ring_theory.polynomial.chebyshev | 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

d7744511

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

1dac236e

bump to nightly-2024-04-07-08

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

b03b8656

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Julian Kuelshammer, Heather Macbeth
 -/
-import Data.Polynomial.Derivative
+import Algebra.Polynomial.Derivative
 import Tactic.LinearCombination
 
 #align_import ring_theory.polynomial.chebyshev from "leanprover-community/mathlib"@"1dac236edca9b4b6f5f00b1ad831e35f89472837"

1dac236e

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -166,7 +166,7 @@ theorem U_eq_X_mul_U_add_T : ∀ n : ℕ, U R (n + 1) = X * U R n + T R (n + 1)
 
 #print Polynomial.Chebyshev.T_eq_U_sub_X_mul_U /-
 theorem T_eq_U_sub_X_mul_U (n : ℕ) : T R (n + 1) = U R (n + 1) - X * U R n := by
-  rw [U_eq_X_mul_U_add_T, add_comm (X * U R n), add_sub_cancel]
+  rw [U_eq_X_mul_U_add_T, add_comm (X * U R n), add_sub_cancel_right]
 #align polynomial.chebyshev.T_eq_U_sub_X_mul_U Polynomial.Chebyshev.T_eq_U_sub_X_mul_U
 -/

1dac236e

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Julian Kuelshammer, Heather Macbeth
 -/
-import Mathbin.Data.Polynomial.Derivative
-import Mathbin.Tactic.LinearCombination
+import Data.Polynomial.Derivative
+import Tactic.LinearCombination
 
 #align_import ring_theory.polynomial.chebyshev from "leanprover-community/mathlib"@"1dac236edca9b4b6f5f00b1ad831e35f89472837"

1dac236e

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Julian Kuelshammer, Heather Macbeth
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.chebyshev
-! leanprover-community/mathlib commit 1dac236edca9b4b6f5f00b1ad831e35f89472837
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Polynomial.Derivative
 import Mathbin.Tactic.LinearCombination
 
+#align_import ring_theory.polynomial.chebyshev from "leanprover-community/mathlib"@"1dac236edca9b4b6f5f00b1ad831e35f89472837"
+
 /-!
 # Chebyshev polynomials

1dac236e

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -91,19 +91,25 @@ theorem T_one : T R 1 = X :=
 #align polynomial.chebyshev.T_one Polynomial.Chebyshev.T_one
 -/
 
+#print Polynomial.Chebyshev.T_add_two /-
 @[simp]
 theorem T_add_two (n : ℕ) : T R (n + 2) = 2 * X * T R (n + 1) - T R n := by rw [T]
 #align polynomial.chebyshev.T_add_two Polynomial.Chebyshev.T_add_two
+-/
 
+#print Polynomial.Chebyshev.T_two /-
 theorem T_two : T R 2 = 2 * X ^ 2 - 1 := by simp only [T, sub_left_inj, sq, mul_assoc]
 #align polynomial.chebyshev.T_two Polynomial.Chebyshev.T_two
+-/
 
+#print Polynomial.Chebyshev.T_of_two_le /-
 theorem T_of_two_le (n : ℕ) (h : 2 ≤ n) : T R n = 2 * X * T R (n - 1) - T R (n - 2) :=
   by
   obtain ⟨n, rfl⟩ := Nat.exists_eq_add_of_le h
   rw [add_comm]
   exact T_add_two R n
 #align polynomial.chebyshev.T_of_two_le Polynomial.Chebyshev.T_of_two_le
+-/
 
 #print Polynomial.Chebyshev.U /-
 /-- `U n` is the `n`-th Chebyshev polynomial of the second kind -/
@@ -121,24 +127,32 @@ theorem U_zero : U R 0 = 1 :=
 #align polynomial.chebyshev.U_zero Polynomial.Chebyshev.U_zero
 -/
 
+#print Polynomial.Chebyshev.U_one /-
 @[simp]
 theorem U_one : U R 1 = 2 * X :=
   rfl
 #align polynomial.chebyshev.U_one Polynomial.Chebyshev.U_one
+-/
 
