linear_algebra.matrix.dot_product | 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

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 -/
 
+import algebra.star.order
 import data.matrix.basic
 import linear_algebra.std_basis

chore(linear_algebra/matrix/dot_product): weaken typeclasses (#18798)

This makes unification slightly harder on Lean, so : _s are added.

Fixes a stupid error in #18783

Diff

@@ -79,16 +79,16 @@ variables [fintype n]
 
 /-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
 @[simp] lemma dot_product_star_self_eq_zero
-  [strict_ordered_ring R] [star_ordered_ring R] [no_zero_divisors R] {v : n → R} :
+  [partial_order R] [non_unital_ring R] [star_ordered_ring R] [no_zero_divisors R] {v : n → R} :
   dot_product (star v) v = 0 ↔ v = 0 :=
-(finset.sum_eq_zero_iff_of_nonneg $ λ i _, @star_mul_self_nonneg _ _ _ _ (v i)).trans $
+(finset.sum_eq_zero_iff_of_nonneg $ λ i _, (@star_mul_self_nonneg _ _ _ _ (v i) : _)).trans $
   by simp [function.funext_iff, mul_eq_zero]
 
 /-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
 @[simp] lemma dot_product_self_star_eq_zero
-  [strict_ordered_ring R] [star_ordered_ring R] [no_zero_divisors R] {v : n → R} :
+  [partial_order R] [non_unital_ring R] [star_ordered_ring R] [no_zero_divisors R] {v : n → R} :
   dot_product v (star v) = 0 ↔ v = 0 :=
-(finset.sum_eq_zero_iff_of_nonneg $ λ i _, @star_mul_self_nonneg' _ _ _ _ (v i)).trans $
+(finset.sum_eq_zero_iff_of_nonneg $ λ i _, (@star_mul_self_nonneg' _ _ _ _ (v i) : _)).trans $
   by simp [function.funext_iff, mul_eq_zero]
 
 end self

feat(linear_algebra/matrix/dot_product): dot_product_self_eq_zero (#18783)

Diff

@@ -30,10 +30,12 @@ matrix, reindex
 -/
 
 universes v w
+variables {R : Type v} {n : Type w}
 
 namespace matrix
 
-variables {R : Type v} [semiring R] {n : Type w} [fintype n]
+section semiring
+variables [semiring R] [fintype n]
 
 @[simp] lemma dot_product_std_basis_eq_mul [decidable_eq n] (v : n → R) (c : R) (i : n) :
   dot_product v (linear_map.std_basis R (λ _, R) i c) = v i * c :=
@@ -65,4 +67,30 @@ dot_product_eq _ _ $ λ u, (h u).symm ▸ (zero_dot_product u).symm
 lemma dot_product_eq_zero_iff {v : n → R} : (∀ w, dot_product v w = 0) ↔ v = 0 :=
 ⟨λ h, dot_product_eq_zero v h, λ h w, h.symm ▸ zero_dot_product w⟩
 
+end semiring
+
+section self
+variables [fintype n]
+
+@[simp] lemma dot_product_self_eq_zero [linear_ordered_ring R] {v : n → R} :
+  dot_product v v = 0 ↔ v = 0 :=
+(finset.sum_eq_zero_iff_of_nonneg $ λ i _, mul_self_nonneg (v i)).trans $
+  by simp [function.funext_iff]
+
+/-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
+@[simp] lemma dot_product_star_self_eq_zero
+  [strict_ordered_ring R] [star_ordered_ring R] [no_zero_divisors R] {v : n → R} :
+  dot_product (star v) v = 0 ↔ v = 0 :=
+(finset.sum_eq_zero_iff_of_nonneg $ λ i _, @star_mul_self_nonneg _ _ _ _ (v i)).trans $
+  by simp [function.funext_iff, mul_eq_zero]
+
+/-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
+@[simp] lemma dot_product_self_star_eq_zero
+  [strict_ordered_ring R] [star_ordered_ring R] [no_zero_divisors R] {v : n → R} :
+  dot_product v (star v) = 0 ↔ v = 0 :=
+(finset.sum_eq_zero_iff_of_nonneg $ λ i _, @star_mul_self_nonneg' _ _ _ _ (v i)).trans $
+  by simp [function.funext_iff, mul_eq_zero]
+
+end self
+
 end matrix

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -65,7 +65,7 @@ theorem dotProduct_stdBasis_one [DecidableEq n] (v : n → R) (i : n) :
 theorem dotProduct_eq (v w : n → R) (h : ∀ u, dotProduct v u = dotProduct w u) : v = w :=
   by
   funext x
-  classical
+  classical rw [← dot_product_std_basis_one v x, ← dot_product_std_basis_one w x, h]
 #align matrix.dot_product_eq Matrix.dotProduct_eq
 -/

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -65,7 +65,7 @@ theorem dotProduct_stdBasis_one [DecidableEq n] (v : n → R) (i : n) :
 theorem dotProduct_eq (v w : n → R) (h : ∀ u, dotProduct v u = dotProduct w u) : v = w :=
   by
   funext x
-  classical rw [← dot_product_std_basis_one v x, ← dot_product_std_basis_one w x, h]
+  classical
 #align matrix.dot_product_eq Matrix.dotProduct_eq
 -/

bump to nightly-2024-01-07-06

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

7af124c5

Diff

@@ -96,7 +96,7 @@ variable [Fintype n]
 #print Matrix.dotProduct_self_eq_zero /-
 @[simp]
 theorem dotProduct_self_eq_zero [LinearOrderedRing R] {v : n → R} : dotProduct v v = 0 ↔ v = 0 :=
-  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => mul_self_nonneg (v i)).trans <| by
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => hMul_self_nonneg (v i)).trans <| by
     simp [Function.funext_iff]
 #align matrix.dot_product_self_eq_zero Matrix.dotProduct_self_eq_zero
 -/

bump to nightly-2023-11-15-06

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

38c8ceef

Diff

@@ -116,7 +116,7 @@ theorem dotProduct_star_self_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrd
 @[simp]
 theorem dotProduct_self_star_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrderedRing R]
     [NoZeroDivisors R] {v : n → R} : dotProduct v (star v) = 0 ↔ v = 0 :=
-  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@star_mul_self_nonneg' _ _ _ _ (v i) : _)).trans <|
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@mul_star_self_nonneg _ _ _ _ (v i) : _)).trans <|
     by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zero
 -/

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 -/
-import Mathbin.Algebra.Star.Order
-import Mathbin.Data.Matrix.Basic
-import Mathbin.LinearAlgebra.StdBasis
+import Algebra.Star.Order
+import Data.Matrix.Basic
+import LinearAlgebra.StdBasis
 
 #align_import linear_algebra.matrix.dot_product from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.dot_product
-! 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.Star.Order
 import Mathbin.Data.Matrix.Basic
 import Mathbin.LinearAlgebra.StdBasis
 
+#align_import linear_algebra.matrix.dot_product from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"
+
 /-!
 # Dot product of two vectors

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -45,6 +45,7 @@ section Semiring
 
 variable [Semiring R] [Fintype n]
 
+#print Matrix.dotProduct_stdBasis_eq_mul /-
 @[simp]
 theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n) :
     dotProduct v (LinearMap.stdBasis R (fun _ => R) i c) = v i * c :=
@@ -53,30 +54,41 @@ theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n)
   exact fun _ _ hb => by rw [LinearMap.stdBasis_ne _ _ _ _ hb, MulZeroClass.mul_zero]
   exact fun hi => False.elim (hi <| Finset.mem_univ _)
 #align matrix.dot_product_std_basis_eq_mul Matrix.dotProduct_stdBasis_eq_mul
+-/
 
+#print Matrix.dotProduct_stdBasis_one /-
 @[simp]
 theorem dotProduct_stdBasis_one [DecidableEq n] (v : n → R) (i : n) :
     dotProduct v (LinearMap.stdBasis R (fun _ => R) i 1) = v i := by
   rw [dot_product_std_basis_eq_mul, mul_one]
 #align matrix.dot_product_std_basis_one Matrix.dotProduct_stdBasis_one
+-/
 
+#print Matrix.dotProduct_eq /-
 theorem dotProduct_eq (v w : n → R) (h : ∀ u, dotProduct v u = dotProduct w u) : v = w :=
   by
   funext x
   classical rw [← dot_product_std_basis_one v x, ← dot_product_std_basis_one w x, h]
 #align matrix.dot_product_eq Matrix.dotProduct_eq
+-/
 
+#print Matrix.dotProduct_eq_iff /-
 theorem dotProduct_eq_iff {v w : n → R} : (∀ u, dotProduct v u = dotProduct w u) ↔ v = w :=
   ⟨fun h => dotProduct_eq v w h, fun h _ => h ▸ rfl⟩
 #align matrix.dot_product_eq_iff Matrix.dotProduct_eq_iff
+-/
 
+#print Matrix.dotProduct_eq_zero /-
 theorem dotProduct_eq_zero (v : n → R) (h : ∀ w, dotProduct v w = 0) : v = 0 :=
   dotProduct_eq _ _ fun u => (h u).symm ▸ (zero_dotProduct u).symm
 #align matrix.dot_product_eq_zero Matrix.dotProduct_eq_zero
+-/
 
+#print Matrix.dotProduct_eq_zero_iff /-
 theorem dotProduct_eq_zero_iff {v : n → R} : (∀ w, dotProduct v w = 0) ↔ v = 0 :=
   ⟨fun h => dotProduct_eq_zero v h, fun h w => h.symm ▸ zero_dotProduct w⟩
 #align matrix.dot_product_eq_zero_iff Matrix.dotProduct_eq_zero_iff
+-/
 
 end Semiring
 
@@ -84,12 +96,15 @@ section Self
 
 variable [Fintype n]
 
+#print Matrix.dotProduct_self_eq_zero /-
 @[simp]
 theorem dotProduct_self_eq_zero [LinearOrderedRing R] {v : n → R} : dotProduct v v = 0 ↔ v = 0 :=
   (Finset.sum_eq_zero_iff_of_nonneg fun i _ => mul_self_nonneg (v i)).trans <| by
     simp [Function.funext_iff]
 #align matrix.dot_product_self_eq_zero Matrix.dotProduct_self_eq_zero
+-/
 
