algebra.star.chsh | Mathlib porting status

(last sync)

feat(algebra/star/basic): refactor star_ordered_ring to include add_submonoid.closure (#18854)

Per Zulip, this refactors star_ordered_ring so that the condition star_ordered_ring.nonneg_iff is changed from ∀ r : R, 0 ≤ r ↔ ∃ s, r = star s * s to something morally equivalent to ∀ x : R, 0 ≤ x ↔ x ∈ add_submonoid.closure (set.range (λ s : R, star s * s)).

In fact, we actually change the structure field nonneg_iff to le_iff, which characterizes · ≤ · instead of just 0 ≤ ·. When R is a non_unital_ring, there is effectively no change (see how we recover star_ordered_ring.nonneg_iff and also star_ordered_ring.of_nonneg_iff), but it gives a more useful and sensible condition when R is only a non_unital_semiring. For instance, now conjugate_le_conjugate holds for non_unital_semiring.

There are essentially two reasons for this change.

It would be nice if things like ℚ could be star_ordered_rings. This is a minor reason, but it should be a nice convenience. This instance is added in this PR in a new file.
Much more importantly, we want to declare the positive elements in a star_ordered_ring as an add_submonoid, but to accomplish this with the previous definition requires much more stringent type class assumptions (e.g., C⋆-algebras) and sophisticated machinery (the continuous functional calculus) in order to show that the sum of positive elements is positive. This change essentially allows us to defer that proof obligation to the settings where it will matter that a positive element really does have the form star s * s.

We remark that even for C⋆-algebras, the fact that the sum of positive elements (i.e., those of the form star s * s) is positive is a deep result which was first shown in 1952 by Fukamiya, and then again in 1953 by Kelley and Vaught. These proofs are in essence very similar, but the latter is more aesthetically pleasing, and it is this proof that appears in all the textbooks. I went looking and did not see another proof anywhere in the literature.

We provide a few convenience constructors for star_ordered_ring in the form of reducible definitions which can apply when R is either a non_unital_ring (so we only need to characterize nonnegativity), and / or when positive elements have exactly the form star s * s. In this way, we can effectively maintain the status quo (see the instances for real and complex).

Diff

@@ -133,7 +133,7 @@ begin
         T.A₀_sa, T.A₁_sa, T.B₀_sa, T.B₁_sa, mul_comm B₀, mul_comm B₁], },
     rw idem',
     conv_rhs { congr, skip, congr, rw ←sa, },
-    convert smul_le_smul_of_nonneg (star_mul_self_nonneg : 0 ≤ star P * P) _,
+    convert smul_le_smul_of_nonneg (star_mul_self_nonneg P) _,
     { simp, },
     { apply_instance, },
     { norm_num, } },
@@ -221,11 +221,11 @@ begin
     have P2_nonneg : 0 ≤ P^2,
     { rw [sq],
       conv { congr, skip, congr, rw ←P_sa, },
-      convert (star_mul_self_nonneg : 0 ≤ star P * P), },
+      convert (star_mul_self_nonneg P), },
     have Q2_nonneg : 0 ≤ Q^2,
     { rw [sq],
       conv { congr, skip, congr, rw ←Q_sa, },
-      convert (star_mul_self_nonneg : 0 ≤ star Q * Q), },
+      convert (star_mul_self_nonneg Q), },
     convert smul_le_smul_of_nonneg (add_nonneg P2_nonneg Q2_nonneg)
       (le_of_lt (show 0 < √2⁻¹, by norm_num)), -- `norm_num` can't directly show `0 ≤ √2⁻¹`
     simp, },

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2023-12-25-06

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

c71f3cc2

Diff

@@ -151,7 +151,7 @@ theorem CHSH_inequality_of_comm [OrderedCommRing R] [StarOrderedRing R] [Algebra
       skip
       congr
       rw [← sa]
-    convert smul_le_smul_of_nonneg (star_mul_self_nonneg P) _
+    convert smul_le_smul_of_nonneg_left (star_mul_self_nonneg P) _
     · simp
     · infer_instance
     · norm_num
@@ -260,7 +260,8 @@ theorem tsirelson_inequality [OrderedRing R] [StarOrderedRing R] [Algebra ℝ R]
         rw [← Q_sa]
       convert star_mul_self_nonneg Q
     convert
-      smul_le_smul_of_nonneg (add_nonneg P2_nonneg Q2_nonneg) (le_of_lt (show 0 < √2⁻¹ by norm_num))
+      smul_le_smul_of_nonneg_left (add_nonneg P2_nonneg Q2_nonneg)
+        (le_of_lt (show 0 < √2⁻¹ by norm_num))
     -- `norm_num` can't directly show `0 ≤ √2⁻¹`
     simp
   apply le_of_sub_nonneg

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) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.Algebra.CharP.Invertible
-import Mathbin.Data.Real.Sqrt
+import Algebra.CharP.Invertible
+import Data.Real.Sqrt
 
 #align_import algebra.star.chsh from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"

bump to nightly-2023-09-02-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

a4ca67cb

Diff

@@ -86,7 +86,7 @@ The physical interpretation is that `A₀` and `A₁` are a pair of boolean obse
 are spacelike separated from another pair `B₀` and `B₁` of boolean observables.
 -/
 @[nolint has_nonempty_instance]
-structure IsCHSHTuple {R} [Monoid R] [StarSemigroup R] (A₀ A₁ B₀ B₁ : R) where
+structure IsCHSHTuple {R} [Monoid R] [StarMul R] (A₀ A₁ B₀ B₁ : R) where
   A₀_inv : A₀ ^ 2 = 1
   A₁_inv : A₁ ^ 2 = 1
   B₀_inv : B₀ ^ 2 = 1

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) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module algebra.star.chsh
-! leanprover-community/mathlib commit 31c24aa72e7b3e5ed97a8412470e904f82b81004
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.CharP.Invertible
 import Mathbin.Data.Real.Sqrt
 
+#align_import algebra.star.chsh from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"
+
 /-!
 # The Clauser-Horne-Shimony-Holt inequality and Tsirelson's inequality.

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -107,6 +107,7 @@ structure IsCHSHTuple {R} [Monoid R] [StarSemigroup R] (A₀ A₁ B₀ B₁ : R)
 
 variable {R : Type u}
 
+#print CHSH_id /-
 theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1) (A₁_inv : A₁ ^ 2 = 1)
     (B₀_inv : B₀ ^ 2 = 1) (B₁_inv : B₁ ^ 2 = 1) :
     (2 - A₀ * B₀ - A₀ * B₁ - A₁ * B₀ + A₁ * B₁) * (2 - A₀ * B₀ - A₀ * B₁ - A₁ * B₀ + A₁ * B₁) =
@@ -122,7 +123,9 @@ theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1)
       mul_one, add_right_neg, add_zero, sub_eq_add_neg, A₀_inv, mul_one, add_right_neg,
       MulZeroClass.zero_mul]
 #align CHSH_id CHSH_id
+-/
 
+#print CHSH_inequality_of_comm /-
 /-- Given a CHSH tuple (A₀, A₁, B₀, B₁) in a *commutative* ordered `*`-algebra over ℝ,
 `A₀ * B₀ + A₀ * B₁ + A₁ * B₀ - A₁ * B₁ ≤ 2`.
 
@@ -158,6 +161,7 @@ theorem CHSH_inequality_of_comm [OrderedCommRing R] [StarOrderedRing R] [Algebra
   apply le_of_sub_nonneg
   simpa only [sub_add_eq_sub_sub, ← sub_add] using i₁
 #align CHSH_inequality_of_comm CHSH_inequality_of_comm
+-/
 
 /-!
 We now prove some rather specialized lemmas in preparation for the Tsirelson inequality,
@@ -165,7 +169,6 @@ which we hide in a namespace as they are unlikely to be useful elsewhere.
 -/
 
 
--- mathport name: «expr√2»
 local notation "√2" => (Real.sqrt 2 : ℝ)
 
 namespace tsirelson_inequality
@@ -176,6 +179,7 @@ we prepare some easy lemmas about √2.
 -/
 
 
+#print TsirelsonInequality.tsirelson_inequality_aux /-
 -- This calculation, which we need for Tsirelson's bound,
 -- defeated me. Thanks for the rescue from Shing Tak Lam!
 theorem tsirelson_inequality_aux : √2 * √2 ^ 3 = √2 * (2 * √2⁻¹ + 4 * (√2⁻¹ * 2⁻¹)) :=
@@ -184,14 +188,18 @@ theorem tsirelson_inequality_aux : √2 * √2 ^ 3 = √2 * (2 * √2⁻¹ + 4 *
   convert congr_arg (· ^ 2) (@Real.sq_sqrt 2 (by norm_num)) using 1 <;> simp only [← pow_mul] <;>
     norm_num
 #align tsirelson_inequality.tsirelson_inequality_aux TsirelsonInequality.tsirelson_inequality_aux
+-/
 
