal.lift.{u} (#{ x : A // IsAlgebraic R x }) ≤ max (Cardinal.lift.{v} (#R)) ℵ₀ :=
   (cardinal_mk_lift_le_mul R A).trans <|
     (mul_le_mul_right' (lift_le.2 cardinal_mk_le_max) _).trans <| by simp
 #align algebraic.cardinal_mk_lift_le_max Algebraic.cardinal_mk_lift_le_max
 
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 @[simp]
 theorem cardinal_mk_lift_of_infinite [Infinite R] :
     Cardinal.lift.{u} (#{ x : A // IsAlgebraic R x }) = Cardinal.lift.{v} (#R) :=
@@ -108,12 +78,6 @@ theorem cardinal_mk_lift_of_infinite [Infinite R] :
 
 variable [Countable R]
 
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 @[simp]
 protected theorem countable : Set.Countable { x : A | IsAlgebraic R x } :=
   by
@@ -122,12 +86,6 @@ protected theorem countable : Set.Countable { x : A | IsAlgebraic R x } :=
   simp
 #align algebraic.countable Algebraic.countable
 
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-Case conversion may be inaccurate. Consider using '#align algebraic.cardinal_mk_of_countble_of_char_zero Algebraic.cardinal_mk_of_countble_of_charZeroₓ'. -/
 @[simp]
 theorem cardinal_mk_of_countble_of_charZero [CharZero A] [IsDomain R] :
     (#{ x : A // IsAlgebraic R x }) = ℵ₀ :=
@@ -141,32 +99,14 @@ section NonLift
 variable (R A : Type u) [CommRing R] [CommRing A] [IsDomain A] [Algebra R A]
   [NoZeroSMulDivisors R A]
 
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 theorem cardinal_mk_le_mul : (#{ x : A // IsAlgebraic R x }) ≤ (#R[X]) * ℵ₀ := by
   rw [← lift_id (#_), ← lift_id (#R[X])]; exact cardinal_mk_lift_le_mul R A
 #align algebraic.cardinal_mk_le_mul Algebraic.cardinal_mk_le_mul
 
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-Case conversion may be inaccurate. Consider using '#align algebraic.cardinal_mk_le_max Algebraic.cardinal_mk_le_maxₓ'. -/
 theorem cardinal_mk_le_max : (#{ x : A // IsAlgebraic R x }) ≤ max (#R) ℵ₀ := by
   rw [← lift_id (#_), ← lift_id (#R)]; exact cardinal_mk_lift_le_max R A
 #align algebraic.cardinal_mk_le_max Algebraic.cardinal_mk_le_max
 
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-  forall (R : Type.{u1}) (A : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))] [_inst_4 : Algebra.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u1} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u1} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u1} R A (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u1} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))))))) (Module.toMulActionWithZero.{u1, u1} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))) (Algebra.toModule.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_4)))))] [_inst_6 : Infinite.{succ u1} R], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} A (fun (x : A) => IsAlgebraic.{u1, u1} R A _inst_1 (CommRing.toRing.{u1} A _inst_2) _inst_4 x))) (Cardinal.mk.{u1} R)
-but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_4 : Algebra.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u1} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2) _inst_3))) (Algebra.toSMul.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_4)] [_inst_6 : Infinite.{succ u1} R], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} A (fun (x : A) => IsAlgebraic.{u1, u1} R A _inst_1 (CommRing.toRing.{u1} A _inst_2) _inst_4 x))) (Cardinal.mk.{u1} R)
-Case conversion may be inaccurate. Consider using '#align algebraic.cardinal_mk_of_infinite Algebraic.cardinal_mk_of_infiniteₓ'. -/
 @[simp]
 theorem cardinal_mk_of_infinite [Infinite R] : (#{ x : A // IsAlgebraic R x }) = (#R) :=
   lift_inj.1 <| cardinal_mk_lift_of_infinite R A

38df578a

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -147,10 +147,8 @@ lean 3 declaration is
 but is expected to have type
   forall (R : Type.{u1}) (A : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_4 : Algebra.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u1} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2) _inst_3))) (Algebra.toSMul.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_4)], LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} A (fun (x : A) => IsAlgebraic.{u1, u1} R A _inst_1 (CommRing.toRing.{u1} A _inst_2) _inst_4 x))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Cardinal.mk.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Cardinal.aleph0.{u1})
 Case conversion may be inaccurate. Consider using '#align algebraic.cardinal_mk_le_mul Algebraic.cardinal_mk_le_mulₓ'. -/
-theorem cardinal_mk_le_mul : (#{ x : A // IsAlgebraic R x }) ≤ (#R[X]) * ℵ₀ :=
-  by
-  rw [← lift_id (#_), ← lift_id (#R[X])]
-  exact cardinal_mk_lift_le_mul R A
+theorem cardinal_mk_le_mul : (#{ x : A // IsAlgebraic R x }) ≤ (#R[X]) * ℵ₀ := by
+  rw [← lift_id (#_), ← lift_id (#R[X])]; exact cardinal_mk_lift_le_mul R A
 #align algebraic.cardinal_mk_le_mul Algebraic.cardinal_mk_le_mul
 
