linear_algebra.matrix.absolute_value | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

ab0a2959

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

9d2f0748

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 -/
-import Mathbin.Data.Int.AbsoluteValue
-import Mathbin.LinearAlgebra.Matrix.Determinant
+import Data.Int.AbsoluteValue
+import LinearAlgebra.Matrix.Determinant
 
 #align_import linear_algebra.matrix.absolute_value from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"

9d2f0748

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.absolute_value
-! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Int.AbsoluteValue
 import Mathbin.LinearAlgebra.Matrix.Determinant
 
+#align_import linear_algebra.matrix.absolute_value from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+
 /-!
 # Absolute values and matrices

9d2f0748

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -43,6 +43,7 @@ variable {R S : Type _} [CommRing R] [Nontrivial R] [LinearOrderedCommRing S]
 
 variable {n : Type _} [Fintype n] [DecidableEq n]
 
+#print Matrix.det_le /-
 theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i j, abv (A i j) ≤ x) :
     abv A.det ≤ Nat.factorial (Fintype.card n) • x ^ Fintype.card n :=
   calc
@@ -57,7 +58,9 @@ theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i
     _ = Nat.factorial (Fintype.card n) • x ^ Fintype.card n := by
       rw [sum_const, Finset.card_univ, Fintype.card_perm]
 #align matrix.det_le Matrix.det_le
+-/
 
+#print Matrix.det_sum_le /-
 theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv : AbsoluteValue R S}
     {x : S} (hx : ∀ k i j, abv (A k i j) ≤ x) :
     abv (det (∑ k in s, A k)) ≤
@@ -69,7 +72,9 @@ theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv
       _ ≤ ∑ k in s, x := (sum_le_sum fun k _ => hx k i j)
       _ = s.card • x := sum_const _
 #align matrix.det_sum_le Matrix.det_sum_le
+-/
 
+#print Matrix.det_sum_smul_le /-
 theorem det_sum_smul_le {ι : Type _} (s : Finset ι) {c : ι → R} {A : ι → Matrix n n R}
     {abv : AbsoluteValue R S} {x : S} (hx : ∀ k i j, abv (A k i j) ≤ x) {y : S}
     (hy : ∀ k, abv (c k) ≤ y) :
@@ -82,6 +87,7 @@ theorem det_sum_smul_le {ι : Type _} (s : Finset ι) {c : ι → R} {A : ι →
         abv (c k * A k i j) = abv (c k) * abv (A k i j) := abv.map_mul _ _
         _ ≤ y * x := mul_le_mul (hy k) (hx k i j) (abv.nonneg _) ((abv.nonneg _).trans (hy k))
 #align matrix.det_sum_smul_le Matrix.det_sum_smul_le
+-/
 
 end Matrix

9d2f0748

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -56,7 +56,6 @@ theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i
       (sum_congr rfl fun _ _ => by rw [prod_const, Finset.card_univ])
     _ = Nat.factorial (Fintype.card n) • x ^ Fintype.card n := by
       rw [sum_const, Finset.card_univ, Fintype.card_perm]
-    
 #align matrix.det_le Matrix.det_le
 
 theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv : AbsoluteValue R S}
@@ -69,7 +68,6 @@ theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv
       _ ≤ ∑ k in s, abv (A k i j) := (abv.sum_le _ _)
       _ ≤ ∑ k in s, x := (sum_le_sum fun k _ => hx k i j)
       _ = s.card • x := sum_const _
-      
 #align matrix.det_sum_le Matrix.det_sum_le
 
 theorem det_sum_smul_le {ι : Type _} (s : Finset ι) {c : ι → R} {A : ι → Matrix n n R}
@@ -83,7 +81,6 @@ theorem det_sum_smul_le {ι : Type _} (s : Finset ι) {c : ι → R} {A : ι →
       calc
         abv (c k * A k i j) = abv (c k) * abv (A k i j) := abv.map_mul _ _
         _ ≤ y * x := mul_le_mul (hy k) (hx k i j) (abv.nonneg _) ((abv.nonneg _).trans (hy k))
-        
 #align matrix.det_sum_smul_le Matrix.det_sum_smul_le
 
 end Matrix

9d2f0748

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -31,9 +31,9 @@ This file proves some bounds on matrices involving absolute values.
 -/
 