+#print TsirelsonInequality.sqrt_two_inv_mul_self /-
 theorem sqrt_two_inv_mul_self : √2⁻¹ * √2⁻¹ = (2⁻¹ : ℝ) := by rw [← mul_inv]; norm_num
 #align tsirelson_inequality.sqrt_two_inv_mul_self TsirelsonInequality.sqrt_two_inv_mul_self
+-/
 
 end tsirelson_inequality
 
 open tsirelson_inequality
 
+#print tsirelson_inequality /-
 /-- In a noncommutative ordered `*`-algebra over ℝ,
 Tsirelson's bound for a CHSH tuple (A₀, A₁, B₀, B₁) is
 `A₀ * B₀ + A₀ * B₁ + A₁ * B₀ - A₁ * B₁ ≤ 2^(3/2) • 1`.
@@ -261,4 +269,5 @@ theorem tsirelson_inequality [OrderedRing R] [StarOrderedRing R] [Algebra ℝ R]
   apply le_of_sub_nonneg
   simpa only [sub_add_eq_sub_sub, ← sub_add, w] using Pos
 #align tsirelson_inequality tsirelson_inequality
+-/

bump to nightly-2023-06-08-03

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

8f04dc2b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module algebra.star.chsh
-! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
+! leanprover-community/mathlib commit 31c24aa72e7b3e5ed97a8412470e904f82b81004
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -151,7 +151,7 @@ theorem CHSH_inequality_of_comm [OrderedCommRing R] [StarOrderedRing R] [Algebra
       skip
       congr
       rw [← sa]
-    convert smul_le_smul_of_nonneg (star_mul_self_nonneg : 0 ≤ star P * P) _
+    convert smul_le_smul_of_nonneg (star_mul_self_nonneg P) _
     · simp
     · infer_instance
     · norm_num
@@ -245,7 +245,7 @@ theorem tsirelson_inequality [OrderedRing R] [StarOrderedRing R] [Algebra ℝ R]
         skip
         congr
         rw [← P_sa]
-      convert (star_mul_self_nonneg : 0 ≤ star P * P)
+      convert star_mul_self_nonneg P
     have Q2_nonneg : 0 ≤ Q ^ 2 := by
       rw [sq]
       conv =>
@@ -253,7 +253,7 @@ theorem tsirelson_inequality [OrderedRing R] [StarOrderedRing R] [Algebra ℝ R]
         skip
         congr
         rw [← Q_sa]
-      convert (star_mul_self_nonneg : 0 ≤ star Q * Q)
+      convert star_mul_self_nonneg Q
     convert
       smul_le_smul_of_nonneg (add_nonneg P2_nonneg Q2_nonneg) (le_of_lt (show 0 < √2⁻¹ by norm_num))
     -- `norm_num` can't directly show `0 ≤ √2⁻¹`

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -245,7 +245,7 @@ theorem tsirelson_inequality [OrderedRing R] [StarOrderedRing R] [Algebra ℝ R]
         skip
         congr
         rw [← P_sa]
-      convert(star_mul_self_nonneg : 0 ≤ star P * P)
+      convert (star_mul_self_nonneg : 0 ≤ star P * P)
     have Q2_nonneg : 0 ≤ Q ^ 2 := by
       rw [sq]
       conv =>
@@ -253,9 +253,9 @@ theorem tsirelson_inequality [OrderedRing R] [StarOrderedRing R] [Algebra ℝ R]
         skip
         congr
         rw [← Q_sa]
-      convert(star_mul_self_nonneg : 0 ≤ star Q * Q)
-    convert smul_le_smul_of_nonneg (add_nonneg P2_nonneg Q2_nonneg)
-        (le_of_lt (show 0 < √2⁻¹ by norm_num))
+      convert (star_mul_self_nonneg : 0 ≤ star Q * Q)
+    convert
+      smul_le_smul_of_nonneg (add_nonneg P2_nonneg Q2_nonneg) (le_of_lt (show 0 < √2⁻¹ by norm_num))
     -- `norm_num` can't directly show `0 ≤ √2⁻¹`
     simp
   apply le_of_sub_nonneg

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -107,9 +107,6 @@ structure IsCHSHTuple {R} [Monoid R] [StarSemigroup R] (A₀ A₁ B₀ B₁ : R)
 
 variable {R : Type u}
 
-/- warning: CHSH_id -> CHSH_id is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align CHSH_id CHSH_idₓ'. -/
 theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1) (A₁_inv : A₁ ^ 2 = 1)
     (B₀_inv : B₀ ^ 2 = 1) (B₁_inv : B₁ ^ 2 = 1) :
     (2 - A₀ * B₀ - A₀ * B₁ - A₁ * B₀ + A₁ * B₁) * (2 - A₀ * B₀ - A₀ * B₁ - A₁ * B₀ + A₁ * B₁) =
@@ -126,12 +123,6 @@ theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1)
       MulZeroClass.zero_mul]
 #align CHSH_id CHSH_id
 
-/- warning: CHSH_inequality_of_comm -> CHSH_inequality_of_comm is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : OrderedCommRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))] [_inst_3 : Algebra.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.monoidWithZero (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_3)))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (Ring.toMonoid.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toHasLe.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₁ B₁)) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : OrderedCommRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))] [_inst_3 : Algebra.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.instMonoidWithZeroReal (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (Algebra.toModule.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))) _inst_3)))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))))) (StarRing.toStarSemigroup.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₁ B₁)) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (Semiring.toNatCast.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
-Case conversion may be inaccurate. Consider using '#align CHSH_inequality_of_comm CHSH_inequality_of_commₓ'. -/
 /-- Given a CHSH tuple (A₀, A₁, B₀, B₁) in a *commutative* ordered `*`-algebra over ℝ,
 `A₀ * B₀ + A₀ * B₁ + A₁ * B₀ - A₁ * B₁ ≤ 2`.
 
@@ -185,12 +176,6 @@ we prepare some easy lemmas about √2.
 -/
 
 
-/- warning: tsirelson_inequality.tsirelson_inequality_aux -> TsirelsonInequality.tsirelson_inequality_aux is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align tsirelson_inequality.tsirelson_inequality_aux TsirelsonInequality.tsirelson_inequality_auxₓ'. -/
 -- This calculation, which we need for Tsirelson's bound,
 -- defeated me. Thanks for the rescue from Shing Tak Lam!
 theorem tsirelson_inequality_aux : √2 * √2 ^ 3 = √2 * (2 * √2⁻¹ + 4 * (√2⁻¹ * 2⁻¹)) :=
@@ -200,12 +185,6 @@ theorem tsirelson_inequality_aux : √2 * √2 ^ 3 = √2 * (2 * √2⁻¹ + 4 *
     norm_num
 #align tsirelson_inequality.tsirelson_inequality_aux TsirelsonInequality.tsirelson_inequality_aux
 
-/- warning: tsirelson_inequality.sqrt_two_inv_mul_self -> TsirelsonInequality.sqrt_two_inv_mul_self is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Inv.inv.{0} Real Real.hasInv (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (Inv.inv.{0} Real Real.hasInv (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (Inv.inv.{0} Real Real.hasInv (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))
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-  Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Inv.inv.{0} Real Real.instInvReal (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Inv.inv.{0} Real Real.instInvReal (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Inv.inv.{0} Real Real.instInvReal (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
-Case conversion may be inaccurate. Consider using '#align tsirelson_inequality.sqrt_two_inv_mul_self TsirelsonInequality.sqrt_two_inv_mul_selfₓ'. -/
 theorem sqrt_two_inv_mul_self : √2⁻¹ * √2⁻¹ = (2⁻¹ : ℝ) := by rw [← mul_inv]; norm_num
 #align tsirelson_inequality.sqrt_two_inv_mul_self TsirelsonInequality.sqrt_two_inv_mul_self
 
@@ -213,9 +192,6 @@ end tsirelson_inequality
 
 open tsirelson_inequality
 
-/- warning: tsirelson_inequality -> tsirelson_inequality is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tsirelson_inequality tsirelson_inequalityₓ'. -/
 /-- In a noncommutative ordered `*`-algebra over ℝ,
 Tsirelson's bound for a CHSH tuple (A₀, A₁, B₀, B₁) is
 `A₀ * B₀ + A₀ * B₁ + A₁ * B₀ - A₁ * B₁ ≤ 2^(3/2) • 1`.