+#print Polynomial.Chebyshev.U_add_two /-
 @[simp]
 theorem U_add_two (n : ℕ) : U R (n + 2) = 2 * X * U R (n + 1) - U R n := by rw [U]
 #align polynomial.chebyshev.U_add_two Polynomial.Chebyshev.U_add_two
+-/
 
+#print Polynomial.Chebyshev.U_two /-
 theorem U_two : U R 2 = 4 * X ^ 2 - 1 := by simp only [U]; ring
 #align polynomial.chebyshev.U_two Polynomial.Chebyshev.U_two
+-/
 
+#print Polynomial.Chebyshev.U_of_two_le /-
 theorem U_of_two_le (n : ℕ) (h : 2 ≤ n) : U R n = 2 * X * U R (n - 1) - U R (n - 2) :=
   by
   obtain ⟨n, rfl⟩ := Nat.exists_eq_add_of_le h
   rw [add_comm]
   exact U_add_two R n
 #align polynomial.chebyshev.U_of_two_le Polynomial.Chebyshev.U_of_two_le
+-/
 
 #print Polynomial.Chebyshev.U_eq_X_mul_U_add_T /-
 theorem U_eq_X_mul_U_add_T : ∀ n : ℕ, U R (n + 1) = X * U R n + T R (n + 1)
@@ -159,6 +173,7 @@ theorem T_eq_U_sub_X_mul_U (n : ℕ) : T R (n + 1) = U R (n + 1) - X * U R n :=
 #align polynomial.chebyshev.T_eq_U_sub_X_mul_U Polynomial.Chebyshev.T_eq_U_sub_X_mul_U
 -/
 
+#print Polynomial.Chebyshev.T_eq_X_mul_T_sub_pol_U /-
 theorem T_eq_X_mul_T_sub_pol_U : ∀ n : ℕ, T R (n + 2) = X * T R (n + 1) - (1 - X ^ 2) * U R n
   | 0 => by simp only [T_one, T_two, U_zero]; ring
   | 1 => by
@@ -175,14 +190,18 @@ theorem T_eq_X_mul_T_sub_pol_U : ∀ n : ℕ, T R (n + 2) = X * T R (n + 1) - (1
         by ring
       _ = X * T R (n + 2 + 1) - (1 - X ^ 2) * U R (n + 2) := by rw [T_add_two _ (n + 1), U_add_two]
 #align polynomial.chebyshev.T_eq_X_mul_T_sub_pol_U Polynomial.Chebyshev.T_eq_X_mul_T_sub_pol_U
+-/
 
+#print Polynomial.Chebyshev.one_sub_X_sq_mul_U_eq_pol_in_T /-
 theorem one_sub_X_sq_mul_U_eq_pol_in_T (n : ℕ) :
     (1 - X ^ 2) * U R n = X * T R (n + 1) - T R (n + 2) := by
   rw [T_eq_X_mul_T_sub_pol_U, ← sub_add, sub_self, zero_add]
 #align polynomial.chebyshev.one_sub_X_sq_mul_U_eq_pol_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_U_eq_pol_in_T
+-/
 
 variable {R S}
 
+#print Polynomial.Chebyshev.map_T /-
 @[simp]
 theorem map_T (f : R →+* S) : ∀ n : ℕ, map f (T R n) = T S n
   | 0 => by simp only [T_zero, Polynomial.map_one]
@@ -193,7 +212,9 @@ theorem map_T (f : R →+* S) : ∀ n : ℕ, map f (T R n) = T S n
       Polynomial.map_one]
     rw [map_T (n + 1), map_T n]
 #align polynomial.chebyshev.map_T Polynomial.Chebyshev.map_T
+-/
 
+#print Polynomial.Chebyshev.map_U /-
 @[simp]
 theorem map_U (f : R →+* S) : ∀ n : ℕ, map f (U R n) = U S n
   | 0 => by simp only [U_zero, Polynomial.map_one]
@@ -208,7 +229,9 @@ theorem map_U (f : R →+* S) : ∀ n : ℕ, map f (U R n) = U S n
       Polynomial.map_one]
     rw [map_U (n + 1), map_U n]
 #align polynomial.chebyshev.map_U Polynomial.Chebyshev.map_U
+-/
 