 
-open BigOperators
+open scoped BigOperators
 
-open Matrix
+open scoped Matrix
 
 namespace Matrix

9d2f0748

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -43,9 +43,6 @@ variable {R S : Type _} [CommRing R] [Nontrivial R] [LinearOrderedCommRing S]
 
 variable {n : Type _} [Fintype n] [DecidableEq n]
 
-/- warning: matrix.det_le -> Matrix.det_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.det_le Matrix.det_leₓ'. -/
 theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i j, abv (A i j) ≤ x) :
     abv A.det ≤ Nat.factorial (Fintype.card n) • x ^ Fintype.card n :=
   calc
@@ -62,9 +59,6 @@ theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i
     
 #align matrix.det_le Matrix.det_le
 
-/- warning: matrix.det_sum_le -> Matrix.det_sum_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.det_sum_le Matrix.det_sum_leₓ'. -/
 theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv : AbsoluteValue R S}
     {x : S} (hx : ∀ k i j, abv (A k i j) ≤ x) :
     abv (det (∑ k in s, A k)) ≤
@@ -78,9 +72,6 @@ theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv
       
 #align matrix.det_sum_le Matrix.det_sum_le
 
-/- warning: matrix.det_sum_smul_le -> Matrix.det_sum_smul_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.det_sum_smul_le Matrix.det_sum_smul_leₓ'. -/
 theorem det_sum_smul_le {ι : Type _} (s : Finset ι) {c : ι → R} {A : ι → Matrix n n R}
     {abv : AbsoluteValue R S} {x : S} (hx : ∀ k i j, abv (A k i j) ≤ x) {y : S}
     (hy : ∀ k, abv (c k) ≤ y) :

9d2f0748

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -44,10 +44,7 @@ variable {R S : Type _} [CommRing R] [Nontrivial R] [LinearOrderedCommRing S]
 variable {n : Type _} [Fintype n] [DecidableEq n]
 
 /- warning: matrix.det_le -> Matrix.det_le is a dubious translation:
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(AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (StrictOrderedSemiring.toSemiring.{u1} S (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} S (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))))) x (Fintype.card.{u3} n _inst_4))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.det_le Matrix.det_leₓ'. -/
 theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i j, abv (A i j) ≤ x) :
     abv A.det ≤ Nat.factorial (Fintype.card n) • x ^ Fintype.card n :=
@@ -66,10 +63,7 @@ theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i
 #align matrix.det_le Matrix.det_le
 
 /- warning: matrix.det_sum_le -> Matrix.det_sum_le is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.det_sum_le Matrix.det_sum_leₓ'. -/
 theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv : AbsoluteValue R S}
     {x : S} (hx : ∀ k i j, abv (A k i j) ≤ x) :
@@ -85,10 +79,7 @@ theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv
 #align matrix.det_sum_le Matrix.det_sum_le
 
 /- warning: matrix.det_sum_smul_le -> Matrix.det_sum_smul_le is a dubious translation:
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R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (StrictOrderedSemiring.toSemiring.{u1} S (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} S (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3))))))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Finset.card.{u4} ι s) y) x) (Fintype.card.{u3} n _inst_4)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.det_sum_smul_le Matrix.det_sum_smul_leₓ'. -/
 theorem det_sum_smul_le {ι : Type _} (s : Finset ι) {c : ι → R} {A : ι → Matrix n n R}
     {abv : AbsoluteValue R S} {x : S} (hx : ∀ k i j, abv (A k i j) ≤ x) {y : S}

9d2f0748

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -45,7 +45,7 @@ variable {n : Type _} [Fintype n] [DecidableEq n]
 