+#print Matrix.dotProduct_star_self_eq_zero /-
 /-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
 @[simp]
 theorem dotProduct_star_self_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrderedRing R]
@@ -97,7 +112,9 @@ theorem dotProduct_star_self_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrd
   (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@star_mul_self_nonneg _ _ _ _ (v i) : _)).trans <|
     by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_star_self_eq_zero Matrix.dotProduct_star_self_eq_zero
+-/
 
+#print Matrix.dotProduct_self_star_eq_zero /-
 /-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
 @[simp]
 theorem dotProduct_self_star_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrderedRing R]
@@ -105,6 +122,7 @@ theorem dotProduct_self_star_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrd
   (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@star_mul_self_nonneg' _ _ _ _ (v i) : _)).trans <|
     by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zero
+-/
 
 end Self

bump to nightly-2023-06-08-03

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

8f04dc2b

Diff

@@ -4,10 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.dot_product
-! leanprover-community/mathlib commit 5ac1dab1670014b4c07a82c86a67f3d064a1b3e1
+! 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.Star.Order
 import Mathbin.Data.Matrix.Basic
 import Mathbin.LinearAlgebra.StdBasis

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -44,12 +44,6 @@ section Semiring
 
 variable [Semiring R] [Fintype n]
 
-/- warning: matrix.dot_product_std_basis_eq_mul -> Matrix.dotProduct_stdBasis_eq_mul is a dubious translation:
-lean 3 declaration is
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 @[simp]
 theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n) :
     dotProduct v (LinearMap.stdBasis R (fun _ => R) i c) = v i * c :=
@@ -59,56 +53,26 @@ theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n)
   exact fun hi => False.elim (hi <| Finset.mem_univ _)
 #align matrix.dot_product_std_basis_eq_mul Matrix.dotProduct_stdBasis_eq_mul
 
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 @[simp]
 theorem dotProduct_stdBasis_one [DecidableEq n] (v : n → R) (i : n) :
     dotProduct v (LinearMap.stdBasis R (fun _ => R) i 1) = v i := by
   rw [dot_product_std_basis_eq_mul, mul_one]
 #align matrix.dot_product_std_basis_one Matrix.dotProduct_stdBasis_one
 
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 theorem dotProduct_eq (v w : n → R) (h : ∀ u, dotProduct v u = dotProduct w u) : v = w :=
   by
   funext x
   classical rw [← dot_product_std_basis_one v x, ← dot_product_std_basis_one w x, h]
 #align matrix.dot_product_eq Matrix.dotProduct_eq
 
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 theorem dotProduct_eq_iff {v w : n → R} : (∀ u, dotProduct v u = dotProduct w u) ↔ v = w :=
   ⟨fun h => dotProduct_eq v w h, fun h _ => h ▸ rfl⟩
 #align matrix.dot_product_eq_iff Matrix.dotProduct_eq_iff
 
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 theorem dotProduct_eq_zero (v : n → R) (h : ∀ w, dotProduct v w = 0) : v = 0 :=
   dotProduct_eq _ _ fun u => (h u).symm ▸ (zero_dotProduct u).symm
 #align matrix.dot_product_eq_zero Matrix.dotProduct_eq_zero
 
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 theorem dotProduct_eq_zero_iff {v : n → R} : (∀ w, dotProduct v w = 0) ↔ v = 0 :=
   ⟨fun h => dotProduct_eq_zero v h, fun h w => h.symm ▸ zero_dotProduct w⟩
 #align matrix.dot_product_eq_zero_iff Matrix.dotProduct_eq_zero_iff
@@ -119,24 +83,12 @@ section Self
 
 variable [Fintype n]
 
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 @[simp]
 theorem dotProduct_self_eq_zero [LinearOrderedRing R] {v : n → R} : dotProduct v v = 0 ↔ v = 0 :=
   (Finset.sum_eq_zero_iff_of_nonneg fun i _ => mul_self_nonneg (v i)).trans <| by
     simp [Function.funext_iff]
 #align matrix.dot_product_self_eq_zero Matrix.dotProduct_self_eq_zero
 
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 /-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
 @[simp]
 theorem dotProduct_star_self_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrderedRing R]
@@ -145,12 +97,6 @@ theorem dotProduct_star_self_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrd
     by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_star_self_eq_zero Matrix.dotProduct_star_self_eq_zero
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zeroₓ'. -/
 /-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
 @[simp]
 theorem dotProduct_self_star_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrderedRing R]

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -48,7 +48,7 @@ variable [Semiring R] [Fintype n]
 lean 3 declaration is
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 but is expected to have type
-  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (c : R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (n -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => n -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (n -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) c)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (v i) c)
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (c : R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (n -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => n -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (n -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) c)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (v i) c)
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_std_basis_eq_mul Matrix.dotProduct_stdBasis_eq_mulₓ'. -/
 @[simp]
 theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n) :
@@ -63,7 +63,7 @@ theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n)
 lean 3 declaration is
   forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : n) => R) i) (forall (i : n), (fun (_x : n) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => (fun (_x : n) => R) i) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => (fun (_x : n) => R) i) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : n) => R) i) (forall (i : n), (fun (_x : n) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => (fun (_x : n) => R) i) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => (fun (_x : n) => R) i) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) => R -> (forall (i : n), (fun (_x : n) => R) i)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R ((fun (_x : n) => R) i) (forall (i : n), (fun (_x : n) => R) i) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => (fun (_x : n) => R) i) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => (fun (_x : n) => R) i) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) (OfNat.ofNat.{u1} ((fun (_x : n) => R) i) 1 (OfNat.mk.{u1} ((fun (_x : n) => R) i) 1 (One.one.{u1} ((fun (_x : n) => R) i) (AddMonoidWithOne.toOne.{u1} ((fun (_x : n) => R) i) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))))))))) (v i)
 but is expected to have type
-  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (n -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => n -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (n -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))) (v i)
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (n -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => n -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (n -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))) (v i)
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_std_basis_one Matrix.dotProduct_stdBasis_oneₓ'. -/
 @[simp]
 theorem dotProduct_stdBasis_one [DecidableEq n] (v : n → R) (i : n) :

bump to nightly-2023-05-18-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

b46e9d53

Diff

@@ -48,7 +48,7 @@ variable [Semiring R] [Fintype n]
 lean 3 declaration is
   forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (c : R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : n) => R) i) (forall (i : n), (fun (_x : n) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => (fun (_x : n) => R) i) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => (fun (_x : n) => R) i) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : n) => R) i) (forall (i : n), (fun (_x : n) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => (fun (_x : n) => R) i) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => (fun (_x : n) => R) i) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) => R -> (forall (i : n), (fun (_x : n) => R) i)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R ((fun (_x : n) => R) i) (forall (i : n), (fun (_x : n) => R) i) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => (fun (_x : n) => R) i) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => (fun (_x : n) => R) i) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) c)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (v i) c)
 but is expected to have type
-  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (c : R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (n -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => n -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (n -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) c)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (v i) c)
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (c : R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (n -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => n -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (n -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) c)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (v i) c)
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_std_basis_eq_mul Matrix.dotProduct_stdBasis_eq_mulₓ'. -/
 @[simp]
 theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n) :
@@ -63,7 +63,7 @@ theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n)
 lean 3 declaration is
   forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : n) => R) i) (forall (i : n), (fun (_x : n) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => (fun (_x : n) => R) i) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => (fun (_x : n) => R) i) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : n) => R) i) (forall (i : n), (fun (_x : n) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => (fun (_x : n) => R) i) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => (fun (_x : n) => R) i) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) => R -> (forall (i : n), (fun (_x : n) => R) i)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R ((fun (_x : n) => R) i) (forall (i : n), (fun (_x : n) => R) i) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => (fun (_x : n) => R) i) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => (fun (_x : n) => R) i) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) (OfNat.ofNat.{u1} ((fun (_x : n) => R) i) 1 (OfNat.mk.{u1} ((fun (_x : n) => R) i) 1 (One.one.{u1} ((fun (_x : n) => R) i) (AddMonoidWithOne.toOne.{u1} ((fun (_x : n) => R) i) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))))))))) (v i)
 but is expected to have type
-  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (n -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => n -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (n -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))) (v i)
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (n -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => n -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (n -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))) (v i)
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_std_basis_one Matrix.dotProduct_stdBasis_oneₓ'. -/
 @[simp]
 theorem dotProduct_stdBasis_one [DecidableEq n] (v : n → R) (i : n) :

bump to nightly-2023-04-15-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/0e2aab2b0d521f060f62a14d2cf2e2c54e8491d6