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -206,10 +206,7 @@ lean 3 declaration is
 but is expected to have type
   Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Inv.inv.{0} Real Real.instInvReal (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Inv.inv.{0} Real Real.instInvReal (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Inv.inv.{0} Real Real.instInvReal (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
 Case conversion may be inaccurate. Consider using '#align tsirelson_inequality.sqrt_two_inv_mul_self TsirelsonInequality.sqrt_two_inv_mul_selfₓ'. -/
-theorem sqrt_two_inv_mul_self : √2⁻¹ * √2⁻¹ = (2⁻¹ : ℝ) :=
-  by
-  rw [← mul_inv]
-  norm_num
+theorem sqrt_two_inv_mul_self : √2⁻¹ * √2⁻¹ = (2⁻¹ : ℝ) := by rw [← mul_inv]; norm_num
 #align tsirelson_inequality.sqrt_two_inv_mul_self TsirelsonInequality.sqrt_two_inv_mul_self
 
 end tsirelson_inequality

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -108,10 +108,7 @@ structure IsCHSHTuple {R} [Monoid R] [StarSemigroup R] (A₀ A₁ B₀ B₁ : R)
 variable {R : Type u}
 
 /- warning: CHSH_id -> CHSH_id is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align CHSH_id CHSH_idₓ'. -/
 theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1) (A₁_inv : A₁ ^ 2 = 1)
     (B₀_inv : B₀ ^ 2 = 1) (B₁_inv : B₁ ^ 2 = 1) :
@@ -220,10 +217,7 @@ end tsirelson_inequality
 open tsirelson_inequality
 
 /- warning: tsirelson_inequality -> tsirelson_inequality is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : OrderedRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1))] [_inst_3 : Algebra.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.monoidWithZero (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) _inst_3)))] [_inst_5 : StarModule.{0, u1} Real R (InvolutiveStar.toHasStar.{0} Real (StarAddMonoid.toHasInvolutiveStar.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing)))))) (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.starRing))) (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2)))) (SMulZeroClass.toHasSmul.{0, u1} Real R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real R (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (Module.toMulActionWithZero.{0, u1} Real R (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) _inst_3)))))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (Ring.toMonoid.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toHasLe.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₁ B₁)) (SMul.smul.{0, u1} Real R (SMulZeroClass.toHasSmul.{0, u1} Real R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real R (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (Module.toMulActionWithZero.{0, u1} Real R (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) _inst_3))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : OrderedRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))) (OrderedRing.toPartialOrder.{u1} R _inst_1)] [_inst_3 : Algebra.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.instMonoidWithZeroReal (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1))) (Algebra.toModule.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) _inst_3)))] [_inst_5 : StarModule.{0, u1} Real R (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalCommSemiring.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalCommSemiring.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing))) (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))) (OrderedRing.toPartialOrder.{u1} R _inst_1) _inst_2)))) (Algebra.toSMul.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) _inst_3)] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)))) (StarRing.toStarSemigroup.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))) (OrderedRing.toPartialOrder.{u1} R _inst_1) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedRing.toPartialOrder.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₁ B₁)) (HSMul.hSMul.{0, u1, u1} Real R R (instHSMul.{0, u1} Real R (Algebra.toSMul.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) _inst_3)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align tsirelson_inequality tsirelson_inequalityₓ'. -/
 /-- In a noncommutative ordered `*`-algebra over ℝ,
 Tsirelson's bound for a CHSH tuple (A₀, A₁, B₀, B₁) is

bump to nightly-2023-05-16-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

9cb92e8c

Diff

@@ -131,7 +131,7 @@ theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1)
 
 /- warning: CHSH_inequality_of_comm -> CHSH_inequality_of_comm is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : OrderedCommRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))] [_inst_3 : Algebra.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.monoidWithZero (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_3)))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (Ring.toMonoid.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₁ B₁)) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))))))
+  forall {R : Type.{u1}} [_inst_1 : OrderedCommRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))] [_inst_3 : Algebra.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.monoidWithZero (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_3)))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (Ring.toMonoid.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toHasLe.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₁ B₁)) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : OrderedCommRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))] [_inst_3 : Algebra.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.instMonoidWithZeroReal (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (Algebra.toModule.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))) _inst_3)))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))))) (StarRing.toStarSemigroup.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₁ B₁)) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (Semiring.toNatCast.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
 Case conversion may be inaccurate. Consider using '#align CHSH_inequality_of_comm CHSH_inequality_of_commₓ'. -/
@@ -221,7 +221,7 @@ open tsirelson_inequality
 
 /- warning: tsirelson_inequality -> tsirelson_inequality is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : OrderedRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1))] [_inst_3 : Algebra.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.monoidWithZero (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) _inst_3)))] [_inst_5 : StarModule.{0, u1} Real R (InvolutiveStar.toHasStar.{0} Real (StarAddMonoid.toHasInvolutiveStar.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing)))))) (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.starRing))) (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2)))) (SMulZeroClass.toHasSmul.{0, u1} Real R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real R (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (Module.toMulActionWithZero.{0, u1} Real R (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) _inst_3)))))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (Ring.toMonoid.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₁ B₁)) (SMul.smul.{0, u1} Real R (SMulZeroClass.toHasSmul.{0, u1} Real R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real R (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (Module.toMulActionWithZero.{0, u1} Real R (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) _inst_3))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))))))
+  forall {R : Type.{u1}} [_inst_1 : OrderedRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1))] [_inst_3 : Algebra.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.monoidWithZero (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) _inst_3)))] [_inst_5 : StarModule.{0, u1} Real R (InvolutiveStar.toHasStar.{0} Real (StarAddMonoid.toHasInvolutiveStar.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing)))))) (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.starRing))) (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2)))) (SMulZeroClass.toHasSmul.{0, u1} Real R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real R (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (Module.toMulActionWithZero.{0, u1} Real R (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) _inst_3)))))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (Ring.toMonoid.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toHasLe.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₁ B₁)) (SMul.smul.{0, u1} Real R (SMulZeroClass.toHasSmul.{0, u1} Real R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real R (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (Module.toMulActionWithZero.{0, u1} Real R (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) _inst_3))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : OrderedRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))) (OrderedRing.toPartialOrder.{u1} R _inst_1)] [_inst_3 : Algebra.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.instMonoidWithZeroReal (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1))) (Algebra.toModule.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) _inst_3)))] [_inst_5 : StarModule.{0, u1} Real R (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalCommSemiring.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalCommSemiring.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing))) (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))) (OrderedRing.toPartialOrder.{u1} R _inst_1) _inst_2)))) (Algebra.toSMul.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) _inst_3)] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)))) (StarRing.toStarSemigroup.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))) (OrderedRing.toPartialOrder.{u1} R _inst_1) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedRing.toPartialOrder.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₁ B₁)) (HSMul.hSMul.{0, u1, u1} Real R R (instHSMul.{0, u1} Real R (Algebra.toSMul.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) _inst_3)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align tsirelson_inequality tsirelson_inequalityₓ'. -/