 /- warning: matrix.det_le -> Matrix.det_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : LinearOrderedCommRing.{u2} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {A : Matrix.{u3, u3, u1} n n R} {abv : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))} {x : S}, (forall (i : n) (j : n), LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (A i j)) x) -> (LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (Ring.toMonoid.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) x (Fintype.card.{u3} n _inst_4))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : LinearOrderedCommRing.{u2} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {A : Matrix.{u3, u3, u1} n n R} {abv : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))} {x : S}, (forall (i : n) (j : n), LE.le.{u2} S (Preorder.toHasLe.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (A i j)) x) -> (LE.le.{u2} S (Preorder.toHasLe.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (Ring.toMonoid.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) x (Fintype.card.{u3} n _inst_4))))
 but is expected to have type
   forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] [_inst_3 : LinearOrderedCommRing.{u1} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {A : Matrix.{u3, u3, u2} n n R} {abv : AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))} {x : S}, (forall (i : n) (j : n), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (A i j)) x) -> (LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (StrictOrderedSemiring.toSemiring.{u1} S (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} S (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))))) x (Fintype.card.{u3} n _inst_4))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_le Matrix.det_leₓ'. -/
@@ -67,7 +67,7 @@ theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i
 
 /- warning: matrix.det_sum_le -> Matrix.det_sum_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : LinearOrderedCommRing.{u2} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {A : ι -> (Matrix.{u3, u3, u1} n n R)} {abv : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (A k i j)) x) -> (LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u3 u1, u4} (Matrix.{u3, u3, u1} n n R) ι (Matrix.addCommMonoid.{u1, u3, u3} n n R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) s (fun (k : ι) => A k)))) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (Ring.toMonoid.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Finset.card.{u4} ι s) x) (Fintype.card.{u3} n _inst_4))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : LinearOrderedCommRing.{u2} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {A : ι -> (Matrix.{u3, u3, u1} n n R)} {abv : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u2} S (Preorder.toHasLe.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (A k i j)) x) -> (LE.le.{u2} S (Preorder.toHasLe.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u3 u1, u4} (Matrix.{u3, u3, u1} n n R) ι (Matrix.addCommMonoid.{u1, u3, u3} n n R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) s (fun (k : ι) => A k)))) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (Ring.toMonoid.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Finset.card.{u4} ι s) x) (Fintype.card.{u3} n _inst_4))))
 but is expected to have type
   forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] [_inst_3 : LinearOrderedCommRing.{u1} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {A : ι -> (Matrix.{u3, u3, u2} n n R)} {abv : AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (A k i j)) x) -> (LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (StrictOrderedSemiring.toSemiring.{u1} S (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} S (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Finset.card.{u4} ι s) x) (Fintype.card.{u3} n _inst_4))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_sum_le Matrix.det_sum_leₓ'. -/
@@ -86,7 +86,7 @@ theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv
 
 /- warning: matrix.det_sum_smul_le -> Matrix.det_sum_smul_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : LinearOrderedCommRing.{u2} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {c : ι -> R} {A : ι -> (Matrix.{u3, u3, u1} n n R)} {abv : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (A k i j)) x) -> (forall {y : S}, (forall (k : ι), LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (c k)) y) -> (LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u3 u1, u4} (Matrix.{u3, u3, u1} n n R) ι (Matrix.addCommMonoid.{u1, u3, u3} n n R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) s (fun (k : ι) => SMul.smul.{u1, max u3 u1} R (Matrix.{u3, u3, u1} n n R) (Matrix.hasSmul.{u1, u3, u3, u1} n n R R (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (c k) (A k))))) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (Ring.toMonoid.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Finset.card.{u4} ι s) y) x) (Fintype.card.{u3} n _inst_4)))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : LinearOrderedCommRing.{u2} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {c : ι -> R} {A : ι -> (Matrix.{u3, u3, u1} n n R)} {abv : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u2} S (Preorder.toHasLe.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (A k i j)) x) -> (forall {y : S}, (forall (k : ι), LE.le.{u2} S (Preorder.toHasLe.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (c k)) y) -> (LE.le.{u2} S (Preorder.toHasLe.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u3 u1, u4} (Matrix.{u3, u3, u1} n n R) ι (Matrix.addCommMonoid.{u1, u3, u3} n n R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) s (fun (k : ι) => SMul.smul.{u1, max u3 u1} R (Matrix.{u3, u3, u1} n n R) (Matrix.hasSmul.{u1, u3, u3, u1} n n R R (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (c k) (A k))))) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (Ring.toMonoid.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Finset.card.{u4} ι s) y) x) (Fintype.card.{u3} n _inst_4)))))
 but is expected to have type
   forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] [_inst_3 : LinearOrderedCommRing.{u1} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {c : ι -> R} {A : ι -> (Matrix.{u3, u3, u2} n n R)} {abv : AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (A k i j)) x) -> (forall {y : S}, (forall (k : ι), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (c k)) y) -> (LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (StrictOrderedSemiring.toSemiring.{u1} S (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} S (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3))))))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Finset.card.{u4} ι s) y) x) (Fintype.card.{u3} n _inst_4)))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_sum_smul_le Matrix.det_sum_smul_leₓ'. -/