 /- warning: algebraic.cardinal_mk_le_max -> Algebraic.cardinal_mk_le_max is a dubious translation:
@@ -159,10 +157,8 @@ lean 3 declaration is
 but is expected to have type
   forall (R : Type.{u1}) (A : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_4 : Algebra.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u1} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2) _inst_3))) (Algebra.toSMul.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_4)], LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} A (fun (x : A) => IsAlgebraic.{u1, u1} R A _inst_1 (CommRing.toRing.{u1} A _inst_2) _inst_4 x))) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.mk.{u1} R) Cardinal.aleph0.{u1})
 Case conversion may be inaccurate. Consider using '#align algebraic.cardinal_mk_le_max Algebraic.cardinal_mk_le_maxₓ'. -/
-theorem cardinal_mk_le_max : (#{ x : A // IsAlgebraic R x }) ≤ max (#R) ℵ₀ :=
-  by
-  rw [← lift_id (#_), ← lift_id (#R)]
-  exact cardinal_mk_lift_le_max R A
+theorem cardinal_mk_le_max : (#{ x : A // IsAlgebraic R x }) ≤ max (#R) ℵ₀ := by
+  rw [← lift_id (#_), ← lift_id (#R)]; exact cardinal_mk_lift_le_max R A
 #align algebraic.cardinal_mk_le_max Algebraic.cardinal_mk_le_max
 
 /- warning: algebraic.cardinal_mk_of_infinite -> Algebraic.cardinal_mk_of_infinite is a dubious translation:

38df578a

bump to nightly-2023-05-24-03

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

2c55cf2c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Violeta Hernández Palacios
 
 ! This file was ported from Lean 3 source module algebra.algebraic_card
-! leanprover-community/mathlib commit 40494fe75ecbd6d2ec61711baa630cf0a7b7d064
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.Algebraic
 /-!
 ### Cardinality of algebraic numbers
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file, we prove variants of the following result: the cardinality of algebraic numbers under
 an R-algebra is at most `# R[X] * ℵ₀`.

40494fe7

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

Diff

@@ -30,11 +30,23 @@ open Cardinal Polynomial
 
 namespace Algebraic
 
+/- warning: algebraic.infinite_of_char_zero -> Algebraic.infinite_of_charZero is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] [_inst_5 : CharZero.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (AddCommGroupWithOne.toAddGroupWithOne.{u2} A (Ring.toAddCommGroupWithOne.{u2} A _inst_3)))], Set.Infinite.{u2} A (setOf.{u2} A (fun (x : A) => IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 x))
+but is expected to have type
+  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommRing.{u2} R] [_inst_2 : IsDomain.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))] [_inst_3 : Ring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A _inst_3)] [_inst_5 : CharZero.{u1} A (AddGroupWithOne.toAddMonoidWithOne.{u1} A (Ring.toAddGroupWithOne.{u1} A _inst_3))], Set.Infinite.{u1} A (setOf.{u1} A (fun (x : A) => IsAlgebraic.{u2, u1} R A _inst_1 _inst_3 _inst_4 x))
+Case conversion may be inaccurate. Consider using '#align algebraic.infinite_of_char_zero Algebraic.infinite_of_charZeroₓ'. -/
 theorem infinite_of_charZero (R A : Type _) [CommRing R] [IsDomain R] [Ring A] [Algebra R A]
     [CharZero A] : { x : A | IsAlgebraic R x }.Infinite :=
   infinite_of_injective_forall_mem Nat.cast_injective isAlgebraic_nat
 #align algebraic.infinite_of_char_zero Algebraic.infinite_of_charZero
 