bump to nightly-2023-05-08-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

63e712c6

Diff

@@ -111,7 +111,7 @@ variable {R : Type u}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {A₀ : R} {A₁ : R} {B₀ : R} {B₁ : R}, (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) A₀ (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) A₁ (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) B₀ (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) B₁ (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) A₀ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) A₁ B₁)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) A₀ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) A₁ B₁))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 4 (OfNat.mk.{u1} R 4 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) A₀ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) A₁ B₁))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {A₀ : R} {A₁ : R} {B₀ : R} {B₁ : R}, (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) A₀ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) A₁ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) B₀ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) B₁ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₀ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₁ B₁)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₀ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₁ B₁))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 4 (instOfNat.{u1} R 4 (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₀ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₁ B₁))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {A₀ : R} {A₁ : R} {B₀ : R} {B₁ : R}, (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) A₀ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) A₁ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) B₀ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) B₁ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₀ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₁ B₁)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₀ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₁ B₁))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 4 (instOfNat.{u1} R 4 (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₀ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₁ B₁))))
 Case conversion may be inaccurate. Consider using '#align CHSH_id CHSH_idₓ'. -/
 theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1) (A₁_inv : A₁ ^ 2 = 1)
     (B₀_inv : B₀ ^ 2 = 1) (B₁_inv : B₁ ^ 2 = 1) :
@@ -133,7 +133,7 @@ theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : OrderedCommRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))] [_inst_3 : Algebra.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.monoidWithZero (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_3)))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (Ring.toMonoid.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₁ B₁)) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : OrderedCommRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))] [_inst_3 : Algebra.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.instMonoidWithZeroReal (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (Algebra.toModule.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))) _inst_3)))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))))) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₁ B₁)) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+  forall {R : Type.{u1}} [_inst_1 : OrderedCommRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))] [_inst_3 : Algebra.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.instMonoidWithZeroReal (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (Algebra.toModule.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))) _inst_3)))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))))) (StarRing.toStarSemigroup.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₁ B₁)) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (Semiring.toNatCast.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
 Case conversion may be inaccurate. Consider using '#align CHSH_inequality_of_comm CHSH_inequality_of_commₓ'. -/
 /-- Given a CHSH tuple (A₀, A₁, B₀, B₁) in a *commutative* ordered `*`-algebra over ℝ,
 `A₀ * B₀ + A₀ * B₁ + A₁ * B₀ - A₁ * B₁ ≤ 2`.
@@ -223,7 +223,7 @@ open tsirelson_inequality
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : OrderedRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1))] [_inst_3 : Algebra.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.monoidWithZero (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) _inst_3)))] [_inst_5 : StarModule.{0, u1} Real R (InvolutiveStar.toHasStar.{0} Real (StarAddMonoid.toHasInvolutiveStar.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing)))))) (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.starRing))) (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2)))) (SMulZeroClass.toHasSmul.{0, u1} Real R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real R (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (Module.toMulActionWithZero.{0, u1} Real R (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) _inst_3)))))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (Ring.toMonoid.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₁ B₁)) (SMul.smul.{0, u1} Real R (SMulZeroClass.toHasSmul.{0, u1} Real R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real R (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (Module.toMulActionWithZero.{0, u1} Real R (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) _inst_3))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : OrderedRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedRing.toPartialOrder.{u1} R _inst_1)] [_inst_3 : Algebra.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.instMonoidWithZeroReal (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1))) (Algebra.toModule.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) _inst_3)))] [_inst_5 : StarModule.{0, u1} Real R (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedRing.toPartialOrder.{u1} R _inst_1) _inst_2)))) (Algebra.toSMul.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) _inst_3)] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)))) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedRing.toPartialOrder.{u1} R _inst_1) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedRing.toPartialOrder.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₁ B₁)) (HSMul.hSMul.{0, u1, u1} Real R R (instHSMul.{0, u1} Real R (Algebra.toSMul.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) _inst_3)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))
+  forall {R : Type.{u1}} [_inst_1 : OrderedRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))) (OrderedRing.toPartialOrder.{u1} R _inst_1)] [_inst_3 : Algebra.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.instMonoidWithZeroReal (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1))) (Algebra.toModule.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) _inst_3)))] [_inst_5 : StarModule.{0, u1} Real R (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalCommSemiring.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalCommSemiring.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing))) (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))) (OrderedRing.toPartialOrder.{u1} R _inst_1) _inst_2)))) (Algebra.toSMul.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) _inst_3)] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)))) (StarRing.toStarSemigroup.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))) (OrderedRing.toPartialOrder.{u1} R _inst_1) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedRing.toPartialOrder.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₁ B₁)) (HSMul.hSMul.{0, u1, u1} Real R R (instHSMul.{0, u1} Real R (Algebra.toSMul.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) _inst_3)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align tsirelson_inequality tsirelson_inequalityₓ'. -/
 /-- In a noncommutative ordered `*`-algebra over ℝ,
 Tsirelson's bound for a CHSH tuple (A₀, A₁, B₀, B₁) is

bump to nightly-2023-04-27-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd

c8f7a684

Diff

@@ -133,7 +133,7 @@ theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : OrderedCommRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))] [_inst_3 : Algebra.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.monoidWithZero (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_3)))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (Ring.toMonoid.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₁ B₁)) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : OrderedCommRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))] [_inst_3 : Algebra.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.instMonoidWithZeroReal (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{0, u1} Real R Real.instCommSemiringReal (OrderedCommRing.toCommRing.{u1} R _inst_1) _inst_3)))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))))) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₁ B₁)) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+  forall {R : Type.{u1}} [_inst_1 : OrderedCommRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))] [_inst_3 : Algebra.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.instMonoidWithZeroReal (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (Algebra.toModule.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))) _inst_3)))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))))) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₁ B₁)) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
 Case conversion may be inaccurate. Consider using '#align CHSH_inequality_of_comm CHSH_inequality_of_commₓ'. -/
 /-- Given a CHSH tuple (A₀, A₁, B₀, B₁) in a *commutative* ordered `*`-algebra over ℝ,
 `A₀ * B₀ + A₀ * B₁ + A₁ * B₀ - A₁ * B₁ ≤ 2`.

bump to nightly-2023-04-04-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

2ee17135

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module algebra.star.chsh
-! leanprover-community/mathlib commit 468b141b14016d54b479eb7a0fff1e360b7e3cf6
+! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Data.Real.Sqrt
 /-!
 # The Clauser-Horne-Shimony-Holt inequality and Tsirelson's inequality.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We establish a version of the Clauser-Horne-Shimony-Holt (CHSH) inequality
 (which is a generalization of Bell's inequality).
 This is a foundational result which implies that

bump to nightly-2023-03-28-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/728baa2f54e6062c5879a3e397ac6bac323e506f

c7ebe29d

Diff

@@ -78,6 +78,7 @@ There is a CHSH tuple in 4-by-4 matrices such that
 
 universe u
 
+#print IsCHSHTuple /-
 /-- A CHSH tuple in a *-monoid consists of 4 self-adjoint involutions `A₀ A₁ B₀ B₁` such that
 the `Aᵢ` commute with the `Bⱼ`.
 
@@ -99,9 +100,16 @@ structure IsCHSHTuple {R} [Monoid R] [StarSemigroup R] (A₀ A₁ B₀ B₁ : R)
   A₁B₀_commutes : A₁ * B₀ = B₀ * A₁
   A₁B₁_commutes : A₁ * B₁ = B₁ * A₁
 #align is_CHSH_tuple IsCHSHTuple
+-/
 
 variable {R : Type u}
 
+/- warning: CHSH_id -> CHSH_id is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₀ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) A₁ B₁))))
+Case conversion may be inaccurate. Consider using '#align CHSH_id CHSH_idₓ'. -/
 theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1) (A₁_inv : A₁ ^ 2 = 1)
     (B₀_inv : B₀ ^ 2 = 1) (B₁_inv : B₁ ^ 2 = 1) :
     (2 - A₀ * B₀ - A₀ * B₁ - A₁ * B₀ + A₁ * B₁) * (2 - A₀ * B₀ - A₀ * B₁ - A₁ * B₀ + A₁ * B₁) =
@@ -118,6 +126,12 @@ theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1)
       MulZeroClass.zero_mul]
 #align CHSH_id CHSH_id
 
+/- warning: CHSH_inequality_of_comm -> CHSH_inequality_of_comm is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : OrderedCommRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))] [_inst_3 : Algebra.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.monoidWithZero (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_3)))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (Ring.toMonoid.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))) _inst_2)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))))) A₁ B₁)) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : OrderedCommRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1))] [_inst_3 : Algebra.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.instMonoidWithZeroReal (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{0, u1} Real R Real.instCommSemiringReal (OrderedCommRing.toCommRing.{u1} R _inst_1) _inst_3)))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (OrderedCommRing.toOrderedCommSemiring.{u1} R _inst_1))))) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (OrderedCommRing.toCommRing.{u1} R _inst_1)))) (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedRing.toPartialOrder.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))))) A₁ B₁)) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R (OrderedCommRing.toOrderedRing.{u1} R _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+Case conversion may be inaccurate. Consider using '#align CHSH_inequality_of_comm CHSH_inequality_of_commₓ'. -/
 /-- Given a CHSH tuple (A₀, A₁, B₀, B₁) in a *commutative* ordered `*`-algebra over ℝ,
 `A₀ * B₀ + A₀ * B₁ + A₁ * B₀ - A₁ * B₁ ≤ 2`.
 