2a116d4b

Diff

@@ -135,7 +135,7 @@ theorem dotProduct_self_eq_zero [LinearOrderedRing R] {v : n → R} : dotProduct
 lean 3 declaration is
   forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : PartialOrder.{u1} R] [_inst_3 : NonUnitalRing.{u1} R] [_inst_4 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2] [_inst_5 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R _inst_3 _inst_2 _inst_4))) (Star.star.{max u2 u1} (n -> R) (Pi.hasStar.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2 _inst_4))))) v) v) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2)] [_inst_4 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))] {_inst_5 : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))) (Star.star.{max u2 u1} (n -> R) (Pi.instStarForAll.{u2, u1} n (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.6390 : n) => R) (fun (i : n) => InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2) _inst_3))))) _inst_5) _inst_5) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))) (Eq.{max (succ u1) (succ u2)} (n -> R) _inst_5 (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.521 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))))
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : PartialOrder.{u1} R] [_inst_3 : NonUnitalRing.{u1} R] [_inst_4 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2] [_inst_5 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)) (SemigroupWithZero.toZero.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3)))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (NonUnitalNonAssocRing.toMul.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} R (StarOrderedRing.instOrderedAddCommGroup.{u1} R _inst_3 _inst_2 _inst_4))) (Star.star.{max u2 u1} (n -> R) (Pi.instStarForAll.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.instOrderedAddCommGroup.{u1} R _inst_3 _inst_2 _inst_4))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2 _inst_4))))) v) v) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (SemigroupWithZero.toZero.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3)))))) (Eq.{max (succ u1) (succ u2)} (n -> R) v (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.524 : n) => R) (fun (i : n) => SemigroupWithZero.toZero.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_star_self_eq_zero Matrix.dotProduct_star_self_eq_zeroₓ'. -/
 /-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
 @[simp]
@@ -149,7 +149,7 @@ theorem dotProduct_star_self_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrd
 lean 3 declaration is
   forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : PartialOrder.{u1} R] [_inst_3 : NonUnitalRing.{u1} R] [_inst_4 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2] [_inst_5 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R _inst_3 _inst_2 _inst_4))) v (Star.star.{max u2 u1} (n -> R) (Pi.hasStar.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2 _inst_4))))) v)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2)] [_inst_4 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))] {_inst_5 : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))) _inst_5 (Star.star.{max u1 u2} (n -> R) (Pi.instStarForAll.{u2, u1} n (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.6393 : n) => R) (fun (i : n) => InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2) _inst_3))))) _inst_5)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))) (Eq.{max (succ u1) (succ u2)} (n -> R) _inst_5 (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.579 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))))
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : PartialOrder.{u1} R] [_inst_3 : NonUnitalRing.{u1} R] [_inst_4 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2] [_inst_5 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)) (SemigroupWithZero.toZero.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3)))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (NonUnitalNonAssocRing.toMul.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} R (StarOrderedRing.instOrderedAddCommGroup.{u1} R _inst_3 _inst_2 _inst_4))) v (Star.star.{max u1 u2} (n -> R) (Pi.instStarForAll.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.instOrderedAddCommGroup.{u1} R _inst_3 _inst_2 _inst_4))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2 _inst_4))))) v)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (SemigroupWithZero.toZero.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3)))))) (Eq.{max (succ u1) (succ u2)} (n -> R) v (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.588 : n) => R) (fun (i : n) => SemigroupWithZero.toZero.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zeroₓ'. -/
 /-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
 @[simp]

bump to nightly-2023-04-14-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ebf83ed9c262adbf983ef64d5e8c2ae94b625f4

574e9440

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.dot_product
-! leanprover-community/mathlib commit 46822d96c0c0a8e58a41a0cba1291620967575c5
+! leanprover-community/mathlib commit 5ac1dab1670014b4c07a82c86a67f3d064a1b3e1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -133,30 +133,30 @@ theorem dotProduct_self_eq_zero [LinearOrderedRing R] {v : n → R} : dotProduct
 
 /- warning: matrix.dot_product_star_self_eq_zero -> Matrix.dotProduct_star_self_eq_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2))] [_inst_4 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2)) _inst_3))) (Star.star.{max u2 u1} (n -> R) (Pi.hasStar.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => 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 (StrictOrderedRing.toRing.{u1} R _inst_2)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2)) _inst_3))))) v) v) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))))))))))
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : PartialOrder.{u1} R] [_inst_3 : NonUnitalRing.{u1} R] [_inst_4 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2] [_inst_5 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R _inst_3 _inst_2 _inst_4))) (Star.star.{max u2 u1} (n -> R) (Pi.hasStar.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2 _inst_4))))) v) v) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2)] [_inst_4 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))) (Star.star.{max u2 u1} (n -> R) (Pi.instStarForAll.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2) _inst_3))))) v) v) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))) (Eq.{max (succ u1) (succ u2)} (n -> R) v (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.521 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))))
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2)] [_inst_4 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))] {_inst_5 : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))) (Star.star.{max u2 u1} (n -> R) (Pi.instStarForAll.{u2, u1} n (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.6390 : n) => R) (fun (i : n) => InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2) _inst_3))))) _inst_5) _inst_5) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))) (Eq.{max (succ u1) (succ u2)} (n -> R) _inst_5 (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.521 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))))
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_star_self_eq_zero Matrix.dotProduct_star_self_eq_zeroₓ'. -/
 /-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
 @[simp]
-theorem dotProduct_star_self_eq_zero [StrictOrderedRing R] [StarOrderedRing R] [NoZeroDivisors R]
-    {v : n → R} : dotProduct (star v) v = 0 ↔ v = 0 :=
-  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => @star_mul_self_nonneg _ _ _ _ (v i)).trans <| by
-    simp [Function.funext_iff, mul_eq_zero]
+theorem dotProduct_star_self_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrderedRing R]
+    [NoZeroDivisors R] {v : n → R} : dotProduct (star v) v = 0 ↔ v = 0 :=
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@star_mul_self_nonneg _ _ _ _ (v i) : _)).trans <|
+    by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_star_self_eq_zero Matrix.dotProduct_star_self_eq_zero
 
 /- warning: matrix.dot_product_self_star_eq_zero -> Matrix.dotProduct_self_star_eq_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2))] [_inst_4 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2)) _inst_3))) v (Star.star.{max u2 u1} (n -> R) (Pi.hasStar.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => 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 (StrictOrderedRing.toRing.{u1} R _inst_2)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2)) _inst_3))))) v)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))))))))))
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : PartialOrder.{u1} R] [_inst_3 : NonUnitalRing.{u1} R] [_inst_4 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2] [_inst_5 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R _inst_3 _inst_2 _inst_4))) v (Star.star.{max u2 u1} (n -> R) (Pi.hasStar.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R _inst_3) _inst_2 _inst_4))))) v)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R _inst_3)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2)] [_inst_4 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))) v (Star.star.{max u1 u2} (n -> R) (Pi.instStarForAll.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2) _inst_3))))) v)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))) (Eq.{max (succ u1) (succ u2)} (n -> R) v (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.579 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))))
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2)] [_inst_4 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))] {_inst_5 : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))) _inst_5 (Star.star.{max u1 u2} (n -> R) (Pi.instStarForAll.{u2, u1} n (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.6393 : n) => R) (fun (i : n) => InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2) _inst_3))))) _inst_5)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))) (Eq.{max (succ u1) (succ u2)} (n -> R) _inst_5 (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.579 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))))
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zeroₓ'. -/
 /-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
 @[simp]
-theorem dotProduct_self_star_eq_zero [StrictOrderedRing R] [StarOrderedRing R] [NoZeroDivisors R]
-    {v : n → R} : dotProduct v (star v) = 0 ↔ v = 0 :=
-  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => @star_mul_self_nonneg' _ _ _ _ (v i)).trans <| by
-    simp [Function.funext_iff, mul_eq_zero]
+theorem dotProduct_self_star_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrderedRing R]
+    [NoZeroDivisors R] {v : n → R} : dotProduct v (star v) = 0 ↔ v = 0 :=
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@star_mul_self_nonneg' _ _ _ _ (v i) : _)).trans <|
+    by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zero
 
 end Self

bump to nightly-2023-04-13-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/347636a7a80595d55bedf6e6fbd996a3c39da69a