+/- warning: algebraic.aleph_0_le_cardinal_mk_of_char_zero -> Algebraic.aleph0_le_cardinal_mk_of_charZero is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] [_inst_5 : CharZero.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (AddCommGroupWithOne.toAddGroupWithOne.{u2} A (Ring.toAddCommGroupWithOne.{u2} A _inst_3)))], LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} Cardinal.aleph0.{u2} (Cardinal.mk.{u2} (Subtype.{succ u2} A (fun (x : A) => IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 x)))
+but is expected to have type
+  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommRing.{u2} R] [_inst_2 : IsDomain.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))] [_inst_3 : Ring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A _inst_3)] [_inst_5 : CharZero.{u1} A (AddGroupWithOne.toAddMonoidWithOne.{u1} A (Ring.toAddGroupWithOne.{u1} A _inst_3))], LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} A (fun (x : A) => IsAlgebraic.{u2, u1} R A _inst_1 _inst_3 _inst_4 x)))
+Case conversion may be inaccurate. Consider using '#align algebraic.aleph_0_le_cardinal_mk_of_char_zero Algebraic.aleph0_le_cardinal_mk_of_charZeroₓ'. -/
 theorem aleph0_le_cardinal_mk_of_charZero (R A : Type _) [CommRing R] [IsDomain R] [Ring A]
     [Algebra R A] [CharZero A] : ℵ₀ ≤ (#{ x : A // IsAlgebraic R x }) :=
   infinite_iff.1 (Set.infinite_coe_iff.2 <| infinite_of_charZero R A)
@@ -45,6 +57,12 @@ section lift
 variable (R : Type u) (A : Type v) [CommRing R] [CommRing A] [IsDomain A] [Algebra R A]
   [NoZeroSMulDivisors R A]
 
+/- warning: algebraic.cardinal_mk_lift_le_mul -> Algebraic.cardinal_mk_lift_le_mul is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_4)))))], LE.le.{succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.hasLe.{max u2 u1} (Cardinal.lift.{u1, u2} (Cardinal.mk.{u2} (Subtype.{succ u2} A (fun (x : A) => IsAlgebraic.{u1, u2} R A _inst_1 (CommRing.toRing.{u2} A _inst_2) _inst_4 x)))) (HMul.hMul.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.{max u2 u1} Cardinal.{max u2 u1} (instHMul.{succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.hasMul.{max u2 u1}) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) Cardinal.aleph0.{max u2 u1})
+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) _inst_3))) (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_4)], LE.le.{max (succ u1) (succ u2)} Cardinal.{max u2 u1} Cardinal.instLECardinal.{max u1 u2} (Cardinal.lift.{u1, u2} (Cardinal.mk.{u2} (Subtype.{succ u2} A (fun (x : A) => IsAlgebraic.{u1, u2} R A _inst_1 (CommRing.toRing.{u2} A _inst_2) _inst_4 x)))) (HMul.hMul.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.{max u1 u2} Cardinal.{max u1 u2} (instHMul.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instMulCardinal.{max u1 u2}) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) Cardinal.aleph0.{max u1 u2})
+Case conversion may be inaccurate. Consider using '#align algebraic.cardinal_mk_lift_le_mul Algebraic.cardinal_mk_lift_le_mulₓ'. -/
 theorem cardinal_mk_lift_le_mul :
     Cardinal.lift.{u} (#{ x : A // IsAlgebraic R x }) ≤ Cardinal.lift.{v} (#R[X]) * ℵ₀ :=
   by
@@ -58,12 +76,24 @@ theorem cardinal_mk_lift_le_mul :
   exact mem_root_set.2 ⟨hg₁ x, hg₂ x⟩
 #align algebraic.cardinal_mk_lift_le_mul Algebraic.cardinal_mk_lift_le_mul
 
+/- warning: algebraic.cardinal_mk_lift_le_max -> Algebraic.cardinal_mk_lift_le_max is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_4)))))], LE.le.{succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.hasLe.{max u2 u1} (Cardinal.lift.{u1, u2} (Cardinal.mk.{u2} (Subtype.{succ u2} A (fun (x : A) => IsAlgebraic.{u1, u2} R A _inst_1 (CommRing.toRing.{u2} A _inst_2) _inst_4 x)))) (LinearOrder.max.{succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.linearOrder.{max u2 u1} (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} R)) Cardinal.aleph0.{max u2 u1})
+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) _inst_3))) (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_4)], LE.le.{max (succ u1) (succ u2)} Cardinal.{max u2 u1} Cardinal.instLECardinal.{max u1 u2} (Cardinal.lift.{u1, u2} (Cardinal.mk.{u2} (Subtype.{succ u2} A (fun (x : A) => IsAlgebraic.{u1, u2} R A _inst_1 (CommRing.toRing.{u2} A _inst_2) _inst_4 x)))) (Max.max.{max (succ u2) (succ u1)} Cardinal.{max u1 u2} (CanonicallyLinearOrderedAddMonoid.toMax.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{max u1 u2}) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} R)) Cardinal.aleph0.{max u1 u2})
+Case conversion may be inaccurate. Consider using '#align algebraic.cardinal_mk_lift_le_max Algebraic.cardinal_mk_lift_le_maxₓ'. -/
 theorem cardinal_mk_lift_le_max :
     Cardinal.lift.{u} (#{ x : A // IsAlgebraic R x }) ≤ max (Cardinal.lift.{v} (#R)) ℵ₀ :=
   (cardinal_mk_lift_le_mul R A).trans <|
     (mul_le_mul_right' (lift_le.2 cardinal_mk_le_max) _).trans <| by simp
 #align algebraic.cardinal_mk_lift_le_max Algebraic.cardinal_mk_lift_le_max
 