9d2f0748

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -47,7 +47,7 @@ variable {n : Type _} [Fintype n] [DecidableEq n]
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : LinearOrderedCommRing.{u2} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {A : Matrix.{u3, u3, u1} n n R} {abv : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))} {x : S}, (forall (i : n) (j : n), LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (A i j)) x) -> (LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (Ring.toMonoid.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) x (Fintype.card.{u3} n _inst_4))))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] [_inst_3 : LinearOrderedCommRing.{u1} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {A : Matrix.{u3, u3, u2} n n R} {abv : AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))} {x : S}, (forall (i : n) (j : n), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (A i j)) x) -> (LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (StrictOrderedSemiring.toSemiring.{u1} S (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} S (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))))) x (Fintype.card.{u3} n _inst_4))))
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] [_inst_3 : LinearOrderedCommRing.{u1} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {A : Matrix.{u3, u3, u2} n n R} {abv : AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))} {x : S}, (forall (i : n) (j : n), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (A i j)) x) -> (LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (StrictOrderedSemiring.toSemiring.{u1} S (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} S (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))))) x (Fintype.card.{u3} n _inst_4))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_le Matrix.det_leₓ'. -/
 theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i j, abv (A i j) ≤ x) :
     abv A.det ≤ Nat.factorial (Fintype.card n) • x ^ Fintype.card n :=
@@ -69,7 +69,7 @@ theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : LinearOrderedCommRing.{u2} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {A : ι -> (Matrix.{u3, u3, u1} n n R)} {abv : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (A k i j)) x) -> (LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u3 u1, u4} (Matrix.{u3, u3, u1} n n R) ι (Matrix.addCommMonoid.{u1, u3, u3} n n R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) s (fun (k : ι) => A k)))) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (Ring.toMonoid.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Finset.card.{u4} ι s) x) (Fintype.card.{u3} n _inst_4))))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] [_inst_3 : LinearOrderedCommRing.{u1} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {A : ι -> (Matrix.{u3, u3, u2} n n R)} {abv : AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (A k i j)) x) -> (LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (StrictOrderedSemiring.toSemiring.{u1} S (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} S (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Finset.card.{u4} ι s) x) (Fintype.card.{u3} n _inst_4))))
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] [_inst_3 : LinearOrderedCommRing.{u1} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {A : ι -> (Matrix.{u3, u3, u2} n n R)} {abv : AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (A k i j)) x) -> (LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (StrictOrderedSemiring.toSemiring.{u1} S (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} S (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Finset.card.{u4} ι s) x) (Fintype.card.{u3} n _inst_4))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_sum_le Matrix.det_sum_leₓ'. -/
 theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv : AbsoluteValue R S}
     {x : S} (hx : ∀ k i j, abv (A k i j) ≤ x) :
@@ -88,7 +88,7 @@ theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : LinearOrderedCommRing.{u2} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {c : ι -> R} {A : ι -> (Matrix.{u3, u3, u1} n n R)} {abv : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (A k i j)) x) -> (forall {y : S}, (forall (k : ι), LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (c k)) y) -> (LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u3 u1, u4} (Matrix.{u3, u3, u1} n n R) ι (Matrix.addCommMonoid.{u1, u3, u3} n n R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) s (fun (k : ι) => SMul.smul.{u1, max u3 u1} R (Matrix.{u3, u3, u1} n n R) (Matrix.hasSmul.{u1, u3, u3, u1} n n R R (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (c k) (A k))))) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (Ring.toMonoid.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Finset.card.{u4} ι s) y) x) (Fintype.card.{u3} n _inst_4)))))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] [_inst_3 : LinearOrderedCommRing.{u1} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {c : ι -> R} {A : ι -> (Matrix.{u3, u3, u2} n n R)} {abv : AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (A k i j)) x) -> (forall {y : S}, (forall (k : ι), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (c k)) y) -> (LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (StrictOrderedSemiring.toSemiring.{u1} S (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} S (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3))))))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Finset.card.{u4} ι s) y) x) (Fintype.card.{u3} n _inst_4)))))
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] [_inst_3 : LinearOrderedCommRing.{u1} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {c : ι -> R} {A : ι -> (Matrix.{u3, u3, u2} n n R)} {abv : AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (A k i j)) x) -> (forall {y : S}, (forall (k : ι), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (c k)) y) -> (LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (StrictOrderedSemiring.toSemiring.{u1} S (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} S (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3))))))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Finset.card.{u4} ι s) y) x) (Fintype.card.{u3} n _inst_4)))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_sum_smul_le Matrix.det_sum_smul_leₓ'. -/
 theorem det_sum_smul_le {ι : Type _} (s : Finset ι) {c : ι → R} {A : ι → Matrix n n R}
     {abv : AbsoluteValue R S} {x : S} (hx : ∀ k i j, abv (A k i j) ≤ x) {y : S}