@@ -171,6 +185,12 @@ we prepare some easy lemmas about √2.
 -/
 
 
+/- warning: tsirelson_inequality.tsirelson_inequality_aux -> TsirelsonInequality.tsirelson_inequality_aux is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align tsirelson_inequality.tsirelson_inequality_aux TsirelsonInequality.tsirelson_inequality_auxₓ'. -/
 -- This calculation, which we need for Tsirelson's bound,
 -- defeated me. Thanks for the rescue from Shing Tak Lam!
 theorem tsirelson_inequality_aux : √2 * √2 ^ 3 = √2 * (2 * √2⁻¹ + 4 * (√2⁻¹ * 2⁻¹)) :=
@@ -180,6 +200,12 @@ theorem tsirelson_inequality_aux : √2 * √2 ^ 3 = √2 * (2 * √2⁻¹ + 4 *
     norm_num
 #align tsirelson_inequality.tsirelson_inequality_aux TsirelsonInequality.tsirelson_inequality_aux
 
+/- warning: tsirelson_inequality.sqrt_two_inv_mul_self -> TsirelsonInequality.sqrt_two_inv_mul_self is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Inv.inv.{0} Real Real.hasInv (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (Inv.inv.{0} Real Real.hasInv (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (Inv.inv.{0} Real Real.hasInv (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))
+but is expected to have type
+  Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Inv.inv.{0} Real Real.instInvReal (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Inv.inv.{0} Real Real.instInvReal (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Inv.inv.{0} Real Real.instInvReal (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+Case conversion may be inaccurate. Consider using '#align tsirelson_inequality.sqrt_two_inv_mul_self TsirelsonInequality.sqrt_two_inv_mul_selfₓ'. -/
 theorem sqrt_two_inv_mul_self : √2⁻¹ * √2⁻¹ = (2⁻¹ : ℝ) :=
   by
   rw [← mul_inv]
@@ -190,6 +216,12 @@ end tsirelson_inequality
 
 open tsirelson_inequality
 
+/- warning: tsirelson_inequality -> tsirelson_inequality is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : OrderedRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1))] [_inst_3 : Algebra.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.monoidWithZero (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) _inst_3)))] [_inst_5 : StarModule.{0, u1} Real R (InvolutiveStar.toHasStar.{0} Real (StarAddMonoid.toHasInvolutiveStar.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing)))))) (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.starRing))) (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2)))) (SMulZeroClass.toHasSmul.{0, u1} Real R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real R (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (Module.toMulActionWithZero.{0, u1} Real R (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) _inst_3)))))] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (Ring.toMonoid.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) (OrderedAddCommGroup.toPartialOrder.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1)) _inst_2)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) A₁ B₁)) (SMul.smul.{0, u1} Real R (SMulZeroClass.toHasSmul.{0, u1} Real R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real R (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real R (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))) (Module.toMulActionWithZero.{0, u1} Real R (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) (Algebra.toModule.{0, u1} Real R Real.commSemiring (Ring.toSemiring.{u1} R (OrderedRing.toRing.{u1} R _inst_1)) _inst_3))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : OrderedRing.{u1} R] [_inst_2 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedRing.toPartialOrder.{u1} R _inst_1)] [_inst_3 : Algebra.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))] [_inst_4 : OrderedSMul.{0, u1} Real R Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) (MulActionWithZero.toSMulWithZero.{0, u1} Real R Real.instMonoidWithZeroReal (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedAddCommMonoid.toAddCommMonoid.{u1} R (OrderedSemiring.toOrderedAddCommMonoid.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real R Real.semiring (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} R (OrderedRing.toOrderedAddCommGroup.{u1} R _inst_1))) (Algebra.toModule.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) _inst_3)))] [_inst_5 : StarModule.{0, u1} Real R (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedRing.toPartialOrder.{u1} R _inst_1) _inst_2)))) (Algebra.toSMul.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) _inst_3)] (A₀ : R) (A₁ : R) (B₀ : R) (B₁ : R), (IsCHSHTuple.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)))) (StarRing.toStarSemigroup.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (OrderedRing.toPartialOrder.{u1} R _inst_1) _inst_2)) A₀ A₁ B₀ B₁) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedRing.toPartialOrder.{u1} R _inst_1))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (OrderedRing.toRing.{u1} R _inst_1))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₀ B₀) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₀ B₁)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₁ B₀)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1))))) A₁ B₁)) (HSMul.hSMul.{0, u1, u1} Real R R (instHSMul.{0, u1} Real R (Algebra.toSMul.{0, u1} Real R Real.instCommSemiringReal (OrderedSemiring.toSemiring.{u1} R (OrderedRing.toOrderedSemiring.{u1} R _inst_1)) _inst_3)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (OrderedRing.toRing.{u1} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align tsirelson_inequality tsirelson_inequalityₓ'. -/
 /-- In a noncommutative ordered `*`-algebra over ℝ,
 Tsirelson's bound for a CHSH tuple (A₀, A₁, B₀, B₁) is
 `A₀ * B₀ + A₀ * B₁ + A₁ * B₀ - A₁ * B₁ ≤ 2^(3/2) • 1`.

bump to nightly-2023-03-17-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

c85864d4

Diff

@@ -243,7 +243,7 @@ theorem tsirelson_inequality [OrderedRing R] [StarOrderedRing R] [Algebra ℝ R]
         skip
         congr
         rw [← P_sa]
-      convert (star_mul_self_nonneg : 0 ≤ star P * P)
+      convert(star_mul_self_nonneg : 0 ≤ star P * P)
     have Q2_nonneg : 0 ≤ Q ^ 2 := by
       rw [sq]
       conv =>
@@ -251,9 +251,9 @@ theorem tsirelson_inequality [OrderedRing R] [StarOrderedRing R] [Algebra ℝ R]
         skip
         congr
         rw [← Q_sa]
-      convert (star_mul_self_nonneg : 0 ≤ star Q * Q)
-    convert
-      smul_le_smul_of_nonneg (add_nonneg P2_nonneg Q2_nonneg) (le_of_lt (show 0 < √2⁻¹ by norm_num))
+      convert(star_mul_self_nonneg : 0 ≤ star Q * Q)
+    convert smul_le_smul_of_nonneg (add_nonneg P2_nonneg Q2_nonneg)
+        (le_of_lt (show 0 < √2⁻¹ by norm_num))
     -- `norm_num` can't directly show `0 ≤ √2⁻¹`
     simp
   apply le_of_sub_nonneg

bump to nightly-2023-03-11-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

cd44fb92

Diff

@@ -114,7 +114,8 @@ theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1)
     ring_nf
     simp only [A₁_inv, B₁_inv, sub_eq_add_neg, add_mul, mul_add, sub_mul, mul_sub, add_assoc,
       neg_add, neg_sub, sub_add, sub_sub, neg_mul, ← sq, A₀_inv, B₀_inv, ← sq, ← mul_assoc, one_mul,
-      mul_one, add_right_neg, add_zero, sub_eq_add_neg, A₀_inv, mul_one, add_right_neg, zero_mul]
+      mul_one, add_right_neg, add_zero, sub_eq_add_neg, A₀_inv, mul_one, add_right_neg,
+      MulZeroClass.zero_mul]
 #align CHSH_id CHSH_id
 
 /-- Given a CHSH tuple (A₀, A₁, B₀, B₁) in a *commutative* ordered `*`-algebra over ℝ,

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

feat: add notation for Real.sqrt (#12056)

This adds the notation √r for Real.sqrt r. The precedence is such that √x⁻¹ is parsed as √(x⁻¹); not because this is particularly desirable, but because it's the default and the choice doesn't really matter.

This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing x.sqrt as that PR does.

While perhaps claiming √ for Real.sqrt is greedy; it:

Is far more common thatn NNReal.sqrt and Nat.sqrt
Is far more interesting to mathlib than sqrt on Float
Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types.
Will be replaced by a more general typeclass in a future PR.

Zulip

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

8640948c

Diff

@@ -145,8 +145,6 @@ which we hide in a namespace as they are unlikely to be useful elsewhere.
 -/
 
 
-local notation "√2" => (Real.sqrt 2 : ℝ)
-
 namespace TsirelsonInequality
 
 /-!
@@ -157,14 +155,14 @@ we prepare some easy lemmas about √2.
 