+/- warning: algebraic.cardinal_mk_lift_of_infinite -> Algebraic.cardinal_mk_lift_of_infinite is a dubious translation:
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+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) _inst_3))) (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_4)] [_inst_6 : Infinite.{succ u1} R], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u2 u1} (Cardinal.lift.{u1, u2} (Cardinal.mk.{u2} (Subtype.{succ u2} A (fun (x : A) => IsAlgebraic.{u1, u2} R A _inst_1 (CommRing.toRing.{u2} A _inst_2) _inst_4 x)))) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} R))
+Case conversion may be inaccurate. Consider using '#align algebraic.cardinal_mk_lift_of_infinite Algebraic.cardinal_mk_lift_of_infiniteₓ'. -/
 @[simp]
 theorem cardinal_mk_lift_of_infinite [Infinite R] :
     Cardinal.lift.{u} (#{ x : A // IsAlgebraic R x }) = Cardinal.lift.{v} (#R) :=
@@ -75,6 +105,12 @@ theorem cardinal_mk_lift_of_infinite [Infinite R] :
 
 variable [Countable R]
 
+/- warning: algebraic.countable -> Algebraic.countable is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_4)))))] [_inst_6 : Countable.{succ u1} R], Set.Countable.{u2} A (setOf.{u2} A (fun (x : A) => IsAlgebraic.{u1, u2} R A _inst_1 (CommRing.toRing.{u2} A _inst_2) _inst_4 x))
+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) _inst_3))) (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_4)] [_inst_6 : Countable.{succ u1} R], Set.Countable.{u2} A (setOf.{u2} A (fun (x : A) => IsAlgebraic.{u1, u2} R A _inst_1 (CommRing.toRing.{u2} A _inst_2) _inst_4 x))
+Case conversion may be inaccurate. Consider using '#align algebraic.countable Algebraic.countableₓ'. -/
 @[simp]
 protected theorem countable : Set.Countable { x : A | IsAlgebraic R x } :=
   by
@@ -83,6 +119,12 @@ protected theorem countable : Set.Countable { x : A | IsAlgebraic R x } :=
   simp
 #align algebraic.countable Algebraic.countable
 
+/- warning: algebraic.cardinal_mk_of_countble_of_char_zero -> Algebraic.cardinal_mk_of_countble_of_charZero is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_4)))))] [_inst_6 : Countable.{succ u1} R] [_inst_7 : CharZero.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (AddCommGroupWithOne.toAddGroupWithOne.{u2} A (Ring.toAddCommGroupWithOne.{u2} A (CommRing.toRing.{u2} A _inst_2))))] [_inst_8 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], Eq.{succ (succ u2)} Cardinal.{u2} (Cardinal.mk.{u2} (Subtype.{succ u2} A (fun (x : A) => IsAlgebraic.{u1, u2} R A _inst_1 (CommRing.toRing.{u2} A _inst_2) _inst_4 x))) Cardinal.aleph0.{u2}
+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) _inst_3))) (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_4)] [_inst_6 : Countable.{succ u1} R] [_inst_7 : CharZero.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A (CommRing.toRing.{u2} A _inst_2)))] [_inst_8 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], Eq.{succ (succ u2)} Cardinal.{u2} (Cardinal.mk.{u2} (Subtype.{succ u2} A (fun (x : A) => IsAlgebraic.{u1, u2} R A _inst_1 (CommRing.toRing.{u2} A _inst_2) _inst_4 x))) Cardinal.aleph0.{u2}
+Case conversion may be inaccurate. Consider using '#align algebraic.cardinal_mk_of_countble_of_char_zero Algebraic.cardinal_mk_of_countble_of_charZeroₓ'. -/
 @[simp]
 theorem cardinal_mk_of_countble_of_charZero [CharZero A] [IsDomain R] :
     (#{ x : A // IsAlgebraic R x }) = ℵ₀ :=
@@ -96,18 +138,36 @@ section NonLift
 variable (R A : Type u) [CommRing R] [CommRing A] [IsDomain A] [Algebra R A]
   [NoZeroSMulDivisors R A]
 
