data.polynomial.cardinal
⟷
Mathlib.Data.Polynomial.Cardinal
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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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -3,7 +3,7 @@ Copyright (c) 2021 Chris Hughes, Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Junyan Xu
-/
-import Data.Polynomial.Basic
+import Algebra.Polynomial.Basic
import SetTheory.Cardinal.Ordinal
#align_import data.polynomial.cardinal from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2021 Chris Hughes, Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Junyan Xu
-/
-import Mathbin.Data.Polynomial.Basic
-import Mathbin.SetTheory.Cardinal.Ordinal
+import Data.Polynomial.Basic
+import SetTheory.Cardinal.Ordinal
#align_import data.polynomial.cardinal from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2021 Chris Hughes, Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Junyan Xu
-
-! This file was ported from Lean 3 source module data.polynomial.cardinal
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Polynomial.Basic
import Mathbin.SetTheory.Cardinal.Ordinal
+#align_import data.polynomial.cardinal from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
+
/-!
# Cardinality of Polynomial Ring
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -30,18 +30,22 @@ open Cardinal
namespace Polynomial
+#print Polynomial.cardinal_mk_eq_max /-
@[simp]
theorem cardinal_mk_eq_max {R : Type u} [Semiring R] [Nontrivial R] : (#R[X]) = max (#R) ℵ₀ :=
(toFinsuppIso R).toEquiv.cardinal_eq.trans <| by
rw [AddMonoidAlgebra, mk_finsupp_lift_of_infinite, lift_uzero, max_comm]; rfl
#align polynomial.cardinal_mk_eq_max Polynomial.cardinal_mk_eq_max
+-/
+#print Polynomial.cardinal_mk_le_max /-
theorem cardinal_mk_le_max {R : Type u} [Semiring R] : (#R[X]) ≤ max (#R) ℵ₀ :=
by
cases subsingleton_or_nontrivial R
· exact (mk_eq_one _).trans_le (le_max_of_le_right one_le_aleph_0)
· exact cardinal_mk_eq_max.le
#align polynomial.cardinal_mk_le_max Polynomial.cardinal_mk_le_max
+-/
end Polynomial
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -24,7 +24,7 @@ of `#R` and `ℵ₀`.
universe u
-open Cardinal Polynomial
+open scoped Cardinal Polynomial
open Cardinal
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -30,24 +30,12 @@ open Cardinal
namespace Polynomial
-/- warning: polynomial.cardinal_mk_eq_max -> Polynomial.cardinal_mk_eq_max is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Polynomial.{u1} R _inst_1)) (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}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Polynomial.{u1} R _inst_1)) (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 polynomial.cardinal_mk_eq_max Polynomial.cardinal_mk_eq_maxₓ'. -/
@[simp]
theorem cardinal_mk_eq_max {R : Type u} [Semiring R] [Nontrivial R] : (#R[X]) = max (#R) ℵ₀ :=
(toFinsuppIso R).toEquiv.cardinal_eq.trans <| by
rw [AddMonoidAlgebra, mk_finsupp_lift_of_infinite, lift_uzero, max_comm]; rfl
#align polynomial.cardinal_mk_eq_max Polynomial.cardinal_mk_eq_max
-/- warning: polynomial.cardinal_mk_le_max -> Polynomial.cardinal_mk_le_max is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (Polynomial.{u1} R _inst_1)) (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}} [_inst_1 : Semiring.{u1} R], LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} (Polynomial.{u1} R _inst_1)) (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 polynomial.cardinal_mk_le_max Polynomial.cardinal_mk_le_maxₓ'. -/
theorem cardinal_mk_le_max {R : Type u} [Semiring R] : (#R[X]) ≤ max (#R) ℵ₀ :=
by
cases subsingleton_or_nontrivial R
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -38,10 +38,8 @@ but is expected to have type
Case conversion may be inaccurate. Consider using '#align polynomial.cardinal_mk_eq_max Polynomial.cardinal_mk_eq_maxₓ'. -/
@[simp]
theorem cardinal_mk_eq_max {R : Type u} [Semiring R] [Nontrivial R] : (#R[X]) = max (#R) ℵ₀ :=
- (toFinsuppIso R).toEquiv.cardinal_eq.trans <|
- by
- rw [AddMonoidAlgebra, mk_finsupp_lift_of_infinite, lift_uzero, max_comm]
- rfl
+ (toFinsuppIso R).toEquiv.cardinal_eq.trans <| by
+ rw [AddMonoidAlgebra, mk_finsupp_lift_of_infinite, lift_uzero, max_comm]; rfl
#align polynomial.cardinal_mk_eq_max Polynomial.cardinal_mk_eq_max
/- warning: polynomial.cardinal_mk_le_max -> Polynomial.cardinal_mk_le_max is a dubious translation:
mathlib commit https://github.com/leanprover-community/mathlib/commit/d95bef0d215ea58c0fd7bbc4b151bf3fe952c095
@@ -32,7 +32,7 @@ namespace Polynomial
/- warning: polynomial.cardinal_mk_eq_max -> Polynomial.cardinal_mk_eq_max is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Polynomial.{u1} R _inst_1)) (LinearOrder.max.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toLinearOrder.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1})) (Cardinal.mk.{u1} R) Cardinal.aleph0.{u1})
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Polynomial.{u1} R _inst_1)) (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}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Polynomial.{u1} R _inst_1)) (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 polynomial.cardinal_mk_eq_max Polynomial.cardinal_mk_eq_maxₓ'. -/
@@ -46,7 +46,7 @@ theorem cardinal_mk_eq_max {R : Type u} [Semiring R] [Nontrivial R] : (#R[X]) =
/- warning: polynomial.cardinal_mk_le_max -> Polynomial.cardinal_mk_le_max is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (Polynomial.{u1} R _inst_1)) (LinearOrder.max.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toLinearOrder.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1})) (Cardinal.mk.{u1} R) Cardinal.aleph0.{u1})
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (Polynomial.{u1} R _inst_1)) (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}} [_inst_1 : Semiring.{u1} R], LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} (Polynomial.{u1} R _inst_1)) (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 polynomial.cardinal_mk_le_max Polynomial.cardinal_mk_le_maxₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Junyan Xu
! This file was ported from Lean 3 source module data.polynomial.cardinal
-! leanprover-community/mathlib commit 62c0a4ef1441edb463095ea02a06e87f3dfe135c
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.SetTheory.Cardinal.Ordinal
/-!