+#print Polynomial.Chebyshev.T_derivative_eq_U /-
 theorem T_derivative_eq_U : ∀ n : ℕ, derivative (T R (n + 1)) = (n + 1) * U R n
   | 0 => by simp only [T_one, U_zero, derivative_X, Nat.cast_zero, zero_add, mul_one]
   | 1 =>
@@ -232,7 +255,9 @@ theorem T_derivative_eq_U : ∀ n : ℕ, derivative (T R (n + 1)) = (n + 1) * U
       _ = (n + 2 + 1) * U R (n + 2) := by ring
       _ = (↑(n + 2) + 1) * U R (n + 2) := by norm_cast
 #align polynomial.chebyshev.T_derivative_eq_U Polynomial.Chebyshev.T_derivative_eq_U
+-/
 
+#print Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T /-
 theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
     (1 - X ^ 2) * derivative (T R (n + 1)) = (n + 1) * (T R n - X * T R (n + 1)) :=
   calc
@@ -243,7 +268,9 @@ theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
       rw [one_sub_X_sq_mul_U_eq_pol_in_T, T_add_two]
     _ = (n + 1) * (T R n - X * T R (n + 1)) := by ring
 #align polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T
+-/
 
+#print Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_U /-
 theorem add_one_mul_T_eq_poly_in_U (n : ℕ) :
     ((n : R[X]) + 1) * T R (n + 1) = X * U R n - (1 - X ^ 2) * derivative (U R n) :=
   by
@@ -273,9 +300,11 @@ theorem add_one_mul_T_eq_poly_in_U (n : ℕ) :
       by rw [h]
     _ = X * U R n - (1 - X ^ 2) * derivative (U R n) := by ring
 #align polynomial.chebyshev.add_one_mul_T_eq_poly_in_U Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_U
+-/
 
 variable (R)
 
+#print Polynomial.Chebyshev.mul_T /-
 /-- The product of two Chebyshev polynomials is the sum of two other Chebyshev polynomials. -/
 theorem mul_T : ∀ m k, 2 * T R m * T R (m + k) = T R (2 * m + k) + T R k
   | 0 => by simp [two_mul, add_mul]
@@ -308,6 +337,7 @@ theorem mul_T : ∀ m k, 2 * T R m * T R (m + k) = T R (2 * m + k) + T R k
     -- the desired identity is an appropriate linear combination of H₁, H₂, h₁, h₂, h₃
     linear_combination 2 * T R (m + k + 2) * h₁ + 2 * X * H₁ - H₂ - h₂ - h₃
 #align polynomial.chebyshev.mul_T Polynomial.Chebyshev.mul_T
+-/
 
 #print Polynomial.Chebyshev.T_mul /-
 /-- The `(m * n)`-th Chebyshev polynomial is the composition of the `m`-th and `n`-th -/

1dac236e

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -150,7 +150,6 @@ theorem U_eq_X_mul_U_add_T : ∀ n : ℕ, U R (n + 1) = X * U R n + T R (n + 1)
         simp only [U_add_two, U_eq_X_mul_U_add_T n, U_eq_X_mul_U_add_T (n + 1)]
       _ = X * (2 * X * U R (n + 1) - U R n) + (2 * X * T R (n + 2) - T R (n + 1)) := by ring
       _ = X * U R (n + 2) + T R (n + 2 + 1) := by simp only [U_add_two, T_add_two]
-      
 #align polynomial.chebyshev.U_eq_X_mul_U_add_T Polynomial.Chebyshev.U_eq_X_mul_U_add_T
 -/
 
@@ -175,7 +174,6 @@ theorem T_eq_X_mul_T_sub_pol_U : ∀ n : ℕ, T R (n + 2) = X * T R (n + 1) - (1
       _ = X * (2 * X * T R (n + 2) - T R (n + 1)) - (1 - X ^ 2) * (2 * X * U R (n + 1) - U R n) :=
         by ring
       _ = X * T R (n + 2 + 1) - (1 - X ^ 2) * U R (n + 2) := by rw [T_add_two _ (n + 1), U_add_two]
-      
 #align polynomial.chebyshev.T_eq_X_mul_T_sub_pol_U Polynomial.Chebyshev.T_eq_X_mul_T_sub_pol_U
 