9d2f0748

bump to nightly-2023-04-28-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780

473bb540

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.absolute_value
-! leanprover-community/mathlib commit ab0a2959c83b06280ef576bc830d4aa5fe8c8e61
+! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
 ! 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.Matrix.Determinant
 /-!
 # Absolute values and matrices
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves some bounds on matrices involving absolute values.
 
 ## Main results

ab0a2959

bump to nightly-2023-04-23-12

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e281deff072232a3c5b3e90034bd65dde396312

26e52e1f

Diff

@@ -40,6 +40,12 @@ variable {R S : Type _} [CommRing R] [Nontrivial R] [LinearOrderedCommRing S]
 
 variable {n : Type _} [Fintype n] [DecidableEq n]
 
+/- warning: matrix.det_le -> Matrix.det_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : LinearOrderedCommRing.{u2} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {A : Matrix.{u3, u3, u1} n n R} {abv : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))} {x : S}, (forall (i : n) (j : n), LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (A i j)) x) -> (LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (Ring.toMonoid.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) x (Fintype.card.{u3} n _inst_4))))
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] [_inst_3 : LinearOrderedCommRing.{u1} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {A : Matrix.{u3, u3, u2} n n R} {abv : AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))} {x : S}, (forall (i : n) (j : n), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A i j)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (A i j)) x) -> (LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (StrictOrderedSemiring.toSemiring.{u1} S (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} S (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))))) x (Fintype.card.{u3} n _inst_4))))
+Case conversion may be inaccurate. Consider using '#align matrix.det_le Matrix.det_leₓ'. -/
 theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i j, abv (A i j) ≤ x) :
     abv A.det ≤ Nat.factorial (Fintype.card n) • x ^ Fintype.card n :=
   calc
@@ -56,6 +62,12 @@ theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i
     
 #align matrix.det_le Matrix.det_le
 
+/- warning: matrix.det_sum_le -> Matrix.det_sum_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : LinearOrderedCommRing.{u2} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {A : ι -> (Matrix.{u3, u3, u1} n n R)} {abv : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (A k i j)) x) -> (LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) (fun (f : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) => R -> S) (AbsoluteValue.hasCoeToFun.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))) abv (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u3 u1, u4} (Matrix.{u3, u3, u1} n n R) ι (Matrix.addCommMonoid.{u1, u3, u3} n n R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) s (fun (k : ι) => A k)))) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (Ring.toMonoid.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (SMul.smul.{0, u2} Nat S (AddMonoid.SMul.{u2} S (AddMonoidWithOne.toAddMonoid.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (StrictOrderedRing.toRing.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))))) (Finset.card.{u4} ι s) x) (Fintype.card.{u3} n _inst_4))))
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] [_inst_3 : LinearOrderedCommRing.{u1} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {A : ι -> (Matrix.{u3, u3, u2} n n R)} {abv : AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (A k i j)) x) -> (LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => A k)))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (StrictOrderedSemiring.toSemiring.{u1} S (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} S (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Finset.card.{u4} ι s) x) (Fintype.card.{u3} n _inst_4))))
+Case conversion may be inaccurate. Consider using '#align matrix.det_sum_le Matrix.det_sum_leₓ'. -/
 theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv : AbsoluteValue R S}
     {x : S} (hx : ∀ k i j, abv (A k i j) ≤ x) :
     abv (det (∑ k in s, A k)) ≤
@@ -69,6 +81,12 @@ theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv
       