# Cardinality of Polynomial Ring
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
The reuslt in this file is that the cardinality of `R[X]` is at most the maximum
of `#R` and `ℵ₀`.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5
@@ -27,6 +27,12 @@ open Cardinal
namespace Polynomial
+/- warning: polynomial.cardinal_mk_eq_max -> Polynomial.cardinal_mk_eq_max is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Polynomial.{u1} R _inst_1)) (LinearOrder.max.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toLinearOrder.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1})) (Cardinal.mk.{u1} R) Cardinal.aleph0.{u1})
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Polynomial.{u1} R _inst_1)) (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 polynomial.cardinal_mk_eq_max Polynomial.cardinal_mk_eq_maxₓ'. -/
@[simp]
theorem cardinal_mk_eq_max {R : Type u} [Semiring R] [Nontrivial R] : (#R[X]) = max (#R) ℵ₀ :=
(toFinsuppIso R).toEquiv.cardinal_eq.trans <|
@@ -35,6 +41,12 @@ theorem cardinal_mk_eq_max {R : Type u} [Semiring R] [Nontrivial R] : (#R[X]) =
rfl
#align polynomial.cardinal_mk_eq_max Polynomial.cardinal_mk_eq_max
+/- warning: polynomial.cardinal_mk_le_max -> Polynomial.cardinal_mk_le_max is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (Polynomial.{u1} R _inst_1)) (LinearOrder.max.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toLinearOrder.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1})) (Cardinal.mk.{u1} R) Cardinal.aleph0.{u1})
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} (Polynomial.{u1} R _inst_1)) (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 polynomial.cardinal_mk_le_max Polynomial.cardinal_mk_le_maxₓ'. -/
theorem cardinal_mk_le_max {R : Type u} [Semiring R] : (#R[X]) ≤ max (#R) ℵ₀ :=
by
cases subsingleton_or_nontrivial R
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Data
(#11751)
Polynomial
and MvPolynomial
are algebraic objects, hence should be under Algebra
(or at least not under Data
)
@@ -3,7 +3,7 @@ Copyright (c) 2021 Chris Hughes, Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Junyan Xu
-/
-import Mathlib.Data.Polynomial.Basic
+import Mathlib.Algebra.Polynomial.Basic
import Mathlib.SetTheory.Cardinal.Ordinal
#align_import data.polynomial.cardinal from "leanprover-community/mathlib"@"62c0a4ef1441edb463095ea02a06e87f3dfe135c"
@@ -2,15 +2,12 @@
Copyright (c) 2021 Chris Hughes, Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Junyan Xu
-
-! This file was ported from Lean 3 source module data.polynomial.cardinal
-! leanprover-community/mathlib commit 62c0a4ef1441edb463095ea02a06e87f3dfe135c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.Polynomial.Basic
import Mathlib.SetTheory.Cardinal.Ordinal
+#align_import data.polynomial.cardinal from "leanprover-community/mathlib"@"62c0a4ef1441edb463095ea02a06e87f3dfe135c"
+
/-!
# Cardinality of Polynomial Ring
@@ -28,13 +28,13 @@ open Cardinal
namespace Polynomial
@[simp]
-theorem cardinal_mk_eq_max {R : Type u} [Semiring R] [Nontrivial R] : (#R[X]) = max (#R) ℵ₀ :=
+theorem cardinal_mk_eq_max {R : Type u} [Semiring R] [Nontrivial R] : #(R[X]) = max #R ℵ₀ :=
(toFinsuppIso R).toEquiv.cardinal_eq.trans <| by
rw [AddMonoidAlgebra, mk_finsupp_lift_of_infinite, lift_uzero, max_comm]
rfl
#align polynomial.cardinal_mk_eq_max Polynomial.cardinal_mk_eq_max
-theorem cardinal_mk_le_max {R : Type u} [Semiring R] : (#R[X]) ≤ max (#R) ℵ₀ := by
+theorem cardinal_mk_le_max {R : Type u} [Semiring R] : #(R[X]) ≤ max #R ℵ₀ := by
cases subsingleton_or_nontrivial R
· exact (mk_eq_one _).trans_le (le_max_of_le_right one_le_aleph0)
· exact cardinal_mk_eq_max.le
by
s! (#3825)
This PR puts, with one exception, every single remaining by
that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh
. The exception is when the by
begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.
Essentially this is s/\n *by$/ by/g
, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated by
s".
@@ -29,8 +29,7 @@ namespace Polynomial
@[simp]
theorem cardinal_mk_eq_max {R : Type u} [Semiring R] [Nontrivial R] : (#R[X]) = max (#R) ℵ₀ :=
- (toFinsuppIso R).toEquiv.cardinal_eq.trans <|
- by
+ (toFinsuppIso R).toEquiv.cardinal_eq.trans <| by
rw [AddMonoidAlgebra, mk_finsupp_lift_of_infinite, lift_uzero, max_comm]
rfl
#align polynomial.cardinal_mk_eq_max Polynomial.cardinal_mk_eq_max
The unported dependencies are