+/- warning: algebraic.cardinal_mk_le_mul -> Algebraic.cardinal_mk_le_mul is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))] [_inst_4 : Algebra.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u1} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u1} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u1} R A (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u1} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))))))) (Module.toMulActionWithZero.{u1, u1} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))) (Algebra.toModule.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_4)))))], LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} A (fun (x : A) => IsAlgebraic.{u1, u1} R A _inst_1 (CommRing.toRing.{u1} A _inst_2) _inst_4 x))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) (Cardinal.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) Cardinal.aleph0.{u1})
+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_4 : Algebra.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u1} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2) _inst_3))) (Algebra.toSMul.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_4)], LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} A (fun (x : A) => IsAlgebraic.{u1, u1} R A _inst_1 (CommRing.toRing.{u1} A _inst_2) _inst_4 x))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Cardinal.mk.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Cardinal.aleph0.{u1})
+Case conversion may be inaccurate. Consider using '#align algebraic.cardinal_mk_le_mul Algebraic.cardinal_mk_le_mulₓ'. -/
 theorem cardinal_mk_le_mul : (#{ x : A // IsAlgebraic R x }) ≤ (#R[X]) * ℵ₀ :=
   by
   rw [← lift_id (#_), ← lift_id (#R[X])]
   exact cardinal_mk_lift_le_mul R A
 #align algebraic.cardinal_mk_le_mul Algebraic.cardinal_mk_le_mul
 
+/- warning: algebraic.cardinal_mk_le_max -> Algebraic.cardinal_mk_le_max is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))] [_inst_4 : Algebra.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u1} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u1} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u1} R A (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u1} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))))))) (Module.toMulActionWithZero.{u1, u1} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))) (Algebra.toModule.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_4)))))], LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} A (fun (x : A) => IsAlgebraic.{u1, u1} R A _inst_1 (CommRing.toRing.{u1} A _inst_2) _inst_4 x))) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (Cardinal.mk.{u1} R) Cardinal.aleph0.{u1})
+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_4 : Algebra.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u1} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2) _inst_3))) (Algebra.toSMul.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_4)], LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} A (fun (x : A) => IsAlgebraic.{u1, u1} R A _inst_1 (CommRing.toRing.{u1} A _inst_2) _inst_4 x))) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.mk.{u1} R) Cardinal.aleph0.{u1})
+Case conversion may be inaccurate. Consider using '#align algebraic.cardinal_mk_le_max Algebraic.cardinal_mk_le_maxₓ'. -/
 theorem cardinal_mk_le_max : (#{ x : A // IsAlgebraic R x }) ≤ max (#R) ℵ₀ :=
   by
   rw [← lift_id (#_), ← lift_id (#R)]
   exact cardinal_mk_lift_le_max R A
 #align algebraic.cardinal_mk_le_max Algebraic.cardinal_mk_le_max
 
+/- warning: algebraic.cardinal_mk_of_infinite -> Algebraic.cardinal_mk_of_infinite is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))] [_inst_4 : Algebra.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u1} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u1} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u1} R A (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u1} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))))))) (Module.toMulActionWithZero.{u1, u1} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))) (Algebra.toModule.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_4)))))] [_inst_6 : Infinite.{succ u1} R], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} A (fun (x : A) => IsAlgebraic.{u1, u1} R A _inst_1 (CommRing.toRing.{u1} A _inst_2) _inst_4 x))) (Cardinal.mk.{u1} R)
+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_4 : Algebra.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_5 : NoZeroSMulDivisors.{u1, u1} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2) _inst_3))) (Algebra.toSMul.{u1, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_4)] [_inst_6 : Infinite.{succ u1} R], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} A (fun (x : A) => IsAlgebraic.{u1, u1} R A _inst_1 (CommRing.toRing.{u1} A _inst_2) _inst_4 x))) (Cardinal.mk.{u1} R)
+Case conversion may be inaccurate. Consider using '#align algebraic.cardinal_mk_of_infinite Algebraic.cardinal_mk_of_infiniteₓ'. -/
 @[simp]
 theorem cardinal_mk_of_infinite [Infinite R] : (#{ x : A // IsAlgebraic R x }) = (#R) :=
   lift_inj.1 <| cardinal_mk_lift_of_infinite R A

40494fe7

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

40494fe7

move(Polynomial): Move out of Data (#11751)

Polynomial and MvPolynomial are algebraic objects, hence should be under Algebra (or at least not under Data)

56e439ec

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Violeta Hernández Palacios
 -/
-import Mathlib.Data.Polynomial.Cardinal
+import Mathlib.Algebra.Polynomial.Cardinal
 import Mathlib.RingTheory.Algebraic
 