 #align matrix.det_sum_le Matrix.det_sum_le
 
+/- warning: matrix.det_sum_smul_le -> Matrix.det_sum_smul_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : LinearOrderedCommRing.{u2} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {c : ι -> R} {A : ι -> (Matrix.{u3, u3, u1} n n R)} {abv : AbsoluteValue.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (StrictOrderedSemiring.toOrderedSemiring.{u2} S (StrictOrderedRing.toStrictOrderedSemiring.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u2} S (Preorder.toLE.{u2} S (PartialOrder.toPreorder.{u2} S (OrderedAddCommGroup.toPartialOrder.{u2} S (StrictOrderedRing.toOrderedAddCommGroup.{u2} S (LinearOrderedRing.toStrictOrderedRing.{u2} S (LinearOrderedCommRing.toLinearOrderedRing.{u2} S _inst_3)))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AbsoluteValue.{u1, u2} R 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+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] [_inst_3 : LinearOrderedCommRing.{u1} S] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] [_inst_5 : DecidableEq.{succ u3} n] {ι : Type.{u4}} (s : Finset.{u4} ι) {c : ι -> R} {A : ι -> (Matrix.{u3, u3, u2} n n R)} {abv : AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))} {x : S}, (forall (k : ι) (i : n) (j : n), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (A k i j)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (A k i j)) x) -> (forall {y : S}, (forall (k : ι), LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (c k)) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (c k)) y) -> (LE.le.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (StrictOrderedRing.toPartialOrder.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (LinearOrderedRing.toStrictOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (LinearOrderedCommRing.toLinearOrderedRing.{u1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R (fun (f : R) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : R) => S) f) (SubadditiveHomClass.toFunLike.{max u2 u1, u2, u1} (AbsoluteValue.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))) R S (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (OrderedSemiring.toSemiring.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))))) (Preorder.toLE.{u1} S (PartialOrder.toPreorder.{u1} S (OrderedSemiring.toPartialOrder.{u1} S (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3))))))) (AbsoluteValue.subadditiveHomClass.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (OrderedCommSemiring.toOrderedSemiring.{u1} S (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} S (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))) abv (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 (Finset.sum.{max u2 u3, u4} (Matrix.{u3, u3, u2} n n R) ι (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) s (fun (k : ι) => HSMul.hSMul.{u2, max u2 u3, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.{u3, u3, u2} n n R) (instHSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (Matrix.smul.{u2, u3, u3, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (c k) (A k))))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Nat.factorial (Fintype.card.{u3} n _inst_4)) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (StrictOrderedSemiring.toSemiring.{u1} S (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} S (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} S (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} S _inst_3)))))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3))))))) (HSMul.hSMul.{0, u1, u1} Nat S S (instHSMul.{0, u1} Nat S (AddMonoid.SMul.{u1} S (AddMonoidWithOne.toAddMonoid.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (Ring.toAddGroupWithOne.{u1} S (StrictOrderedRing.toRing.{u1} S (LinearOrderedRing.toStrictOrderedRing.{u1} S (LinearOrderedCommRing.toLinearOrderedRing.{u1} S _inst_3)))))))) (Finset.card.{u4} ι s) y) x) (Fintype.card.{u3} n _inst_4)))))
+Case conversion may be inaccurate. Consider using '#align matrix.det_sum_smul_le Matrix.det_sum_smul_leₓ'. -/
 theorem det_sum_smul_le {ι : Type _} (s : Finset ι) {c : ι → R} {A : ι → Matrix n n R}
     {abv : AbsoluteValue R S} {x : S} (hx : ∀ k i j, abv (A k i j) ≤ x) {y : S}
     (hy : ∀ k, abv (c k) ≤ y) :