 -- This calculation, which we need for Tsirelson's bound,
 -- defeated me. Thanks for the rescue from Shing Tak Lam!
-theorem tsirelson_inequality_aux : √2 * √2 ^ 3 = √2 * (2 * √2⁻¹ + 4 * (√2⁻¹ * 2⁻¹)) := by
+theorem tsirelson_inequality_aux : √2 * √2 ^ 3 = √2 * (2 * (√2)⁻¹ + 4 * ((√2)⁻¹ * 2⁻¹)) := by
   ring_nf
   rw [mul_inv_cancel (ne_of_gt (Real.sqrt_pos.2 (show (2 : ℝ) > 0 by norm_num)))]
   convert congr_arg (· ^ 2) (@Real.sq_sqrt 2 (by norm_num)) using 1 <;>
     (try simp only [← pow_mul]) <;> norm_num
 #align tsirelson_inequality.tsirelson_inequality_aux TsirelsonInequality.tsirelson_inequality_aux
 
-theorem sqrt_two_inv_mul_self : √2⁻¹ * √2⁻¹ = (2⁻¹ : ℝ) := by
+theorem sqrt_two_inv_mul_self : (√2)⁻¹ * (√2)⁻¹ = (2⁻¹ : ℝ) := by
   rw [← mul_inv]
   norm_num
 #align tsirelson_inequality.sqrt_two_inv_mul_self TsirelsonInequality.sqrt_two_inv_mul_self
@@ -188,9 +186,9 @@ theorem tsirelson_inequality [OrderedRing R] [StarRing R] [StarOrderedRing R] [A
   -- abel will create `ℤ` multiplication. We will `simp` them away to `ℝ` multiplication.
   have M : ∀ (m : ℤ) (a : ℝ) (x : R), m • a • x = ((m : ℝ) * a) • x := fun m a x => by
     rw [zsmul_eq_smul_cast ℝ, ← mul_smul]
-  let P := √2⁻¹ • (A₁ + A₀) - B₀
-  let Q := √2⁻¹ • (A₁ - A₀) + B₁
-  have w : √2 ^ 3 • (1 : R) - A₀ * B₀ - A₀ * B₁ - A₁ * B₀ + A₁ * B₁ = √2⁻¹ • (P ^ 2 + Q ^ 2) := by
+  let P := (√2)⁻¹ • (A₁ + A₀) - B₀
+  let Q := (√2)⁻¹ • (A₁ - A₀) + B₁
+  have w : √2 ^ 3 • (1 : R) - A₀ * B₀ - A₀ * B₁ - A₁ * B₀ + A₁ * B₁ = (√2)⁻¹ • (P ^ 2 + Q ^ 2) := by
     dsimp [P, Q]
     -- distribute out all the powers and products appearing on the RHS
     simp only [sq, sub_mul, mul_sub, add_mul, mul_add, smul_add, smul_sub]
@@ -210,7 +208,7 @@ theorem tsirelson_inequality [OrderedRing R] [StarRing R] [StarOrderedRing R] [A
     -- just look at the coefficients now:
     congr
     exact mul_left_cancel₀ (by norm_num) tsirelson_inequality_aux
-  have pos : 0 ≤ √2⁻¹ • (P ^ 2 + Q ^ 2) := by
+  have pos : 0 ≤ (√2)⁻¹ • (P ^ 2 + Q ^ 2) := by
     have P_sa : star P = P := by
       simp only [P, star_smul, star_add, star_sub, star_id_of_comm, T.A₀_sa, T.A₁_sa, T.B₀_sa,
         T.B₁_sa]

chore: classify porting notes referring to missing linters (#12098)

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

c5b5490c

Diff

@@ -82,7 +82,7 @@ the `Aᵢ` commute with the `Bⱼ`.
 The physical interpretation is that `A₀` and `A₁` are a pair of boolean observables which
 are spacelike separated from another pair `B₀` and `B₁` of boolean observables.
 -/
---@[nolint has_nonempty_instance] Porting note: linter does not exist
+--@[nolint has_nonempty_instance] Porting note(#5171): linter not ported yet
 structure IsCHSHTuple {R} [Monoid R] [StarMul R] (A₀ A₁ B₀ B₁ : R) : Prop where
   A₀_inv : A₀ ^ 2 = 1
   A₁_inv : A₁ ^ 2 = 1

chore(Data/Int/Cast): fix confusion between OfNat and Nat.cast lemmas (#11861)

This renames

Int.cast_ofNat to Int.cast_natCast
Int.int_cast_ofNat to Int.cast_ofNat

I think the history here is that this lemma was previously about Int.ofNat, before we globally fixed the simp-normal form to be Nat.cast.

Since the Int.cast_ofNat name is repurposed, it can't be deprecated. Int.int_cast_ofNat is such a wonky name that it was probably never used.

a7ffab83

Diff

@@ -205,7 +205,7 @@ theorem tsirelson_inequality [OrderedRing R] [StarRing R] [StarOrderedRing R] [A
     -- all terms coincide, but the last one. Simplify all other terms
     simp only [M]
     simp only [neg_mul, one_mul, mul_inv_cancel_of_invertible, Int.cast_one, add_assoc, add_comm,
-      add_left_comm, one_smul, Int.cast_neg, neg_smul, Int.int_cast_ofNat]
+      add_left_comm, one_smul, Int.cast_neg, neg_smul, Int.cast_ofNat]
     simp only [← add_assoc, ← add_smul]
     -- just look at the coefficients now:
     congr

chore: remove mathport name: <expression> lines (#11928)

Quoting [@digama0](https://github.com/digama0):

These were actually never meant to go in the file, they are basically debugging information and only useful on significantly broken mathport files. You can safely remove all of them.

11431c65

Diff

@@ -145,7 +145,6 @@ which we hide in a namespace as they are unlikely to be useful elsewhere.
 -/
 
 
--- mathport name: «expr√2»
 local notation "√2" => (Real.sqrt 2 : ℝ)
 
 namespace TsirelsonInequality

feat: make StarOrderedRing a mixin (#11872)

This makes StarOrderedRing take StarRing as a parameter instead of extending it, and as a result moves the typeclass to Prop. It was already a mixin with respect to the order and algebraic structure. There are two primary motivations:

This makes it possible to directly assume that C(α, R) is a StarOrderedRing with [StarOrderedRing C(α, R)], as currently there is no typeclass on R which would naturally guarantee this property. This is relevant as we want this type class on continuous functions for the continuous functional calculus.
We will eventually want a StarOrderedRing instance on C(α, A) where A is a complex (or even real) C⋆-algebra, and making this a mixin avoids loops with StarRing.

bfa88435

Diff

@@ -118,7 +118,7 @@ set_option linter.uppercaseLean3 false in
 
 (We could work over ℤ[⅟2] if we wanted to!)
 -/
-theorem CHSH_inequality_of_comm [OrderedCommRing R] [StarOrderedRing R] [Algebra ℝ R]
+theorem CHSH_inequality_of_comm [OrderedCommRing R] [StarRing R] [StarOrderedRing R] [Algebra ℝ R]
     [OrderedSMul ℝ R] (A₀ A₁ B₀ B₁ : R) (T : IsCHSHTuple A₀ A₁ B₀ B₁) :
     A₀ * B₀ + A₀ * B₁ + A₁ * B₀ - A₁ * B₁ ≤ 2 := by
   let P := 2 - A₀ * B₀ - A₀ * B₁ - A₁ * B₀ + A₁ * B₁
@@ -183,8 +183,8 @@ of the difference.
 
 (We could work over `ℤ[2^(1/2), 2^(-1/2)]` if we really wanted to!)
 -/
-theorem tsirelson_inequality [OrderedRing R] [StarOrderedRing R] [Algebra ℝ R] [OrderedSMul ℝ R]
-    [StarModule ℝ R] (A₀ A₁ B₀ B₁ : R) (T : IsCHSHTuple A₀ A₁ B₀ B₁) :
+theorem tsirelson_inequality [OrderedRing R] [StarRing R] [StarOrderedRing R] [Algebra ℝ R]
+    [OrderedSMul ℝ R] [StarModule ℝ R] (A₀ A₁ B₀ B₁ : R) (T : IsCHSHTuple A₀ A₁ B₀ B₁) :
     A₀ * B₀ + A₀ * B₁ + A₁ * B₀ - A₁ * B₁ ≤ √2 ^ 3 • (1 : R) := by
   -- abel will create `ℤ` multiplication. We will `simp` them away to `ℝ` multiplication.
   have M : ∀ (m : ℤ) (a : ℝ) (x : R), m • a • x = ((m : ℝ) * a) • x := fun m a x => by

feat: use polyrith/linear_combination in Algebra/Star/CHSH (#11211)

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

bbb8984d

Diff

@@ -5,6 +5,7 @@ Authors: Scott Morrison
 -/
 import Mathlib.Algebra.CharP.Invertible
 import Mathlib.Data.Real.Sqrt
+import Mathlib.Tactic.Polyrith
 
 #align_import algebra.star.chsh from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"
 