b6e2bcea

Diff

@@ -48,7 +48,7 @@ variable [Semiring R] [Fintype n]
 lean 3 declaration is
   forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (c : R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : n) => R) i) (forall (i : n), (fun (_x : n) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => (fun (_x : n) => R) i) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => (fun (_x : n) => R) i) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : n) => R) i) (forall (i : n), (fun (_x : n) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => (fun (_x : n) => R) i) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => (fun (_x : n) => R) i) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) => R -> (forall (i : n), (fun (_x : n) => R) i)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R ((fun (_x : n) => R) i) (forall (i : n), (fun (_x : n) => R) i) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => (fun (_x : n) => R) i) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => (fun (_x : n) => R) i) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) c)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (v i) c)
 but is expected to have type
-  forall {R : Type.{u1}} [n : Semiring.{u1} R] {_inst_1 : Type.{u2}} [_inst_2 : Fintype.{u2} _inst_1] [_inst_3 : DecidableEq.{succ u2} _inst_1] (v : _inst_1 -> R) (c : R) (i : _inst_1), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) v (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R n n (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R n)) R (_inst_1 -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) n))) (Pi.addCommMonoid.{u2, u1} _inst_1 (fun (i : _inst_1) => R) (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) n)))) (Semiring.toModule.{u1} R n) (Pi.module.{u2, u1, u1} _inst_1 (fun (i : _inst_1) => R) R n (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) n))) (fun (i : _inst_1) => Semiring.toModule.{u1} R n))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => _inst_1 -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (_inst_1 -> R) n n (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n))) (Pi.addCommMonoid.{u2, u1} _inst_1 (fun (i : _inst_1) => R) (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n)))) (Semiring.toModule.{u1} R n) (Pi.module.{u2, u1, u1} _inst_1 (fun (i : _inst_1) => R) R n (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n))) (fun (i : _inst_1) => Semiring.toModule.{u1} R n)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (LinearMap.stdBasis.{u1, u2, u1} R _inst_1 n (fun (_x : _inst_1) => R) (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n))) (fun (i : _inst_1) => Semiring.toModule.{u1} R n) (fun (a : _inst_1) (b : _inst_1) => _inst_3 a b) i) c)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n)))) (v i) c)
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (c : R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (n -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.52 : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => n -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (n -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) c)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (v i) c)
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_std_basis_eq_mul Matrix.dotProduct_stdBasis_eq_mulₓ'. -/
 @[simp]
 theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n) :
@@ -63,7 +63,7 @@ theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n)
 lean 3 declaration is
   forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : n) => R) i) (forall (i : n), (fun (_x : n) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => (fun (_x : n) => R) i) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => (fun (_x : n) => R) i) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : n) => R) i) (forall (i : n), (fun (_x : n) => R) i) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => (fun (_x : n) => R) i) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => (fun (_x : n) => R) i) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) => R -> (forall (i : n), (fun (_x : n) => R) i)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R ((fun (_x : n) => R) i) (forall (i : n), (fun (_x : n) => R) i) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => (fun (_x : n) => R) i) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => (fun (_x : n) => R) i) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) (OfNat.ofNat.{u1} ((fun (_x : n) => R) i) 1 (OfNat.mk.{u1} ((fun (_x : n) => R) i) 1 (One.one.{u1} ((fun (_x : n) => R) i) (AddMonoidWithOne.toOne.{u1} ((fun (_x : n) => R) i) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))))))))) (v i)
 but is expected to have type
-  forall {R : Type.{u1}} [n : Semiring.{u1} R] {_inst_1 : Type.{u2}} [_inst_2 : Fintype.{u2} _inst_1] [_inst_3 : DecidableEq.{succ u2} _inst_1] (v : _inst_1 -> R) (i : _inst_1), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) v (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R n n (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R n)) R (_inst_1 -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) n))) (Pi.addCommMonoid.{u2, u1} _inst_1 (fun (i : _inst_1) => R) (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) n)))) (Semiring.toModule.{u1} R n) (Pi.module.{u2, u1, u1} _inst_1 (fun (i : _inst_1) => R) R n (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) n))) (fun (i : _inst_1) => Semiring.toModule.{u1} R n))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => _inst_1 -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (_inst_1 -> R) n n (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n))) (Pi.addCommMonoid.{u2, u1} _inst_1 (fun (i : _inst_1) => R) (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n)))) (Semiring.toModule.{u1} R n) (Pi.module.{u2, u1, u1} _inst_1 (fun (i : _inst_1) => R) R n (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n))) (fun (i : _inst_1) => Semiring.toModule.{u1} R n)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (LinearMap.stdBasis.{u1, u2, u1} R _inst_1 n (fun (_x : _inst_1) => R) (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n))) (fun (i : _inst_1) => Semiring.toModule.{u1} R n) (fun (a : _inst_1) (b : _inst_1) => _inst_3 a b) i) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R n))))) (v i)
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (n -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.179 : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => n -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (n -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))) (v i)
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_std_basis_one Matrix.dotProduct_stdBasis_oneₓ'. -/
 @[simp]
 theorem dotProduct_stdBasis_one [DecidableEq n] (v : n → R) (i : n) :
@@ -75,7 +75,7 @@ theorem dotProduct_stdBasis_one [DecidableEq n] (v : n → R) (i : n) :
 lean 3 declaration is
   forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] (v : n -> R) (w : n -> R), (forall (u : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v u) (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) w u)) -> (Eq.{max (succ u2) (succ u1)} (n -> R) v w)
 but is expected to have type
-  forall {R : Type.{u1}} [n : Semiring.{u1} R] {_inst_1 : Type.{u2}} [_inst_2 : Fintype.{u2} _inst_1] (v : _inst_1 -> R) (w : _inst_1 -> R), (forall (u : _inst_1 -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) v u) (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) w u)) -> (Eq.{max (succ u1) (succ u2)} (_inst_1 -> R) v w)
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] (v : n -> R) (w : n -> R), (forall (u : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v u) (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) w u)) -> (Eq.{max (succ u1) (succ u2)} (n -> R) v w)
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_eq Matrix.dotProduct_eqₓ'. -/
 theorem dotProduct_eq (v w : n → R) (h : ∀ u, dotProduct v u = dotProduct w u) : v = w :=
   by
@@ -87,7 +87,7 @@ theorem dotProduct_eq (v w : n → R) (h : ∀ u, dotProduct v u = dotProduct w
 lean 3 declaration is
   forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] {v : n -> R} {w : n -> R}, Iff (forall (u : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v u) (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) w u)) (Eq.{max (succ u2) (succ u1)} (n -> R) v w)
 but is expected to have type
-  forall {R : Type.{u1}} [n : Semiring.{u1} R] {_inst_1 : Type.{u2}} [_inst_2 : Fintype.{u2} _inst_1] {v : _inst_1 -> R} {w : _inst_1 -> R}, Iff (forall (u : _inst_1 -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) v u) (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) w u)) (Eq.{max (succ u1) (succ u2)} (_inst_1 -> R) v w)
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] {v : n -> R} {w : n -> R}, Iff (forall (u : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v u) (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) w u)) (Eq.{max (succ u1) (succ u2)} (n -> R) v w)
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_eq_iff Matrix.dotProduct_eq_iffₓ'. -/
 theorem dotProduct_eq_iff {v w : n → R} : (∀ u, dotProduct v u = dotProduct w u) ↔ v = w :=
   ⟨fun h => dotProduct_eq v w h, fun h _ => h ▸ rfl⟩
@@ -97,7 +97,7 @@ theorem dotProduct_eq_iff {v w : n → R} : (∀ u, dotProduct v u = dotProduct
 lean 3 declaration is
   forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] (v : n -> R), (forall (w : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v w) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [n : Semiring.{u1} R] {_inst_1 : Type.{u2}} [_inst_2 : Fintype.{u2} _inst_1] (v : _inst_1 -> R), (forall (w : _inst_1 -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) v w) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R n))))) -> (Eq.{max (succ u1) (succ u2)} (_inst_1 -> R) v (OfNat.ofNat.{max u1 u2} (_inst_1 -> R) 0 (Zero.toOfNat0.{max u1 u2} (_inst_1 -> R) (Pi.instZero.{u2, u1} _inst_1 (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.355 : _inst_1) => R) (fun (i : _inst_1) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R n))))))
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] (v : n -> R), (forall (w : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v w) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{max (succ u1) (succ u2)} (n -> R) v (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.359 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_eq_zero Matrix.dotProduct_eq_zeroₓ'. -/
 theorem dotProduct_eq_zero (v : n → R) (h : ∀ w, dotProduct v w = 0) : v = 0 :=
   dotProduct_eq _ _ fun u => (h u).symm ▸ (zero_dotProduct u).symm
@@ -107,7 +107,7 @@ theorem dotProduct_eq_zero (v : n → R) (h : ∀ w, dotProduct v w = 0) : v = 0
 lean 3 declaration is
   forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] {v : n -> R}, Iff (forall (w : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v w) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [n : Semiring.{u1} R] {_inst_1 : Type.{u2}} [_inst_2 : Fintype.{u2} _inst_1] {v : _inst_1 -> R}, Iff (forall (w : _inst_1 -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) v w) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R n))))) (Eq.{max (succ u1) (succ u2)} (_inst_1 -> R) v (OfNat.ofNat.{max u1 u2} (_inst_1 -> R) 0 (Zero.toOfNat0.{max u1 u2} (_inst_1 -> R) (Pi.instZero.{u2, u1} _inst_1 (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.403 : _inst_1) => R) (fun (i : _inst_1) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R n))))))
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] {v : n -> R}, Iff (forall (w : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v w) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (Eq.{max (succ u1) (succ u2)} (n -> R) v (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.407 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_eq_zero_iff Matrix.dotProduct_eq_zero_iffₓ'. -/
 theorem dotProduct_eq_zero_iff {v : n → R} : (∀ w, dotProduct v w = 0) ↔ v = 0 :=
   ⟨fun h => dotProduct_eq_zero v h, fun h w => h.symm ▸ zero_dotProduct w⟩
@@ -119,12 +119,24 @@ section Self
 
 variable [Fintype n]
 
+/- warning: matrix.dot_product_self_eq_zero -> Matrix.dotProduct_self_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : LinearOrderedRing.{u1} R] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R _inst_2)))) v v) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R _inst_2))))))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R _inst_2))))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : LinearOrderedRing.{u1} R] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R _inst_2))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toLinearOrderedSemiring.{u1} R _inst_2)))) v v) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toLinearOrderedSemiring.{u1} R _inst_2)))))))) (Eq.{max (succ u1) (succ u2)} (n -> R) v (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.467 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toLinearOrderedSemiring.{u1} R _inst_2)))))))))
+Case conversion may be inaccurate. Consider using '#align matrix.dot_product_self_eq_zero Matrix.dotProduct_self_eq_zeroₓ'. -/
 @[simp]
 theorem dotProduct_self_eq_zero [LinearOrderedRing R] {v : n → R} : dotProduct v v = 0 ↔ v = 0 :=
   (Finset.sum_eq_zero_iff_of_nonneg fun i _ => mul_self_nonneg (v i)).trans <| by
     simp [Function.funext_iff]
 #align matrix.dot_product_self_eq_zero Matrix.dotProduct_self_eq_zero
 
+/- warning: matrix.dot_product_star_self_eq_zero -> Matrix.dotProduct_star_self_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2))] [_inst_4 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2)) _inst_3))) (Star.star.{max u2 u1} (n -> R) (Pi.hasStar.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => 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 (StrictOrderedRing.toRing.{u1} R _inst_2)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2)) _inst_3))))) v) v) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2)] [_inst_4 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))) (Star.star.{max u2 u1} (n -> R) (Pi.instStarForAll.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2) _inst_3))))) v) v) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))) (Eq.{max (succ u1) (succ u2)} (n -> R) v (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.521 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))))
+Case conversion may be inaccurate. Consider using '#align matrix.dot_product_star_self_eq_zero Matrix.dotProduct_star_self_eq_zeroₓ'. -/
 /-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
 @[simp]
 theorem dotProduct_star_self_eq_zero [StrictOrderedRing R] [StarOrderedRing R] [NoZeroDivisors R]
@@ -133,6 +145,12 @@ theorem dotProduct_star_self_eq_zero [StrictOrderedRing R] [StarOrderedRing R] [
     simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_star_self_eq_zero Matrix.dotProduct_star_self_eq_zero
 
+/- warning: matrix.dot_product_self_star_eq_zero -> Matrix.dotProduct_self_star_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2))] [_inst_4 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StarOrderedRing.orderedAddCommGroup.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2)) _inst_3))) v (Star.star.{max u2 u1} (n -> R) (Pi.hasStar.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => 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 (StrictOrderedRing.toRing.{u1} R _inst_2)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R _inst_2)) _inst_3))))) v)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : StrictOrderedRing.{u1} R] [_inst_3 : StarOrderedRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2)] [_inst_4 : NoZeroDivisors.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))] {v : n -> R}, Iff (Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_1 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))) v (Star.star.{max u1 u2} (n -> R) (Pi.instStarForAll.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StarOrderedRing.toStarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (StrictOrderedRing.toRing.{u1} R _inst_2))) (StrictOrderedRing.toPartialOrder.{u1} R _inst_2) _inst_3))))) v)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))) (Eq.{max (succ u1) (succ u2)} (n -> R) v (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.579 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R _inst_2))))))))
+Case conversion may be inaccurate. Consider using '#align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zeroₓ'. -/
 /-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
 @[simp]
 theorem dotProduct_self_star_eq_zero [StrictOrderedRing R] [StarOrderedRing R] [NoZeroDivisors R]

bump to nightly-2023-04-13-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/347636a7a80595d55bedf6e6fbd996a3c39da69a

bd75793a

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.dot_product
-! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
+! leanprover-community/mathlib commit 46822d96c0c0a8e58a41a0cba1291620967575c5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -36,15 +36,19 @@ matrix, reindex
 
 universe v w
 
+variable {R : Type v} {n : Type w}
+
 namespace Matrix
 
-variable {R : Type v} [Semiring R] {n : Type w} [Fintype n]
+section Semiring
+
+variable [Semiring R] [Fintype n]
 