ab0a2959

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -44,13 +44,13 @@ theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i
     abv A.det ≤ Nat.factorial (Fintype.card n) • x ^ Fintype.card n :=
   calc
     abv A.det = abv (∑ σ : Perm n, _) := congr_arg abv (det_apply _)
-    _ ≤ ∑ σ : Perm n, abv _ := abv.sum_le _ _
+    _ ≤ ∑ σ : Perm n, abv _ := (abv.sum_le _ _)
     _ = ∑ σ : Perm n, ∏ i, abv (A (σ i) i) :=
-      sum_congr rfl fun σ hσ => by rw [abv.map_units_int_smul, abv.map_prod]
+      (sum_congr rfl fun σ hσ => by rw [abv.map_units_int_smul, abv.map_prod])
     _ ≤ ∑ σ : Perm n, ∏ i : n, x :=
-      sum_le_sum fun _ _ => prod_le_prod (fun _ _ => abv.NonNeg _) fun _ _ => hx _ _
+      (sum_le_sum fun _ _ => prod_le_prod (fun _ _ => abv.NonNeg _) fun _ _ => hx _ _)
     _ = ∑ σ : Perm n, x ^ Fintype.card n :=
-      sum_congr rfl fun _ _ => by rw [prod_const, Finset.card_univ]
+      (sum_congr rfl fun _ _ => by rw [prod_const, Finset.card_univ])
     _ = Nat.factorial (Fintype.card n) • x ^ Fintype.card n := by
       rw [sum_const, Finset.card_univ, Fintype.card_perm]
     
@@ -63,8 +63,8 @@ theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv
   det_le fun i j =>
     calc
       abv ((∑ k in s, A k) i j) = abv (∑ k in s, A k i j) := by simp only [sum_apply]
-      _ ≤ ∑ k in s, abv (A k i j) := abv.sum_le _ _
-      _ ≤ ∑ k in s, x := sum_le_sum fun k _ => hx k i j
+      _ ≤ ∑ k in s, abv (A k i j) := (abv.sum_le _ _)
+      _ ≤ ∑ k in s, x := (sum_le_sum fun k _ => hx k i j)
       _ = s.card • x := sum_const _
       
 #align matrix.det_sum_le Matrix.det_sum_le

ab0a2959

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

ab0a2959

feat: ∑ x ∈ s, f x to replace ∑ x in s, f x in the future (#6795)

Adds new syntax for sum/product big operators for ∑ x ∈ s, f x. The set s can either be a Finset or a Set with a Fintype instance, in which case it is equivalent to ∑ x ∈ s.toFinset, f x.

Also supports ∑ (x ∈ s) (y ∈ t), f x y for Finset.sum (s ×ˢ t) (fun ⟨x, y⟩ ↦ f x y). Note that these are not dependent products at the moment.

Adds with clauses, so for example ∑ (x ∈ Finset.range 5) (y ∈ Finset.range 5) with x < y, x * y, which inserts a Finset.filter over the domain set.

Supports pattern matching in the variable position. This is by creating an experimental version of extBinder that uses term:max instead of binderIdent.

The new ∑ x ∈ s, f x notation is used in Algebra.BigOperators.Basic for illustration, but the old ∑ x in s, f x still works for backwards compatibility.

Zulip threads here and here

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

001604ae

Diff

@@ -43,7 +43,7 @@ theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i
     _ ≤ ∑ σ : Perm n, abv (Perm.sign σ • ∏ i, A (σ i) i) := abv.sum_le _ _
     _ = ∑ σ : Perm n, ∏ i, abv (A (σ i) i) :=
       (sum_congr rfl fun σ _ => by rw [abv.map_units_int_smul, abv.map_prod])
-    _ ≤ ∑ σ : Perm n, ∏ _i : n, x :=
+    _ ≤ ∑ _σ : Perm n, ∏ _i : n, x :=
       (sum_le_sum fun _ _ => prod_le_prod (fun _ _ => abv.nonneg _) fun _ _ => hx _ _)
     _ = ∑ _σ : Perm n, x ^ Fintype.card n :=
       (sum_congr rfl fun _ _ => by rw [prod_const, Finset.card_univ])

ab0a2959

chore: superfluous parentheses part 2 (#12131)