 theorem one_sub_X_sq_mul_U_eq_pol_in_T (n : ℕ) :
@@ -233,7 +231,6 @@ theorem T_derivative_eq_U : ∀ n : ℕ, derivative (T R (n + 1)) = (n + 1) * U
       _ = (n + 1) * U R (n + 2) + 2 * U R (n + 2) := by rw [U_add_two]
       _ = (n + 2 + 1) * U R (n + 2) := by ring
       _ = (↑(n + 2) + 1) * U R (n + 2) := by norm_cast
-      
 #align polynomial.chebyshev.T_derivative_eq_U Polynomial.Chebyshev.T_derivative_eq_U
 
 theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
@@ -245,7 +242,6 @@ theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
     _ = (n + 1) * (X * T R (n + 1) - (2 * X * T R (n + 1) - T R n)) := by
       rw [one_sub_X_sq_mul_U_eq_pol_in_T, T_add_two]
     _ = (n + 1) * (T R n - X * T R (n + 1)) := by ring
-    
 #align polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T
 
 theorem add_one_mul_T_eq_poly_in_U (n : ℕ) :
@@ -276,7 +272,6 @@ theorem add_one_mul_T_eq_poly_in_U (n : ℕ) :
           U R (n + 1) :=
       by rw [h]
     _ = X * U R n - (1 - X ^ 2) * derivative (U R n) := by ring
-    
 #align polynomial.chebyshev.add_one_mul_T_eq_poly_in_U Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_U
 
 variable (R)

1dac236e

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -64,7 +64,7 @@ namespace Polynomial.Chebyshev
 
 open Polynomial
 
-open Polynomial
+open scoped Polynomial
 
 variable (R S : Type _) [CommRing R] [CommRing S]

1dac236e

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -91,31 +91,13 @@ theorem T_one : T R 1 = X :=
 #align polynomial.chebyshev.T_one Polynomial.Chebyshev.T_one
 -/
 
-/- warning: polynomial.chebyshev.T_add_two -> Polynomial.Chebyshev.T_add_two is a dubious translation:
-lean 3 declaration is
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 @[simp]
 theorem T_add_two (n : ℕ) : T R (n + 2) = 2 * X * T R (n + 1) - T R n := by rw [T]
 #align polynomial.chebyshev.T_add_two Polynomial.Chebyshev.T_add_two
 
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 theorem T_two : T R 2 = 2 * X ^ 2 - 1 := by simp only [T, sub_left_inj, sq, mul_assoc]
 #align polynomial.chebyshev.T_two Polynomial.Chebyshev.T_two
 
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 theorem T_of_two_le (n : ℕ) (h : 2 ≤ n) : T R n = 2 * X * T R (n - 1) - T R (n - 2) :=
   by
   obtain ⟨n, rfl⟩ := Nat.exists_eq_add_of_le h
@@ -139,42 +121,18 @@ theorem U_zero : U R 0 = 1 :=
 #align polynomial.chebyshev.U_zero Polynomial.Chebyshev.U_zero
 -/
 
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 @[simp]
 theorem U_one : U R 1 = 2 * X :=
   rfl
 #align polynomial.chebyshev.U_one Polynomial.Chebyshev.U_one
 
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 @[simp]
 theorem U_add_two (n : ℕ) : U R (n + 2) = 2 * X * U R (n + 1) - U R n := by rw [U]
 #align polynomial.chebyshev.U_add_two Polynomial.Chebyshev.U_add_two
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.U_two Polynomial.Chebyshev.U_twoₓ'. -/
 theorem U_two : U R 2 = 4 * X ^ 2 - 1 := by simp only [U]; ring
 #align polynomial.chebyshev.U_two Polynomial.Chebyshev.U_two
 