 /- warning: matrix.dot_product_std_basis_eq_mul -> Matrix.dotProduct_stdBasis_eq_mul is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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+  forall {R : Type.{u1}} [n : Semiring.{u1} R] {_inst_1 : Type.{u2}} [_inst_2 : Fintype.{u2} _inst_1] [_inst_3 : DecidableEq.{succ u2} _inst_1] (v : _inst_1 -> R) (c : R) (i : _inst_1), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) v (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R n n (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R n)) R (_inst_1 -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) n))) (Pi.addCommMonoid.{u2, u1} _inst_1 (fun (i : _inst_1) => R) (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) n)))) (Semiring.toModule.{u1} R n) (Pi.module.{u2, u1, u1} _inst_1 (fun (i : _inst_1) => R) R n (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.48 : _inst_1) => R) i) n))) (fun (i : _inst_1) => Semiring.toModule.{u1} R n))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => _inst_1 -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (_inst_1 -> R) n n (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n))) (Pi.addCommMonoid.{u2, u1} _inst_1 (fun (i : _inst_1) => R) (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n)))) (Semiring.toModule.{u1} R n) (Pi.module.{u2, u1, u1} _inst_1 (fun (i : _inst_1) => R) R n (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n))) (fun (i : _inst_1) => Semiring.toModule.{u1} R n)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (LinearMap.stdBasis.{u1, u2, u1} R _inst_1 n (fun (_x : _inst_1) => R) (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n))) (fun (i : _inst_1) => Semiring.toModule.{u1} R n) (fun (a : _inst_1) (b : _inst_1) => _inst_3 a b) i) c)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n)))) (v i) c)
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_std_basis_eq_mul Matrix.dotProduct_stdBasis_eq_mulₓ'. -/
 @[simp]
 theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n) :
@@ -57,9 +61,9 @@ theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n)
 
 /- warning: matrix.dot_product_std_basis_one -> Matrix.dotProduct_stdBasis_one is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Type.{u2}} [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u2} n] (v : n -> R) (i : n), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (n -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => n -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (n -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} n (fun (i : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} n (fun (i : n) => R) R _inst_1 (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R n _inst_1 (fun (_x : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : n) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : n) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : n) => R) i) _inst_1))) (fun (i : n) => Semiring.toModule.{u1} R _inst_1) (fun (a : n) (b : n) => _inst_3 a b) i) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))) (v i)
+  forall {R : Type.{u1}} [n : Semiring.{u1} R] {_inst_1 : Type.{u2}} [_inst_2 : Fintype.{u2} _inst_1] [_inst_3 : DecidableEq.{succ u2} _inst_1] (v : _inst_1 -> R) (i : _inst_1), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) v (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R n n (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R n)) R (_inst_1 -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) n))) (Pi.addCommMonoid.{u2, u1} _inst_1 (fun (i : _inst_1) => R) (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) n)))) (Semiring.toModule.{u1} R n) (Pi.module.{u2, u1, u1} _inst_1 (fun (i : _inst_1) => R) R n (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.175 : _inst_1) => R) i) n))) (fun (i : _inst_1) => Semiring.toModule.{u1} R n))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => _inst_1 -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (_inst_1 -> R) n n (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n))) (Pi.addCommMonoid.{u2, u1} _inst_1 (fun (i : _inst_1) => R) (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n)))) (Semiring.toModule.{u1} R n) (Pi.module.{u2, u1, u1} _inst_1 (fun (i : _inst_1) => R) R n (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n))) (fun (i : _inst_1) => Semiring.toModule.{u1} R n)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (LinearMap.stdBasis.{u1, u2, u1} R _inst_1 n (fun (_x : _inst_1) => R) (fun (i : _inst_1) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : _inst_1) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : _inst_1) => R) i) n))) (fun (i : _inst_1) => Semiring.toModule.{u1} R n) (fun (a : _inst_1) (b : _inst_1) => _inst_3 a b) i) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R n))))) (v i)
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_std_basis_one Matrix.dotProduct_stdBasis_oneₓ'. -/
 @[simp]
 theorem dotProduct_stdBasis_one [DecidableEq n] (v : n → R) (i : n) :
@@ -69,9 +73,9 @@ theorem dotProduct_stdBasis_one [DecidableEq n] (v : n → R) (i : n) :
 
 /- warning: matrix.dot_product_eq -> Matrix.dotProduct_eq is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Type.{u2}} [_inst_2 : Fintype.{u2} n] (v : n -> R) (w : n -> R), (forall (u : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v u) (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) w u)) -> (Eq.{max (succ u2) (succ u1)} (n -> R) v w)
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] (v : n -> R) (w : n -> R), (forall (u : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v u) (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) w u)) -> (Eq.{max (succ u2) (succ u1)} (n -> R) v w)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Type.{u2}} [_inst_2 : Fintype.{u2} n] (v : n -> R) (w : n -> R), (forall (u : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v u) (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) w u)) -> (Eq.{max (succ u1) (succ u2)} (n -> R) v w)
+  forall {R : Type.{u1}} [n : Semiring.{u1} R] {_inst_1 : Type.{u2}} [_inst_2 : Fintype.{u2} _inst_1] (v : _inst_1 -> R) (w : _inst_1 -> R), (forall (u : _inst_1 -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) v u) (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) w u)) -> (Eq.{max (succ u1) (succ u2)} (_inst_1 -> R) v w)
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_eq Matrix.dotProduct_eqₓ'. -/
 theorem dotProduct_eq (v w : n → R) (h : ∀ u, dotProduct v u = dotProduct w u) : v = w :=
   by
@@ -81,9 +85,9 @@ theorem dotProduct_eq (v w : n → R) (h : ∀ u, dotProduct v u = dotProduct w
 
 /- warning: matrix.dot_product_eq_iff -> Matrix.dotProduct_eq_iff is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Type.{u2}} [_inst_2 : Fintype.{u2} n] {v : n -> R} {w : n -> R}, Iff (forall (u : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v u) (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) w u)) (Eq.{max (succ u2) (succ u1)} (n -> R) v w)
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] {v : n -> R} {w : n -> R}, Iff (forall (u : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v u) (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) w u)) (Eq.{max (succ u2) (succ u1)} (n -> R) v w)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Type.{u2}} [_inst_2 : Fintype.{u2} n] {v : n -> R} {w : n -> R}, Iff (forall (u : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v u) (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) w u)) (Eq.{max (succ u1) (succ u2)} (n -> R) v w)
+  forall {R : Type.{u1}} [n : Semiring.{u1} R] {_inst_1 : Type.{u2}} [_inst_2 : Fintype.{u2} _inst_1] {v : _inst_1 -> R} {w : _inst_1 -> R}, Iff (forall (u : _inst_1 -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) v u) (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) w u)) (Eq.{max (succ u1) (succ u2)} (_inst_1 -> R) v w)
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_eq_iff Matrix.dotProduct_eq_iffₓ'. -/
 theorem dotProduct_eq_iff {v w : n → R} : (∀ u, dotProduct v u = dotProduct w u) ↔ v = w :=
   ⟨fun h => dotProduct_eq v w h, fun h _ => h ▸ rfl⟩
@@ -91,9 +95,9 @@ theorem dotProduct_eq_iff {v w : n → R} : (∀ u, dotProduct v u = dotProduct
 
 /- warning: matrix.dot_product_eq_zero -> Matrix.dotProduct_eq_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Type.{u2}} [_inst_2 : Fintype.{u2} n] (v : n -> R), (forall (w : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v w) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))))
+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] (v : n -> R), (forall (w : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v w) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Type.{u2}} [_inst_2 : Fintype.{u2} n] (v : n -> R), (forall (w : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v w) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{max (succ u1) (succ u2)} (n -> R) v (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.355 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))))
+  forall {R : Type.{u1}} [n : Semiring.{u1} R] {_inst_1 : Type.{u2}} [_inst_2 : Fintype.{u2} _inst_1] (v : _inst_1 -> R), (forall (w : _inst_1 -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) v w) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R n))))) -> (Eq.{max (succ u1) (succ u2)} (_inst_1 -> R) v (OfNat.ofNat.{max u1 u2} (_inst_1 -> R) 0 (Zero.toOfNat0.{max u1 u2} (_inst_1 -> R) (Pi.instZero.{u2, u1} _inst_1 (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.355 : _inst_1) => R) (fun (i : _inst_1) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R n))))))
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_eq_zero Matrix.dotProduct_eq_zeroₓ'. -/
 theorem dotProduct_eq_zero (v : n → R) (h : ∀ w, dotProduct v w = 0) : v = 0 :=
   dotProduct_eq _ _ fun u => (h u).symm ▸ (zero_dotProduct u).symm
@@ -101,13 +105,43 @@ theorem dotProduct_eq_zero (v : n → R) (h : ∀ w, dotProduct v w = 0) : v = 0
 