@@ -104,12 +105,11 @@ theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1)
     (B₀_inv : B₀ ^ 2 = 1) (B₁_inv : B₁ ^ 2 = 1) :
     (2 - A₀ * B₀ - A₀ * B₁ - A₁ * B₀ + A₁ * B₁) * (2 - A₀ * B₀ - A₀ * B₁ - A₁ * B₀ + A₁ * B₁) =
       4 * (2 - A₀ * B₀ - A₀ * B₁ - A₁ * B₀ + A₁ * B₁) := by
-  -- If we had a Gröbner basis algorithm, this would be trivial.
-  -- Without one, it is somewhat tedious!
-  rw [← sub_eq_zero]
-  ring_nf
-  simp_all
-  ring_nf
+  -- polyrith suggests:
+  linear_combination
+    (2 * B₀ * B₁ + 2) * A₀_inv + (B₀ ^ 2 - 2 * B₀ * B₁ + B₁ ^ 2) * A₁_inv +
+        (A₀ ^ 2 + 2 * A₀ * A₁ + 1) * B₀_inv +
+      (A₀ ^ 2 - 2 * A₀ * A₁ + 1) * B₁_inv
 set_option linter.uppercaseLean3 false in
 #align CHSH_id CHSH_id

chore: prepare Lean version bump with explicit simp (#10999)

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

38bce757

Diff

@@ -129,7 +129,7 @@ theorem CHSH_inequality_of_comm [OrderedCommRing R] [StarOrderedRing R] [Algebra
       rw [idem, h, ← mul_smul]
       norm_num
     have sa : star P = P := by
-      dsimp
+      dsimp [P]
       simp only [star_add, star_sub, star_mul, star_ofNat, star_one, T.A₀_sa, T.A₁_sa, T.B₀_sa,
         T.B₁_sa, mul_comm B₀, mul_comm B₁]
     simpa only [← idem', sa]
@@ -192,7 +192,7 @@ theorem tsirelson_inequality [OrderedRing R] [StarOrderedRing R] [Algebra ℝ R]
   let P := √2⁻¹ • (A₁ + A₀) - B₀
   let Q := √2⁻¹ • (A₁ - A₀) + B₁
   have w : √2 ^ 3 • (1 : R) - A₀ * B₀ - A₀ * B₁ - A₁ * B₀ + A₁ * B₁ = √2⁻¹ • (P ^ 2 + Q ^ 2) := by
-    dsimp
+    dsimp [P, Q]
     -- distribute out all the powers and products appearing on the RHS
     simp only [sq, sub_mul, mul_sub, add_mul, mul_add, smul_add, smul_sub]
     -- pull all coefficients out to the front, and combine `√2`s where possible
@@ -213,9 +213,11 @@ theorem tsirelson_inequality [OrderedRing R] [StarOrderedRing R] [Algebra ℝ R]
     exact mul_left_cancel₀ (by norm_num) tsirelson_inequality_aux
   have pos : 0 ≤ √2⁻¹ • (P ^ 2 + Q ^ 2) := by
     have P_sa : star P = P := by
-      simp only [star_smul, star_add, star_sub, star_id_of_comm, T.A₀_sa, T.A₁_sa, T.B₀_sa, T.B₁_sa]
+      simp only [P, star_smul, star_add, star_sub, star_id_of_comm, T.A₀_sa, T.A₁_sa, T.B₀_sa,
+        T.B₁_sa]
     have Q_sa : star Q = Q := by
-      simp only [star_smul, star_add, star_sub, star_id_of_comm, T.A₀_sa, T.A₁_sa, T.B₀_sa, T.B₁_sa]
+      simp only [Q, star_smul, star_add, star_sub, star_id_of_comm, T.A₀_sa, T.A₁_sa, T.B₀_sa,
+        T.B₁_sa]
     have P2_nonneg : 0 ≤ P ^ 2 := by simpa only [P_sa, sq] using star_mul_self_nonneg P
     have Q2_nonneg : 0 ≤ Q ^ 2 := by simpa only [Q_sa, sq] using star_mul_self_nonneg Q
     exact smul_nonneg (by positivity) (add_nonneg P2_nonneg Q2_nonneg)

chore(*): golf (#10417)

e4bee60a

Diff

@@ -216,26 +216,9 @@ theorem tsirelson_inequality [OrderedRing R] [StarOrderedRing R] [Algebra ℝ R]
       simp only [star_smul, star_add, star_sub, star_id_of_comm, T.A₀_sa, T.A₁_sa, T.B₀_sa, T.B₁_sa]
     have Q_sa : star Q = Q := by
       simp only [star_smul, star_add, star_sub, star_id_of_comm, T.A₀_sa, T.A₁_sa, T.B₀_sa, T.B₁_sa]
-    have P2_nonneg : 0 ≤ P ^ 2 := by
-      rw [sq]
-      conv =>
-        congr
-        skip
-        congr
-        rw [← P_sa]
-      convert (star_mul_self_nonneg P)
-    have Q2_nonneg : 0 ≤ Q ^ 2 := by
-      rw [sq]
-      conv =>
-        congr
-        skip
-        congr
-        rw [← Q_sa]
-      convert (star_mul_self_nonneg Q)
-    convert smul_le_smul_of_nonneg_left (add_nonneg P2_nonneg Q2_nonneg)
-        (le_of_lt (show 0 < √2⁻¹ by norm_num))
-    -- `norm_num` can't directly show `0 ≤ √2⁻¹`
-    simp
+    have P2_nonneg : 0 ≤ P ^ 2 := by simpa only [P_sa, sq] using star_mul_self_nonneg P
+    have Q2_nonneg : 0 ≤ Q ^ 2 := by simpa only [Q_sa, sq] using star_mul_self_nonneg Q
+    exact smul_nonneg (by positivity) (add_nonneg P2_nonneg Q2_nonneg)
   apply le_of_sub_nonneg
   simpa only [sub_add_eq_sub_sub, ← sub_add, w, Nat.cast_zero] using pos
 #align tsirelson_inequality tsirelson_inequality

refactor: Deduplicate monotonicity of • lemmas (#9179)

Remove the duplicates introduced in #8869 by sorting the lemmas in Algebra.Order.SMul into three files:

Algebra.Order.Module.Defs for the order isomorphism induced by scalar multiplication by a positivity element
Algebra.Order.Module.Pointwise for the order properties of scalar multiplication of sets. This file is new. I credit myself for https://github.com/leanprover-community/mathlib/pull/9078
Algebra.Order.Module.OrderedSMul: The material about OrderedSMul per se. Inherits the copyright header from Algebra.Order.SMul. This file should eventually be deleted.

I move each #align to the correct file. On top of that, I delete unused redundant OrderedSMul instances (they were useful in Lean 3, but not anymore) and eq_of_smul_eq_smul_of_pos_of_le/eq_of_smul_eq_smul_of_neg_of_le since those lemmas are weird and unused.

ea70e843

Diff

@@ -132,14 +132,8 @@ theorem CHSH_inequality_of_comm [OrderedCommRing R] [StarOrderedRing R] [Algebra
       dsimp
       simp only [star_add, star_sub, star_mul, star_ofNat, star_one, T.A₀_sa, T.A₁_sa, T.B₀_sa,
         T.B₁_sa, mul_comm B₀, mul_comm B₁]
-    rw [idem']
-    conv_rhs =>
-      arg 2
-      arg 1
-      rw [← sa]
-    convert smul_le_smul_of_nonneg (R := ℝ) (star_mul_self_nonneg P) _
-    · simp
-    · norm_num
+    simpa only [← idem', sa]
+      using smul_nonneg (by norm_num : (0 : ℝ) ≤ 1 / 4) (star_mul_self_nonneg P)
   apply le_of_sub_nonneg
   simpa only [sub_add_eq_sub_sub, ← sub_add] using i₁
 set_option linter.uppercaseLean3 false in
@@ -238,7 +232,7 @@ theorem tsirelson_inequality [OrderedRing R] [StarOrderedRing R] [Algebra ℝ R]
         congr
         rw [← Q_sa]
       convert (star_mul_self_nonneg Q)
-    convert smul_le_smul_of_nonneg (add_nonneg P2_nonneg Q2_nonneg)
+    convert smul_le_smul_of_nonneg_left (add_nonneg P2_nonneg Q2_nonneg)
         (le_of_lt (show 0 < √2⁻¹ by norm_num))
     -- `norm_num` can't directly show `0 ≤ √2⁻¹`
     simp

chore: bump std and aesop (#7746)

This includes leanprover/std4#301 which requires slight tweaks to the List.sublists API.