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 theorem U_of_two_le (n : ℕ) (h : 2 ≤ n) : U R n = 2 * X * U R (n - 1) - U R (n - 2) :=
   by
   obtain ⟨n, rfl⟩ := Nat.exists_eq_add_of_le h
@@ -202,12 +160,6 @@ theorem T_eq_U_sub_X_mul_U (n : ℕ) : T R (n + 1) = U R (n + 1) - X * U R n :=
 #align polynomial.chebyshev.T_eq_U_sub_X_mul_U Polynomial.Chebyshev.T_eq_U_sub_X_mul_U
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_eq_X_mul_T_sub_pol_U Polynomial.Chebyshev.T_eq_X_mul_T_sub_pol_Uₓ'. -/
 theorem T_eq_X_mul_T_sub_pol_U : ∀ n : ℕ, T R (n + 2) = X * T R (n + 1) - (1 - X ^ 2) * U R n
   | 0 => by simp only [T_one, T_two, U_zero]; ring
   | 1 => by
@@ -226,12 +178,6 @@ theorem T_eq_X_mul_T_sub_pol_U : ∀ n : ℕ, T R (n + 2) = X * T R (n + 1) - (1
       
 #align polynomial.chebyshev.T_eq_X_mul_T_sub_pol_U Polynomial.Chebyshev.T_eq_X_mul_T_sub_pol_U
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.one_sub_X_sq_mul_U_eq_pol_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_U_eq_pol_in_Tₓ'. -/
 theorem one_sub_X_sq_mul_U_eq_pol_in_T (n : ℕ) :
     (1 - X ^ 2) * U R n = X * T R (n + 1) - T R (n + 2) := by
   rw [T_eq_X_mul_T_sub_pol_U, ← sub_add, sub_self, zero_add]
@@ -239,12 +185,6 @@ theorem one_sub_X_sq_mul_U_eq_pol_in_T (n : ℕ) :
 
 variable {R S}
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.map_T Polynomial.Chebyshev.map_Tₓ'. -/
 @[simp]
 theorem map_T (f : R →+* S) : ∀ n : ℕ, map f (T R n) = T S n
   | 0 => by simp only [T_zero, Polynomial.map_one]
@@ -256,12 +196,6 @@ theorem map_T (f : R →+* S) : ∀ n : ℕ, map f (T R n) = T S n
     rw [map_T (n + 1), map_T n]
 #align polynomial.chebyshev.map_T Polynomial.Chebyshev.map_T
 
-/- warning: polynomial.chebyshev.map_U -> Polynomial.Chebyshev.map_U is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (n : Nat), Eq.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (Polynomial.Chebyshev.U.{u2} S _inst_2 n)
-but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (n : Nat), Eq.{succ u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.map.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) f (Polynomial.Chebyshev.U.{u2} R _inst_1 n)) (Polynomial.Chebyshev.U.{u1} S _inst_2 n)
-Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.map_U Polynomial.Chebyshev.map_Uₓ'. -/
 @[simp]
 theorem map_U (f : R →+* S) : ∀ n : ℕ, map f (U R n) = U S n
   | 0 => by simp only [U_zero, Polynomial.map_one]
@@ -277,9 +211,6 @@ theorem map_U (f : R →+* S) : ∀ n : ℕ, map f (U R n) = U S n
     rw [map_U (n + 1), map_U n]
 #align polynomial.chebyshev.map_U Polynomial.Chebyshev.map_U
 
-/- warning: polynomial.chebyshev.T_derivative_eq_U -> Polynomial.Chebyshev.T_derivative_eq_U is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_derivative_eq_U Polynomial.Chebyshev.T_derivative_eq_Uₓ'. -/
 theorem T_derivative_eq_U : ∀ n : ℕ, derivative (T R (n + 1)) = (n + 1) * U R n
   | 0 => by simp only [T_one, U_zero, derivative_X, Nat.cast_zero, zero_add, mul_one]
   | 1 =>
@@ -305,9 +236,6 @@ theorem T_derivative_eq_U : ∀ n : ℕ, derivative (T R (n + 1)) = (n + 1) * U
       
 #align polynomial.chebyshev.T_derivative_eq_U Polynomial.Chebyshev.T_derivative_eq_U
 
-/- warning: polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T -> Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_Tₓ'. -/
 theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
     (1 - X ^ 2) * derivative (T R (n + 1)) = (n + 1) * (T R n - X * T R (n + 1)) :=
   calc
@@ -320,9 +248,6 @@ theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
     