 /- warning: matrix.dot_product_eq_zero_iff -> Matrix.dotProduct_eq_zero_iff is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} {n : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Fintype.{u2} n] {v : n -> R}, Iff (forall (w : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v w) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Type.{u2}} [_inst_2 : Fintype.{u2} n] {v : n -> R}, Iff (forall (w : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v w) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (Eq.{max (succ u1) (succ u2)} (n -> R) v (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.403 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))))
+  forall {R : Type.{u1}} [n : Semiring.{u1} R] {_inst_1 : Type.{u2}} [_inst_2 : Fintype.{u2} _inst_1] {v : _inst_1 -> R}, Iff (forall (w : _inst_1 -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} _inst_1 R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R n))) v w) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R n))))) (Eq.{max (succ u1) (succ u2)} (_inst_1 -> R) v (OfNat.ofNat.{max u1 u2} (_inst_1 -> R) 0 (Zero.toOfNat0.{max u1 u2} (_inst_1 -> R) (Pi.instZero.{u2, u1} _inst_1 (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.403 : _inst_1) => R) (fun (i : _inst_1) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R n))))))
 Case conversion may be inaccurate. Consider using '#align matrix.dot_product_eq_zero_iff Matrix.dotProduct_eq_zero_iffₓ'. -/
 theorem dotProduct_eq_zero_iff {v : n → R} : (∀ w, dotProduct v w = 0) ↔ v = 0 :=
   ⟨fun h => dotProduct_eq_zero v h, fun h w => h.symm ▸ zero_dotProduct w⟩
 #align matrix.dot_product_eq_zero_iff Matrix.dotProduct_eq_zero_iff
 
+end Semiring
+
+section Self
+
+variable [Fintype n]
+
+@[simp]
+theorem dotProduct_self_eq_zero [LinearOrderedRing R] {v : n → R} : dotProduct v v = 0 ↔ v = 0 :=
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => mul_self_nonneg (v i)).trans <| by
+    simp [Function.funext_iff]
+#align matrix.dot_product_self_eq_zero Matrix.dotProduct_self_eq_zero
+
+/-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
+@[simp]
+theorem dotProduct_star_self_eq_zero [StrictOrderedRing R] [StarOrderedRing R] [NoZeroDivisors R]
+    {v : n → R} : dotProduct (star v) v = 0 ↔ v = 0 :=
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => @star_mul_self_nonneg _ _ _ _ (v i)).trans <| by
+    simp [Function.funext_iff, mul_eq_zero]
+#align matrix.dot_product_star_self_eq_zero Matrix.dotProduct_star_self_eq_zero
+
+/-- Note that this applies to `ℂ` via `complex.strict_ordered_comm_ring`. -/
+@[simp]
+theorem dotProduct_self_star_eq_zero [StrictOrderedRing R] [StarOrderedRing R] [NoZeroDivisors R]
+    {v : n → R} : dotProduct v (star v) = 0 ↔ v = 0 :=
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => @star_mul_self_nonneg' _ _ _ _ (v i)).trans <| by
+    simp [Function.funext_iff, mul_eq_zero]
+#align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zero
+
+end Self
+
 end Matrix

19cb3751

bump to nightly-2023-04-09-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/284fdd2962e67d2932fa3a79ce19fcf92d38e228

32290448

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.dot_product
-! leanprover-community/mathlib commit 738c19f572805cff525a93aa4ffbdf232df05aa8
+! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.LinearAlgebra.StdBasis
 /-!
 # Dot product of two vectors
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains some results on the map `matrix.dot_product`, which maps two
 vectors `v w : n → R` to the sum of the entrywise products `v i * w i`.

bump to nightly-2023-04-06-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

2687d71c

Diff

@@ -37,6 +37,12 @@ namespace Matrix
 
 variable {R : Type v} [Semiring R] {n : Type w} [Fintype n]
 
+/- warning: matrix.dot_product_std_basis_eq_mul -> Matrix.dotProduct_stdBasis_eq_mul is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.dot_product_std_basis_eq_mul Matrix.dotProduct_stdBasis_eq_mulₓ'. -/
 @[simp]
 theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n) :
     dotProduct v (LinearMap.stdBasis R (fun _ => R) i c) = v i * c :=
@@ -46,26 +52,56 @@ theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n)
   exact fun hi => False.elim (hi <| Finset.mem_univ _)
 #align matrix.dot_product_std_basis_eq_mul Matrix.dotProduct_stdBasis_eq_mul
 
+/- warning: matrix.dot_product_std_basis_one -> Matrix.dotProduct_stdBasis_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.dot_product_std_basis_one Matrix.dotProduct_stdBasis_oneₓ'. -/
 @[simp]
 theorem dotProduct_stdBasis_one [DecidableEq n] (v : n → R) (i : n) :
     dotProduct v (LinearMap.stdBasis R (fun _ => R) i 1) = v i := by
   rw [dot_product_std_basis_eq_mul, mul_one]
 #align matrix.dot_product_std_basis_one Matrix.dotProduct_stdBasis_one
 
+/- warning: matrix.dot_product_eq -> Matrix.dotProduct_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.dot_product_eq Matrix.dotProduct_eqₓ'. -/
 theorem dotProduct_eq (v w : n → R) (h : ∀ u, dotProduct v u = dotProduct w u) : v = w :=
   by
   funext x
   classical rw [← dot_product_std_basis_one v x, ← dot_product_std_basis_one w x, h]
 #align matrix.dot_product_eq Matrix.dotProduct_eq
 
+/- warning: matrix.dot_product_eq_iff -> Matrix.dotProduct_eq_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Type.{u2}} [_inst_2 : Fintype.{u2} n] {v : n -> R} {w : n -> R}, Iff (forall (u : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v u) (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) w u)) (Eq.{max (succ u2) (succ u1)} (n -> R) v w)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Type.{u2}} [_inst_2 : Fintype.{u2} n] {v : n -> R} {w : n -> R}, Iff (forall (u : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v u) (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) w u)) (Eq.{max (succ u1) (succ u2)} (n -> R) v w)
+Case conversion may be inaccurate. Consider using '#align matrix.dot_product_eq_iff Matrix.dotProduct_eq_iffₓ'. -/
 theorem dotProduct_eq_iff {v w : n → R} : (∀ u, dotProduct v u = dotProduct w u) ↔ v = w :=
   ⟨fun h => dotProduct_eq v w h, fun h _ => h ▸ rfl⟩
 #align matrix.dot_product_eq_iff Matrix.dotProduct_eq_iff
 
+/- warning: matrix.dot_product_eq_zero -> Matrix.dotProduct_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Type.{u2}} [_inst_2 : Fintype.{u2} n] (v : n -> R), (forall (w : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v w) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.dot_product_eq_zero Matrix.dotProduct_eq_zeroₓ'. -/
 theorem dotProduct_eq_zero (v : n → R) (h : ∀ w, dotProduct v w = 0) : v = 0 :=
   dotProduct_eq _ _ fun u => (h u).symm ▸ (zero_dotProduct u).symm
 #align matrix.dot_product_eq_zero Matrix.dotProduct_eq_zero
 
+/- warning: matrix.dot_product_eq_zero_iff -> Matrix.dotProduct_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Type.{u2}} [_inst_2 : Fintype.{u2} n] {v : n -> R}, Iff (forall (w : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v w) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (Eq.{max (succ u2) (succ u1)} (n -> R) v (OfNat.ofNat.{max u2 u1} (n -> R) 0 (OfNat.mk.{max u2 u1} (n -> R) 0 (Zero.zero.{max u2 u1} (n -> R) (Pi.instZero.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Type.{u2}} [_inst_2 : Fintype.{u2} n] {v : n -> R}, Iff (forall (w : n -> R), Eq.{succ u1} R (Matrix.dotProduct.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) v w) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (Eq.{max (succ u1) (succ u2)} (n -> R) v (OfNat.ofNat.{max u1 u2} (n -> R) 0 (Zero.toOfNat0.{max u1 u2} (n -> R) (Pi.instZero.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.DotProduct._hyg.403 : n) => R) (fun (i : n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align matrix.dot_product_eq_zero_iff Matrix.dotProduct_eq_zero_iffₓ'. -/
 theorem dotProduct_eq_zero_iff {v : n → R} : (∀ w, dotProduct v w = 0) ↔ v = 0 :=
   ⟨fun h => dotProduct_eq_zero v h, fun h w => h.symm ▸ zero_dotProduct w⟩
 #align matrix.dot_product_eq_zero_iff Matrix.dotProduct_eq_zero_iff

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -42,7 +42,7 @@ theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n)
     dotProduct v (LinearMap.stdBasis R (fun _ => R) i c) = v i * c :=
   by
   rw [dot_product, Finset.sum_eq_single i, LinearMap.stdBasis_same]
-  exact fun _ _ hb => by rw [LinearMap.stdBasis_ne _ _ _ _ hb, mul_zero]
+  exact fun _ _ hb => by rw [LinearMap.stdBasis_ne _ _ _ _ hb, MulZeroClass.mul_zero]
   exact fun hi => False.elim (hi <| Finset.mem_univ _)
 #align matrix.dot_product_std_basis_eq_mul Matrix.dotProduct_stdBasis_eq_mul

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore: adapt to multiple goal linter 3 (#12372)

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

d29b3780

Diff

@@ -41,8 +41,8 @@ variable [Semiring R] [Fintype n]
 theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n) :
     dotProduct v (LinearMap.stdBasis R (fun _ => R) i c) = v i * c := by
   rw [dotProduct, Finset.sum_eq_single i, LinearMap.stdBasis_same]
-  exact fun _ _ hb => by rw [LinearMap.stdBasis_ne _ _ _ _ hb, mul_zero]
-  exact fun hi => False.elim (hi <| Finset.mem_univ _)
+  · exact fun _ _ hb => by rw [LinearMap.stdBasis_ne _ _ _ _ hb, mul_zero]
+  · exact fun hi => False.elim (hi <| Finset.mem_univ _)
 #align matrix.dot_product_std_basis_eq_mul Matrix.dotProduct_stdBasis_eq_mul
 
 -- @[simp] -- Porting note (#10618): simp can prove this

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

@@ -99,19 +99,19 @@ theorem dotProduct_self_eq_zero [LinearOrderedRing R] {v : n → R} : dotProduct
 
 section StarOrderedRing
 
-variable [PartialOrder R] [NonUnitalRing R] [StarOrderedRing R] [NoZeroDivisors R]
+variable [PartialOrder R] [NonUnitalRing R] [StarRing R] [StarOrderedRing R] [NoZeroDivisors R]
 
 /-- Note that this applies to `ℂ` via `Complex.strictOrderedCommRing`. -/
 @[simp]
 theorem dotProduct_star_self_eq_zero {v : n → R} : dotProduct (star v) v = 0 ↔ v = 0 :=
-  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@star_mul_self_nonneg _ _ _ _ (v i) : _)).trans <|
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (star_mul_self_nonneg (r := v i) : _)).trans <|
     by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_star_self_eq_zero Matrix.dotProduct_star_self_eq_zero
 