 #align_import algebra.algebraic_card from "leanprover-community/mathlib"@"40494fe75ecbd6d2ec61711baa630cf0a7b7d064"

40494fe7

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

a13e8040

Diff

@@ -48,8 +48,8 @@ theorem cardinal_mk_lift_le_mul :
   choose g hg₁ hg₂ using fun x : { x : A | IsAlgebraic R x } => x.coe_prop
   refine' lift_mk_le_lift_mk_mul_of_lift_mk_preimage_le g fun f => _
   rw [lift_le_aleph0, le_aleph0_iff_set_countable]
-  suffices : MapsTo (↑) (g ⁻¹' {f}) (f.rootSet A)
-  exact this.countable_of_injOn (Subtype.coe_injective.injOn _) (f.rootSet_finite A).countable
+  suffices MapsTo (↑) (g ⁻¹' {f}) (f.rootSet A) from
+    this.countable_of_injOn (Subtype.coe_injective.injOn _) (f.rootSet_finite A).countable
   rintro x (rfl : g x = f)
   exact mem_rootSet.2 ⟨hg₁ x, hg₂ x⟩
 #align algebraic.cardinal_mk_lift_le_mul Algebraic.cardinal_mk_lift_le_mul

40494fe7

refactor(Set/Countable): redefine Set.Countable (#9831)

Redefine Set.Countable s as _root_.Countable s. Fix compile, golf some of the broken proofs.

c4152bb6

Diff

@@ -72,7 +72,7 @@ variable [Countable R]
 
 @[simp]
 protected theorem countable : Set.Countable { x : A | IsAlgebraic R x } := by
-  rw [← le_aleph0_iff_set_countable, ← lift_le]
+  rw [← le_aleph0_iff_set_countable, ← lift_le_aleph0]
   apply (cardinal_mk_lift_le_max R A).trans
   simp
 #align algebraic.countable Algebraic.countable

40494fe7

feat(AddMonoidAlgebra*): add notation R[A] for addMonoidAlgebra R A (#7203)

Introduce the notation R[A] for AddMonoidAlgebra R A. This is to align Mathlibs notation with the standard notation for group ring.

The notation is scoped in AddMonoidAlgebra and there is no analogous notation for MonoidAlgebra.

I only used the notation for single-character R and As and only in the range [a-zA-Z].

The extra lines are all in Mathlib/Algebra/MonoidAlgebra/Basic.lean. They are accounted for by extra text in the doc-module and the actual notation.

Affected files:

Counterexamples/ZeroDivisorsInAddMonoidAlgebras
Algebra/AlgebraicCard
Algebra/MonoidAlgebra/Basic
Algebra/MonoidAlgebra/Degree
Algebra/MonoidAlgebra/Division
Algebra/MonoidAlgebra/Grading
Algebra/MonoidAlgebra/NoZeroDivisors
Algebra/MonoidAlgebra/Support
Data/Polynomial/AlgebraMap
Data/Polynomial/Basic
Data/Polynomial/Eval
Data/Polynomial/Laurent
RingTheory/FiniteType

2f19a6b1

Diff

@@ -43,7 +43,7 @@ variable (R : Type u) (A : Type v) [CommRing R] [CommRing A] [IsDomain A] [Algeb
   [NoZeroSMulDivisors R A]
 
 theorem cardinal_mk_lift_le_mul :
-    Cardinal.lift.{u} #{ x : A // IsAlgebraic R x } ≤ Cardinal.lift.{v} #(R[X]) * ℵ₀ := by
+    Cardinal.lift.{u} #{ x : A // IsAlgebraic R x } ≤ Cardinal.lift.{v} #R[X] * ℵ₀ := by
   rw [← mk_uLift, ← mk_uLift]
   choose g hg₁ hg₂ using fun x : { x : A | IsAlgebraic R x } => x.coe_prop
   refine' lift_mk_le_lift_mk_mul_of_lift_mk_preimage_le g fun f => _
@@ -90,8 +90,8 @@ section NonLift
 variable (R A : Type u) [CommRing R] [CommRing A] [IsDomain A] [Algebra R A]
   [NoZeroSMulDivisors R A]
 
-theorem cardinal_mk_le_mul : #{ x : A // IsAlgebraic R x } ≤ #(R[X]) * ℵ₀ := by
-  rw [← lift_id #_, ← lift_id #(R[X])]
+theorem cardinal_mk_le_mul : #{ x : A // IsAlgebraic R x } ≤ #R[X] * ℵ₀ := by
+  rw [← lift_id #_, ← lift_id #R[X]]
   exact cardinal_mk_lift_le_mul R A
 #align algebraic.cardinal_mk_le_mul Algebraic.cardinal_mk_le_mul