Co-authored-by: Moritz Firsching <firsching@google.com>

d48d30ac

Diff

@@ -58,8 +58,8 @@ theorem det_sum_le {ι : Type*} (s : Finset ι) {A : ι → Matrix n n R} {abv :
   det_le fun i j =>
     calc
       abv ((∑ k in s, A k) i j) = abv (∑ k in s, A k i j) := by simp only [sum_apply]
-      _ ≤ ∑ k in s, abv (A k i j) := (abv.sum_le _ _)
-      _ ≤ ∑ _k in s, x := (sum_le_sum fun k _ => hx k i j)
+      _ ≤ ∑ k in s, abv (A k i j) := abv.sum_le _ _
+      _ ≤ ∑ _k in s, x := sum_le_sum fun k _ => hx k i j
       _ = s.card • x := sum_const _
 #align matrix.det_sum_le Matrix.det_sum_le

ab0a2959

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -34,7 +34,6 @@ namespace Matrix
 open Equiv Finset
 
 variable {R S : Type*} [CommRing R] [Nontrivial R] [LinearOrderedCommRing S]
-
 variable {n : Type*} [Fintype n] [DecidableEq n]
 
 theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i j, abv (A i j) ≤ x) :

ab0a2959

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -33,9 +33,9 @@ namespace Matrix
 
 open Equiv Finset
 
-variable {R S : Type _} [CommRing R] [Nontrivial R] [LinearOrderedCommRing S]
+variable {R S : Type*} [CommRing R] [Nontrivial R] [LinearOrderedCommRing S]
 
-variable {n : Type _} [Fintype n] [DecidableEq n]
+variable {n : Type*} [Fintype n] [DecidableEq n]
 
 theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i j, abv (A i j) ≤ x) :
     abv A.det ≤ Nat.factorial (Fintype.card n) • x ^ Fintype.card n :=
@@ -52,7 +52,7 @@ theorem det_le {A : Matrix n n R} {abv : AbsoluteValue R S} {x : S} (hx : ∀ i
       rw [sum_const, Finset.card_univ, Fintype.card_perm]
 #align matrix.det_le Matrix.det_le
 
-theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv : AbsoluteValue R S}
+theorem det_sum_le {ι : Type*} (s : Finset ι) {A : ι → Matrix n n R} {abv : AbsoluteValue R S}
     {x : S} (hx : ∀ k i j, abv (A k i j) ≤ x) :
     abv (det (∑ k in s, A k)) ≤
       Nat.factorial (Fintype.card n) • (Finset.card s • x) ^ Fintype.card n :=
@@ -64,7 +64,7 @@ theorem det_sum_le {ι : Type _} (s : Finset ι) {A : ι → Matrix n n R} {abv
       _ = s.card • x := sum_const _
 #align matrix.det_sum_le Matrix.det_sum_le
 
-theorem det_sum_smul_le {ι : Type _} (s : Finset ι) {c : ι → R} {A : ι → Matrix n n R}
+theorem det_sum_smul_le {ι : Type*} (s : Finset ι) {c : ι → R} {A : ι → Matrix n n R}
     {abv : AbsoluteValue R S} {x : S} (hx : ∀ k i j, abv (A k i j) ≤ x) {y : S}
     (hy : ∀ k, abv (c k) ≤ y) :
     abv (det (∑ k in s, c k • A k)) ≤

ab0a2959

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.absolute_value
-! leanprover-community/mathlib commit ab0a2959c83b06280ef576bc830d4aa5fe8c8e61
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Int.AbsoluteValue
 import Mathlib.LinearAlgebra.Matrix.Determinant
 
+#align_import linear_algebra.matrix.absolute_value from "leanprover-community/mathlib"@"ab0a2959c83b06280ef576bc830d4aa5fe8c8e61"
+
 /-!
 # Absolute values and matrices

ab0a2959

feat: port LinearAlgebra.Matrix.AbsoluteValue (#3597)

9d2364ad

`linear_algebra.matrix.absolute_value` ⟷ `Mathlib.LinearAlgebra.Matrix.AbsoluteValue`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 524

linear_algebra.matrix.absolute_value ⟷ Mathlib.LinearAlgebra.Matrix.AbsoluteValue

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 524

`linear_algebra.matrix.absolute_value` ⟷ `Mathlib.LinearAlgebra.Matrix.AbsoluteValue`