 /-- Note that this applies to `ℂ` via `Complex.strictOrderedCommRing`. -/
 @[simp]
 theorem dotProduct_self_star_eq_zero {v : n → R} : dotProduct v (star v) = 0 ↔ v = 0 :=
-  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@mul_star_self_nonneg _ _ _ _ (v i) : _)).trans <|
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (mul_star_self_nonneg (r := v i) : _)).trans <|
     by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zero

chore: classify simp can do this porting notes (#10619)

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

de765f60

Diff

@@ -45,7 +45,7 @@ theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n)
   exact fun hi => False.elim (hi <| Finset.mem_univ _)
 #align matrix.dot_product_std_basis_eq_mul Matrix.dotProduct_stdBasis_eq_mul
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem dotProduct_stdBasis_one [DecidableEq n] (v : n → R) (i : n) :
     dotProduct v (LinearMap.stdBasis R (fun _ => R) i 1) = v i := by
   rw [dotProduct_stdBasis_eq_mul, mul_one]

chore: Matrix.mulVec and Matrix.vecMul get infix notation (#10297)

Zulip discussion: https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/Notation.20for.20mul_vec.20and.20vec_mul

Co-authored-by: Martin Dvorak <mdvorak@ista.ac.at>

deb48fab

Diff

@@ -148,21 +148,21 @@ lemma mul_conjTranspose_mul_self_eq_zero (A : Matrix m n R) (B : Matrix p n R) :
   simpa only [conjTranspose_conjTranspose] using mul_self_mul_conjTranspose_eq_zero Aᴴ _
 
 lemma conjTranspose_mul_self_mulVec_eq_zero (A : Matrix m n R) (v : n → R) :
-    (Aᴴ * A).mulVec v = 0 ↔ A.mulVec v = 0 := by
+    (Aᴴ * A) *ᵥ v = 0 ↔ A *ᵥ v = 0 := by
   simpa only [← Matrix.col_mulVec, col_eq_zero] using
     conjTranspose_mul_self_mul_eq_zero A (col v)
 
 lemma self_mul_conjTranspose_mulVec_eq_zero (A : Matrix m n R) (v : m → R) :
-    (A * Aᴴ).mulVec v = 0 ↔ Aᴴ.mulVec v = 0 := by
+    (A * Aᴴ) *ᵥ v = 0 ↔ Aᴴ *ᵥ v = 0 := by
   simpa only [conjTranspose_conjTranspose] using conjTranspose_mul_self_mulVec_eq_zero Aᴴ _
 
 lemma vecMul_conjTranspose_mul_self_eq_zero (A : Matrix m n R) (v : n → R) :
-    vecMul v (Aᴴ * A) = 0 ↔ vecMul v Aᴴ = 0 := by
+    v ᵥ* (Aᴴ * A) = 0 ↔ v ᵥ* Aᴴ = 0 := by
   simpa only [← Matrix.row_vecMul, row_eq_zero] using
     mul_conjTranspose_mul_self_eq_zero A (row v)
 
 lemma vecMul_self_mul_conjTranspose_eq_zero (A : Matrix m n R) (v : m → R) :
-    vecMul v (A * Aᴴ) = 0 ↔ vecMul v A = 0 := by
+    v ᵥ* (A * Aᴴ) = 0 ↔ v ᵥ* A = 0 := by
   simpa only [conjTranspose_conjTranspose] using vecMul_conjTranspose_mul_self_eq_zero Aᴴ _
 
 end StarOrderedRing

Matrix.dotProduct inequalities (#9652)

18cc8db1

Diff

@@ -70,6 +70,23 @@ theorem dotProduct_eq_zero_iff {v : n → R} : (∀ w, dotProduct v w = 0) ↔ v
 
 end Semiring
 
+section OrderedSemiring
+
+variable [OrderedSemiring R] [Fintype n]
+
+lemma dotProduct_nonneg_of_nonneg {v w : n → R} (hv : 0 ≤ v) (hw : 0 ≤ w) : 0 ≤ dotProduct v w :=
+  Finset.sum_nonneg (fun i _ => mul_nonneg (hv i) (hw i))
+
+lemma dotProduct_le_dotProduct_of_nonneg_right {u v w : n → R} (huv : u ≤ v) (hw : 0 ≤ w) :
+    dotProduct u w ≤ dotProduct v w :=
+  Finset.sum_le_sum (fun i _ => mul_le_mul_of_nonneg_right (huv i) (hw i))
+
+lemma dotProduct_le_dotProduct_of_nonneg_left {u v w : n → R} (huv : u ≤ v) (hw : 0 ≤ w) :
+    dotProduct w u ≤ dotProduct w v :=
+  Finset.sum_le_sum (fun i _ => mul_le_mul_of_nonneg_left (huv i) (hw i))
+
+end OrderedSemiring
+
 section Self
 
 variable [Fintype m] [Fintype n] [Fintype p]

chore: rename star_mul_self_nonneg' (#8305)

7a1bf932

Diff

@@ -94,7 +94,7 @@ theorem dotProduct_star_self_eq_zero {v : n → R} : dotProduct (star v) v = 0 
 /-- Note that this applies to `ℂ` via `Complex.strictOrderedCommRing`. -/
 @[simp]
 theorem dotProduct_self_star_eq_zero {v : n → R} : dotProduct v (star v) = 0 ↔ v = 0 :=
-  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@star_mul_self_nonneg' _ _ _ _ (v i) : _)).trans <|
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@mul_star_self_nonneg _ _ _ _ (v i) : _)).trans <|
     by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zero

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

@@ -41,7 +41,7 @@ variable [Semiring R] [Fintype n]
 theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n) :
     dotProduct v (LinearMap.stdBasis R (fun _ => R) i c) = v i * c := by
   rw [dotProduct, Finset.sum_eq_single i, LinearMap.stdBasis_same]
-  exact fun _ _ hb => by rw [LinearMap.stdBasis_ne _ _ _ _ hb, MulZeroClass.mul_zero]
+  exact fun _ _ hb => by rw [LinearMap.stdBasis_ne _ _ _ _ hb, mul_zero]
   exact fun hi => False.elim (hi <| Finset.mem_univ _)
 #align matrix.dot_product_std_basis_eq_mul Matrix.dotProduct_stdBasis_eq_mul

feat: star self dot product eq zero and kernel lemmas apply to matrices not just vectors (#6587)

This generalizes two results about vectors to matrices:

dotProduct_star_self_eq_zero to conjTranspose_mul_self_eq_zero
dotProduct_self_star_eq_zero to self_mul_conjTranspose_eq_zero

It also adds lemmas linking the kernel (under left-multiplication, right-multiplication, vecMul, and mulVec) of $A$, $A^HA$, and $AA^H$.

Some of these lemmas are used in the SVD decomposition theorem of R or C matrices #6042

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

ae74c2e5

Diff

@@ -29,9 +29,7 @@ matrix, reindex
 -/
 
 
-universe v w
-
-variable {R : Type v} {n : Type w}
+variable {m n p R : Type*}
 
 namespace Matrix
 
@@ -74,7 +72,7 @@ end Semiring
 
 section Self
 
-variable [Fintype n]
+variable [Fintype m] [Fintype n] [Fintype p]
 
 @[simp]
 theorem dotProduct_self_eq_zero [LinearOrderedRing R] {v : n → R} : dotProduct v v = 0 ↔ v = 0 :=
@@ -82,22 +80,76 @@ theorem dotProduct_self_eq_zero [LinearOrderedRing R] {v : n → R} : dotProduct
     simp [Function.funext_iff]
 #align matrix.dot_product_self_eq_zero Matrix.dotProduct_self_eq_zero
 
+section StarOrderedRing
+
+variable [PartialOrder R] [NonUnitalRing R] [StarOrderedRing R] [NoZeroDivisors R]
+
 /-- Note that this applies to `ℂ` via `Complex.strictOrderedCommRing`. -/
 @[simp]
-theorem dotProduct_star_self_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrderedRing R]
-    [NoZeroDivisors R] {v : n → R} : dotProduct (star v) v = 0 ↔ v = 0 :=
+theorem dotProduct_star_self_eq_zero {v : n → R} : dotProduct (star v) v = 0 ↔ v = 0 :=
   (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@star_mul_self_nonneg _ _ _ _ (v i) : _)).trans <|
     by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_star_self_eq_zero Matrix.dotProduct_star_self_eq_zero
 
 /-- Note that this applies to `ℂ` via `Complex.strictOrderedCommRing`. -/
 @[simp]
-theorem dotProduct_self_star_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrderedRing R]
-    [NoZeroDivisors R] {v : n → R} : dotProduct v (star v) = 0 ↔ v = 0 :=
+theorem dotProduct_self_star_eq_zero {v : n → R} : dotProduct v (star v) = 0 ↔ v = 0 :=
   (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@star_mul_self_nonneg' _ _ _ _ (v i) : _)).trans <|
     by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zero
 