40494fe7

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

@@ -27,12 +27,12 @@ open Cardinal Polynomial
 
 namespace Algebraic
 
-theorem infinite_of_charZero (R A : Type _) [CommRing R] [IsDomain R] [Ring A] [Algebra R A]
+theorem infinite_of_charZero (R A : Type*) [CommRing R] [IsDomain R] [Ring A] [Algebra R A]
     [CharZero A] : { x : A | IsAlgebraic R x }.Infinite :=
   infinite_of_injective_forall_mem Nat.cast_injective isAlgebraic_nat
 #align algebraic.infinite_of_char_zero Algebraic.infinite_of_charZero
 
-theorem aleph0_le_cardinal_mk_of_charZero (R A : Type _) [CommRing R] [IsDomain R] [Ring A]
+theorem aleph0_le_cardinal_mk_of_charZero (R A : Type*) [CommRing R] [IsDomain R] [Ring A]
     [Algebra R A] [CharZero A] : ℵ₀ ≤ #{ x : A // IsAlgebraic R x } :=
   infinite_iff.1 (Set.infinite_coe_iff.2 <| infinite_of_charZero R A)
 #align algebraic.aleph_0_le_cardinal_mk_of_char_zero Algebraic.aleph0_le_cardinal_mk_of_charZero

40494fe7

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) 2022 Violeta Hernández Palacios. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Violeta Hernández Palacios
-
-! This file was ported from Lean 3 source module algebra.algebraic_card
-! leanprover-community/mathlib commit 40494fe75ecbd6d2ec61711baa630cf0a7b7d064
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Polynomial.Cardinal
 import Mathlib.RingTheory.Algebraic
 
+#align_import algebra.algebraic_card from "leanprover-community/mathlib"@"40494fe75ecbd6d2ec61711baa630cf0a7b7d064"
+
 /-!
 ### Cardinality of algebraic numbers

40494fe7

fix: precedence of # (#5623)

d450fcd7

Diff

@@ -36,7 +36,7 @@ theorem infinite_of_charZero (R A : Type _) [CommRing R] [IsDomain R] [Ring A] [
 #align algebraic.infinite_of_char_zero Algebraic.infinite_of_charZero
 
 theorem aleph0_le_cardinal_mk_of_charZero (R A : Type _) [CommRing R] [IsDomain R] [Ring A]
-    [Algebra R A] [CharZero A] : ℵ₀ ≤ (#{ x : A // IsAlgebraic R x }) :=
+    [Algebra R A] [CharZero A] : ℵ₀ ≤ #{ x : A // IsAlgebraic R x } :=
   infinite_iff.1 (Set.infinite_coe_iff.2 <| infinite_of_charZero R A)
 #align algebraic.aleph_0_le_cardinal_mk_of_char_zero Algebraic.aleph0_le_cardinal_mk_of_charZero
 
@@ -46,7 +46,7 @@ variable (R : Type u) (A : Type v) [CommRing R] [CommRing A] [IsDomain A] [Algeb
   [NoZeroSMulDivisors R A]
 
 theorem cardinal_mk_lift_le_mul :
-    Cardinal.lift.{u} (#{ x : A // IsAlgebraic R x }) ≤ Cardinal.lift.{v} (#R[X]) * ℵ₀ := by
+    Cardinal.lift.{u} #{ x : A // IsAlgebraic R x } ≤ Cardinal.lift.{v} #(R[X]) * ℵ₀ := by
   rw [← mk_uLift, ← mk_uLift]
   choose g hg₁ hg₂ using fun x : { x : A | IsAlgebraic R x } => x.coe_prop
   refine' lift_mk_le_lift_mk_mul_of_lift_mk_preimage_le g fun f => _
@@ -58,14 +58,14 @@ theorem cardinal_mk_lift_le_mul :
 #align algebraic.cardinal_mk_lift_le_mul Algebraic.cardinal_mk_lift_le_mul
 
 theorem cardinal_mk_lift_le_max :
-    Cardinal.lift.{u} (#{ x : A // IsAlgebraic R x }) ≤ max (Cardinal.lift.{v} (#R)) ℵ₀ :=
+    Cardinal.lift.{u} #{ x : A // IsAlgebraic R x } ≤ max (Cardinal.lift.{v} #R) ℵ₀ :=
   (cardinal_mk_lift_le_mul R A).trans <|
     (mul_le_mul_right' (lift_le.2 cardinal_mk_le_max) _).trans <| by simp
 #align algebraic.cardinal_mk_lift_le_max Algebraic.cardinal_mk_lift_le_max
 