One other proof also breaks, presumably due to other Std4 commits.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

85acbc3d

Diff

@@ -107,12 +107,9 @@ theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1)
   -- If we had a Gröbner basis algorithm, this would be trivial.
   -- Without one, it is somewhat tedious!
   rw [← sub_eq_zero]
-  repeat'
-    ring_nf
-    simp only [A₁_inv, B₁_inv, sub_eq_add_neg, add_mul, mul_add, sub_mul, mul_sub, add_assoc,
-      neg_add, neg_sub, sub_add, sub_sub, neg_mul, ← sq, A₀_inv, B₀_inv, ← sq, ← mul_assoc, one_mul,
-      mul_one, add_right_neg, add_zero, sub_eq_add_neg, A₀_inv, mul_one, add_right_neg,
-      zero_mul]
+  ring_nf
+  simp_all
+  ring_nf
 set_option linter.uppercaseLean3 false in
 #align CHSH_id CHSH_id

refactor(Algebra/Star/*): Allow for star operation on non-associative algebras (#6562)

Typically a * operation on a mathematical structure R equipped with a multiplication is an involutive anti-automorphism i.e.

∀ r s : R, star (r * s) = star s * star r

Currently mathlib defines a class StarSemigroup to be a semigroup satisfying this property. However, the requirement for the multiplication to be associative is unnecessarily restrictive. There are important classes of star-algebra which are not associative (e.g. JB*-algebras).

This PR removes the requirement for a StarSemigroup to be a semigroup, merely requiring it to have a multiplication.

I've changed the name from StarSemigroup to StarMul since it's no longer a semigroup.

Zulip discussion

Previously opened as a mathlib PR https://github.com/leanprover-community/mathlib/pull/17949

Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

85c04e73

Diff

@@ -82,7 +82,7 @@ The physical interpretation is that `A₀` and `A₁` are a pair of boolean obse
 are spacelike separated from another pair `B₀` and `B₁` of boolean observables.
 -/
 --@[nolint has_nonempty_instance] Porting note: linter does not exist
-structure IsCHSHTuple {R} [Monoid R] [StarSemigroup R] (A₀ A₁ B₀ B₁ : R) : Prop where
+structure IsCHSHTuple {R} [Monoid R] [StarMul R] (A₀ A₁ B₀ B₁ : R) : Prop where
   A₀_inv : A₀ ^ 2 = 1
   A₁_inv : A₁ ^ 2 = 1
   B₀_inv : B₀ ^ 2 = 1

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

277dea95

Diff

@@ -112,7 +112,7 @@ theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1)
     simp only [A₁_inv, B₁_inv, sub_eq_add_neg, add_mul, mul_add, sub_mul, mul_sub, add_assoc,
       neg_add, neg_sub, sub_add, sub_sub, neg_mul, ← sq, A₀_inv, B₀_inv, ← sq, ← mul_assoc, one_mul,
       mul_one, add_right_neg, add_zero, sub_eq_add_neg, A₀_inv, mul_one, add_right_neg,
-      MulZeroClass.zero_mul]
+      zero_mul]
 set_option linter.uppercaseLean3 false in
 #align CHSH_id CHSH_id

chore: bump to nightly-2023-08-17 (#6019)

The major change here is adapting to simp failing if it makes no progress. The vast majority of the redundant simps found due to this change were extracted to #6632.

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

8c53b718

Diff

@@ -170,8 +170,8 @@ we prepare some easy lemmas about √2.
 theorem tsirelson_inequality_aux : √2 * √2 ^ 3 = √2 * (2 * √2⁻¹ + 4 * (√2⁻¹ * 2⁻¹)) := by
   ring_nf
   rw [mul_inv_cancel (ne_of_gt (Real.sqrt_pos.2 (show (2 : ℝ) > 0 by norm_num)))]
-  convert congr_arg (· ^ 2) (@Real.sq_sqrt 2 (by norm_num)) using 1 <;> simp only [← pow_mul] <;>
-    norm_num
+  convert congr_arg (· ^ 2) (@Real.sq_sqrt 2 (by norm_num)) using 1 <;>
+    (try simp only [← pow_mul]) <;> norm_num
 #align tsirelson_inequality.tsirelson_inequality_aux TsirelsonInequality.tsirelson_inequality_aux
 
 theorem sqrt_two_inv_mul_self : √2⁻¹ * √2⁻¹ = (2⁻¹ : ℝ) := by

feat: Linter that checks that Prop classes are Props (#6148)

930dd29d

Diff

@@ -82,7 +82,7 @@ The physical interpretation is that `A₀` and `A₁` are a pair of boolean obse
 are spacelike separated from another pair `B₀` and `B₁` of boolean observables.
 -/
 --@[nolint has_nonempty_instance] Porting note: linter does not exist
-structure IsCHSHTuple {R} [Monoid R] [StarSemigroup R] (A₀ A₁ B₀ B₁ : R) where
+structure IsCHSHTuple {R} [Monoid R] [StarSemigroup R] (A₀ A₁ B₀ B₁ : R) : Prop where
   A₀_inv : A₀ ^ 2 = 1
   A₁_inv : A₁ ^ 2 = 1
   B₀_inv : B₀ ^ 2 = 1

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) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module algebra.star.chsh
-! leanprover-community/mathlib commit 31c24aa72e7b3e5ed97a8412470e904f82b81004
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.CharP.Invertible
 import Mathlib.Data.Real.Sqrt
 
+#align_import algebra.star.chsh from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"
+
 /-!
 # The Clauser-Horne-Shimony-Holt inequality and Tsirelson's inequality.

chore: forward-port leanprover-community/mathlib#18854 (#4840)

This forward-ports all the files from leanprover-community/mathlib#18854 which have already been ported, and it also ports the new file algebra.star.order, which is a split from algebra.star.basic and was necessary to do at the same time.

Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

4d3d2de8

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module algebra.star.chsh
-! leanprover-community/mathlib commit 468b141b14016d54b479eb7a0fff1e360b7e3cf6
+! leanprover-community/mathlib commit 31c24aa72e7b3e5ed97a8412470e904f82b81004
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -143,7 +143,7 @@ theorem CHSH_inequality_of_comm [OrderedCommRing R] [StarOrderedRing R] [Algebra
       arg 2
       arg 1
       rw [← sa]
-    convert smul_le_smul_of_nonneg (R := ℝ) (star_mul_self_nonneg : 0 ≤ star P * P) _
+    convert smul_le_smul_of_nonneg (R := ℝ) (star_mul_self_nonneg P) _
     · simp
     · norm_num
   apply le_of_sub_nonneg
@@ -235,7 +235,7 @@ theorem tsirelson_inequality [OrderedRing R] [StarOrderedRing R] [Algebra ℝ R]
         skip
         congr
         rw [← P_sa]
-      convert(star_mul_self_nonneg : 0 ≤ star P * P)
+      convert (star_mul_self_nonneg P)
     have Q2_nonneg : 0 ≤ Q ^ 2 := by
       rw [sq]
       conv =>
@@ -243,7 +243,7 @@ theorem tsirelson_inequality [OrderedRing R] [StarOrderedRing R] [Algebra ℝ R]
         skip
         congr
         rw [← Q_sa]
-      convert(star_mul_self_nonneg : 0 ≤ star Q * Q)
+      convert (star_mul_self_nonneg Q)
     convert smul_le_smul_of_nonneg (add_nonneg P2_nonneg Q2_nonneg)
         (le_of_lt (show 0 < √2⁻¹ by norm_num))
     -- `norm_num` can't directly show `0 ≤ √2⁻¹`

chore: reenable eta, bump to nightly 2023-05-16 (#3414)

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

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

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

a6e1045f

Diff

@@ -119,7 +119,6 @@ theorem CHSH_id [CommRing R] {A₀ A₁ B₀ B₁ : R} (A₀_inv : A₀ ^ 2 = 1)
 set_option linter.uppercaseLean3 false in
 #align CHSH_id CHSH_id
 
-set_option synthInstance.etaExperiment true in
 /-- Given a CHSH tuple (A₀, A₁, B₀, B₁) in a *commutative* ordered `*`-algebra over ℝ,
 `A₀ * B₀ + A₀ * B₁ + A₁ * B₀ - A₁ * B₁ ≤ 2`.
 
@@ -187,7 +186,6 @@ end TsirelsonInequality
 
 open TsirelsonInequality
 
-set_option synthInstance.etaExperiment true in
 /-- In a noncommutative ordered `*`-algebra over ℝ,
 Tsirelson's bound for a CHSH tuple (A₀, A₁, B₀, B₁) is
 `A₀ * B₀ + A₀ * B₁ + A₁ * B₀ - A₁ * B₁ ≤ 2^(3/2) • 1`.