+@[simp]
+lemma conjTranspose_mul_self_eq_zero {A : Matrix m n R} : Aᴴ * A = 0 ↔ A = 0 :=
+  ⟨fun h => Matrix.ext fun i j =>
+    (congr_fun <| dotProduct_star_self_eq_zero.1 <| Matrix.ext_iff.2 h j j) i,
+  fun h => h ▸ Matrix.mul_zero _⟩
+
+@[simp]
+lemma self_mul_conjTranspose_eq_zero {A : Matrix m n R} : A * Aᴴ = 0 ↔ A = 0 :=
+  ⟨fun h => Matrix.ext fun i j =>
+    (congr_fun <| dotProduct_self_star_eq_zero.1 <| Matrix.ext_iff.2 h i i) j,
+  fun h => h ▸ Matrix.zero_mul _⟩
+
+lemma conjTranspose_mul_self_mul_eq_zero (A : Matrix m n R) (B : Matrix n p R) :
+    (Aᴴ * A) * B = 0 ↔ A * B = 0 := by
+  refine ⟨fun h => ?_, fun h => by simp only [Matrix.mul_assoc, h, Matrix.mul_zero]⟩
+  apply_fun (Bᴴ * ·) at h
+  rwa [Matrix.mul_zero, Matrix.mul_assoc, ← Matrix.mul_assoc, ← conjTranspose_mul,
+    conjTranspose_mul_self_eq_zero] at h
+
+lemma self_mul_conjTranspose_mul_eq_zero (A : Matrix m n R) (B : Matrix m p R) :
+    (A * Aᴴ) * B = 0 ↔ Aᴴ * B = 0 := by
+  simpa only [conjTranspose_conjTranspose] using conjTranspose_mul_self_mul_eq_zero Aᴴ _
+
+lemma mul_self_mul_conjTranspose_eq_zero (A : Matrix m n R) (B : Matrix p m R) :
+    B * (A * Aᴴ) = 0 ↔ B * A = 0 := by
+  rw [← conjTranspose_eq_zero, conjTranspose_mul, conjTranspose_mul, conjTranspose_conjTranspose,
+    self_mul_conjTranspose_mul_eq_zero, ← conjTranspose_mul, conjTranspose_eq_zero]
+
+lemma mul_conjTranspose_mul_self_eq_zero (A : Matrix m n R) (B : Matrix p n R) :
+    B * (Aᴴ * A) = 0 ↔ B * Aᴴ = 0 := by
+  simpa only [conjTranspose_conjTranspose] using mul_self_mul_conjTranspose_eq_zero Aᴴ _
+
+lemma conjTranspose_mul_self_mulVec_eq_zero (A : Matrix m n R) (v : n → R) :
+    (Aᴴ * A).mulVec v = 0 ↔ A.mulVec v = 0 := by
+  simpa only [← Matrix.col_mulVec, col_eq_zero] using
+    conjTranspose_mul_self_mul_eq_zero A (col v)
+
+lemma self_mul_conjTranspose_mulVec_eq_zero (A : Matrix m n R) (v : m → R) :
+    (A * Aᴴ).mulVec v = 0 ↔ Aᴴ.mulVec v = 0 := by
+  simpa only [conjTranspose_conjTranspose] using conjTranspose_mul_self_mulVec_eq_zero Aᴴ _
+
+lemma vecMul_conjTranspose_mul_self_eq_zero (A : Matrix m n R) (v : n → R) :
+    vecMul v (Aᴴ * A) = 0 ↔ vecMul v Aᴴ = 0 := by
+  simpa only [← Matrix.row_vecMul, row_eq_zero] using
+    mul_conjTranspose_mul_self_eq_zero A (row v)
+
+lemma vecMul_self_mul_conjTranspose_eq_zero (A : Matrix m n R) (v : m → R) :
+    vecMul v (A * Aᴴ) = 0 ↔ vecMul v A = 0 := by
+  simpa only [conjTranspose_conjTranspose] using vecMul_conjTranspose_mul_self_eq_zero Aᴴ _
+
+end StarOrderedRing
+
 end Self
 
 end Matrix

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

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.dot_product
-! 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.Star.Order
 import Mathlib.Data.Matrix.Basic
 import Mathlib.LinearAlgebra.StdBasis
 
+#align_import linear_algebra.matrix.dot_product from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"
+
 /-!
 # Dot product of two vectors

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

@@ -4,10 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.dot_product
-! leanprover-community/mathlib commit 5ac1dab1670014b4c07a82c86a67f3d064a1b3e1
+! 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.Star.Order
 import Mathlib.Data.Matrix.Basic
 import Mathlib.LinearAlgebra.StdBasis

chore: tidy various files (#3474)

4fe63cb5

Diff

@@ -37,7 +37,7 @@ variable {R : Type v} {n : Type w}
 
 namespace Matrix
 
-section semiring
+section Semiring
 
 variable [Semiring R] [Fintype n]
 
@@ -72,9 +72,9 @@ theorem dotProduct_eq_zero_iff {v : n → R} : (∀ w, dotProduct v w = 0) ↔ v
   ⟨fun h => dotProduct_eq_zero v h, fun h w => h.symm ▸ zero_dotProduct w⟩
 #align matrix.dot_product_eq_zero_iff Matrix.dotProduct_eq_zero_iff
 
-end semiring
+end Semiring
 
-section self
+section Self
 
 variable [Fintype n]
 
@@ -100,6 +100,6 @@ theorem dotProduct_self_star_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrd
     by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zero
 
-end self
+end Self
 
 end Matrix

chore: forward port mathlib#18810, 18798, 18738 (#3443)

algebra.order.sub.defs, data.real.nnreal: leanprover-community/mathlib#18810, which is itself a backport. Also fixes a docstring typo.
linear_algebra.matrix.dot_product: leanprover-community/mathlib#18798
data.matrix.basic: leanprover-community/mathlib#18738

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

e978148f

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.dot_product
-! leanprover-community/mathlib commit 46822d96c0c0a8e58a41a0cba1291620967575c5
+! leanprover-community/mathlib commit 5ac1dab1670014b4c07a82c86a67f3d064a1b3e1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -86,18 +86,18 @@ theorem dotProduct_self_eq_zero [LinearOrderedRing R] {v : n → R} : dotProduct
 
 /-- Note that this applies to `ℂ` via `Complex.strictOrderedCommRing`. -/
 @[simp]
-theorem dotProduct_star_self_eq_zero [StrictOrderedRing R] [StarOrderedRing R] [NoZeroDivisors R]
-    {v : n → R} : dotProduct (star v) v = 0 ↔ v = 0 :=
-  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => @star_mul_self_nonneg _ _ _ _ (v i)).trans <| by
-    simp [Function.funext_iff, mul_eq_zero]
+theorem dotProduct_star_self_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrderedRing R]
+    [NoZeroDivisors R] {v : n → R} : dotProduct (star v) v = 0 ↔ v = 0 :=
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@star_mul_self_nonneg _ _ _ _ (v i) : _)).trans <|
+    by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_star_self_eq_zero Matrix.dotProduct_star_self_eq_zero
 
 /-- Note that this applies to `ℂ` via `Complex.strictOrderedCommRing`. -/
 @[simp]
-theorem dotProduct_self_star_eq_zero [StrictOrderedRing R] [StarOrderedRing R] [NoZeroDivisors R]
-    {v : n → R} : dotProduct v (star v) = 0 ↔ v = 0 :=
-  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => @star_mul_self_nonneg' _ _ _ _ (v i)).trans <| by
-    simp [Function.funext_iff, mul_eq_zero]
+theorem dotProduct_self_star_eq_zero [PartialOrder R] [NonUnitalRing R] [StarOrderedRing R]
+    [NoZeroDivisors R] {v : n → R} : dotProduct v (star v) = 0 ↔ v = 0 :=
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => (@star_mul_self_nonneg' _ _ _ _ (v i) : _)).trans <|
+    by simp [Function.funext_iff, mul_eq_zero]
 #align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zero
 
 end self

chore: forward port mathlib#18668, 18781, 18783, 18792, 18794 (#3410)

set_theory.cardinal.basic: forward-ports leanprover-community/mathlib#18781, which backports some ad-hoc changes in #3247 in a more principled way
ring_theory.int.basic: these changes were already forward-ported in #3278, but we forgot the SHA.
linear_algebra.dimension: forward-ports leanprover-community/mathlib#18792
linear_algebra.matrix.dot_product: forward-ports leanprover-community/mathlib#18783
linear_algebra.finrank: forward-ports leanprover-community/mathlib#18794 which is itself a backport of #3378, hence no changes to the file

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

902ce181

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.dot_product
-! leanprover-community/mathlib commit 738c19f572805cff525a93aa4ffbdf232df05aa8
+! leanprover-community/mathlib commit 46822d96c0c0a8e58a41a0cba1291620967575c5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -33,9 +33,13 @@ matrix, reindex
 
 universe v w
 
+variable {R : Type v} {n : Type w}
+
 namespace Matrix
 
-variable {R : Type v} [Semiring R] {n : Type w} [Fintype n]
+section semiring
+
+variable [Semiring R] [Fintype n]
 
 @[simp]
 theorem dotProduct_stdBasis_eq_mul [DecidableEq n] (v : n → R) (c : R) (i : n) :
@@ -68,4 +72,34 @@ theorem dotProduct_eq_zero_iff {v : n → R} : (∀ w, dotProduct v w = 0) ↔ v
   ⟨fun h => dotProduct_eq_zero v h, fun h w => h.symm ▸ zero_dotProduct w⟩
 #align matrix.dot_product_eq_zero_iff Matrix.dotProduct_eq_zero_iff
 
+end semiring
+
+section self
+
+variable [Fintype n]
+
+@[simp]
+theorem dotProduct_self_eq_zero [LinearOrderedRing R] {v : n → R} : dotProduct v v = 0 ↔ v = 0 :=
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => mul_self_nonneg (v i)).trans <| by
+    simp [Function.funext_iff]
+#align matrix.dot_product_self_eq_zero Matrix.dotProduct_self_eq_zero
+
+/-- Note that this applies to `ℂ` via `Complex.strictOrderedCommRing`. -/
+@[simp]
+theorem dotProduct_star_self_eq_zero [StrictOrderedRing R] [StarOrderedRing R] [NoZeroDivisors R]
+    {v : n → R} : dotProduct (star v) v = 0 ↔ v = 0 :=
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => @star_mul_self_nonneg _ _ _ _ (v i)).trans <| by
+    simp [Function.funext_iff, mul_eq_zero]
+#align matrix.dot_product_star_self_eq_zero Matrix.dotProduct_star_self_eq_zero
+
+/-- Note that this applies to `ℂ` via `Complex.strictOrderedCommRing`. -/
+@[simp]
+theorem dotProduct_self_star_eq_zero [StrictOrderedRing R] [StarOrderedRing R] [NoZeroDivisors R]
+    {v : n → R} : dotProduct v (star v) = 0 ↔ v = 0 :=
+  (Finset.sum_eq_zero_iff_of_nonneg fun i _ => @star_mul_self_nonneg' _ _ _ _ (v i)).trans <| by
+    simp [Function.funext_iff, mul_eq_zero]
+#align matrix.dot_product_self_star_eq_zero Matrix.dotProduct_self_star_eq_zero
+
+end self
+
 end Matrix