 @[simp]
 theorem cardinal_mk_lift_of_infinite [Infinite R] :
-    Cardinal.lift.{u} (#{ x : A // IsAlgebraic R x }) = Cardinal.lift.{v} (#R) :=
+    Cardinal.lift.{u} #{ x : A // IsAlgebraic R x } = Cardinal.lift.{v} #R :=
   ((cardinal_mk_lift_le_max R A).trans_eq (max_eq_left <| aleph0_le_mk _)).antisymm <|
     lift_mk_le'.2 ⟨⟨fun x => ⟨algebraMap R A x, isAlgebraic_algebraMap _⟩, fun _ _ h =>
       NoZeroSMulDivisors.algebraMap_injective R A (Subtype.ext_iff.1 h)⟩⟩
@@ -82,7 +82,7 @@ protected theorem countable : Set.Countable { x : A | IsAlgebraic R x } := by
 
 @[simp]
 theorem cardinal_mk_of_countable_of_charZero [CharZero A] [IsDomain R] :
-    (#{ x : A // IsAlgebraic R x }) = ℵ₀ :=
+    #{ x : A // IsAlgebraic R x } = ℵ₀ :=
   (Algebraic.countable R A).le_aleph0.antisymm (aleph0_le_cardinal_mk_of_charZero R A)
 #align algebraic.cardinal_mk_of_countble_of_char_zero Algebraic.cardinal_mk_of_countable_of_charZero
 
@@ -93,18 +93,18 @@ section NonLift
 variable (R A : Type u) [CommRing R] [CommRing A] [IsDomain A] [Algebra R A]
   [NoZeroSMulDivisors R A]
 
-theorem cardinal_mk_le_mul : (#{ x : A // IsAlgebraic R x }) ≤ (#R[X]) * ℵ₀ := by
-  rw [← lift_id (#_), ← lift_id (#R[X])]
+theorem cardinal_mk_le_mul : #{ x : A // IsAlgebraic R x } ≤ #(R[X]) * ℵ₀ := by
+  rw [← lift_id #_, ← lift_id #(R[X])]
   exact cardinal_mk_lift_le_mul R A
 #align algebraic.cardinal_mk_le_mul Algebraic.cardinal_mk_le_mul
 
-theorem cardinal_mk_le_max : (#{ x : A // IsAlgebraic R x }) ≤ max (#R) ℵ₀ := by
-  rw [← lift_id (#_), ← lift_id (#R)]
+theorem cardinal_mk_le_max : #{ x : A // IsAlgebraic R x } ≤ max #R ℵ₀ := by
+  rw [← lift_id #_, ← lift_id #R]
   exact cardinal_mk_lift_le_max R A
 #align algebraic.cardinal_mk_le_max Algebraic.cardinal_mk_le_max
 
 @[simp]
-theorem cardinal_mk_of_infinite [Infinite R] : (#{ x : A // IsAlgebraic R x }) = (#R) :=
+theorem cardinal_mk_of_infinite [Infinite R] : #{ x : A // IsAlgebraic R x } = #R :=
   lift_inj.1 <| cardinal_mk_lift_of_infinite R A
 #align algebraic.cardinal_mk_of_infinite Algebraic.cardinal_mk_of_infinite

40494fe7

chore: tidy various files (#4854)

5238ba14

Diff

@@ -81,10 +81,10 @@ protected theorem countable : Set.Countable { x : A | IsAlgebraic R x } := by
 #align algebraic.countable Algebraic.countable
 
 @[simp]
-theorem cardinal_mk_of_countble_of_charZero [CharZero A] [IsDomain R] :
+theorem cardinal_mk_of_countable_of_charZero [CharZero A] [IsDomain R] :
     (#{ x : A // IsAlgebraic R x }) = ℵ₀ :=
   (Algebraic.countable R A).le_aleph0.antisymm (aleph0_le_cardinal_mk_of_charZero R A)
-#align algebraic.cardinal_mk_of_countble_of_char_zero Algebraic.cardinal_mk_of_countble_of_charZero
+#align algebraic.cardinal_mk_of_countble_of_char_zero Algebraic.cardinal_mk_of_countable_of_charZero
 
 end lift

40494fe7

feat: port Algebra.AlgebraicCard (#4236)

5afb4f38

`algebra.algebraic_card` ⟷ `Mathlib.Algebra.AlgebraicCard`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 629

algebra.algebraic_card ⟷ Mathlib.Algebra.AlgebraicCard

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 629

`algebra.algebraic_card` ⟷ `Mathlib.Algebra.AlgebraicCard`