 #align polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T
 
-/- warning: polynomial.chebyshev.add_one_mul_T_eq_poly_in_U -> Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_U is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.add_one_mul_T_eq_poly_in_U Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_Uₓ'. -/
 theorem add_one_mul_T_eq_poly_in_U (n : ℕ) :
     ((n : R[X]) + 1) * T R (n + 1) = X * U R n - (1 - X ^ 2) * derivative (U R n) :=
   by
@@ -356,12 +281,6 @@ theorem add_one_mul_T_eq_poly_in_U (n : ℕ) :
 
 variable (R)
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.mul_T Polynomial.Chebyshev.mul_Tₓ'. -/
 /-- The product of two Chebyshev polynomials is the sum of two other Chebyshev polynomials. -/
 theorem mul_T : ∀ m k, 2 * T R m * T R (m + k) = T R (2 * m + k) + T R k
   | 0 => by simp [two_mul, add_mul]

1dac236e

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -166,9 +166,7 @@ lean 3 declaration is
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 4 (instOfNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 4 (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.U_two Polynomial.Chebyshev.U_twoₓ'. -/
-theorem U_two : U R 2 = 4 * X ^ 2 - 1 := by
-  simp only [U]
-  ring
+theorem U_two : U R 2 = 4 * X ^ 2 - 1 := by simp only [U]; ring
 #align polynomial.chebyshev.U_two Polynomial.Chebyshev.U_two
 
 /- warning: polynomial.chebyshev.U_of_two_le -> Polynomial.Chebyshev.U_of_two_le is a dubious translation:
@@ -186,12 +184,8 @@ theorem U_of_two_le (n : ℕ) (h : 2 ≤ n) : U R n = 2 * X * U R (n - 1) - U R
 
 #print Polynomial.Chebyshev.U_eq_X_mul_U_add_T /-
 theorem U_eq_X_mul_U_add_T : ∀ n : ℕ, U R (n + 1) = X * U R n + T R (n + 1)
-  | 0 => by
-    simp only [U_zero, U_one, T_one]
-    ring
-  | 1 => by
-    simp only [U_one, T_two, U_two]
-    ring
+  | 0 => by simp only [U_zero, U_one, T_one]; ring
+  | 1 => by simp only [U_one, T_two, U_two]; ring
   | n + 2 =>
     calc
       U R (n + 2 + 1) = 2 * X * (X * U R (n + 1) + T R (n + 2)) - (X * U R n + T R (n + 1)) := by
@@ -215,9 +209,7 @@ but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_eq_X_mul_T_sub_pol_U Polynomial.Chebyshev.T_eq_X_mul_T_sub_pol_Uₓ'. -/
 theorem T_eq_X_mul_T_sub_pol_U : ∀ n : ℕ, T R (n + 2) = X * T R (n + 1) - (1 - X ^ 2) * U R n
-  | 0 => by
-    simp only [T_one, T_two, U_zero]
-    ring
+  | 0 => by simp only [T_one, T_two, U_zero]; ring
   | 1 => by
     simp only [T_add_two, T_zero, T_add_two, U_one, T_one]
     ring

1dac236e

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -286,10 +286,7 @@ theorem map_U (f : R →+* S) : ∀ n : ℕ, map f (U R n) = U S n
 #align polynomial.chebyshev.map_U Polynomial.Chebyshev.map_U
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_derivative_eq_U Polynomial.Chebyshev.T_derivative_eq_Uₓ'. -/
 theorem T_derivative_eq_U : ∀ n : ℕ, derivative (T R (n + 1)) = (n + 1) * U R n
   | 0 => by simp only [T_one, U_zero, derivative_X, Nat.cast_zero, zero_add, mul_one]
@@ -317,10 +314,7 @@ theorem T_derivative_eq_U : ∀ n : ℕ, derivative (T R (n + 1)) = (n + 1) * U
 #align polynomial.chebyshev.T_derivative_eq_U Polynomial.Chebyshev.T_derivative_eq_U
 
 /- warning: polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T -> Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_Tₓ'. -/
 theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
     (1 - X ^ 2) * derivative (T R (n + 1)) = (n + 1) * (T R n - X * T R (n + 1)) :=
@@ -335,10 +329,7 @@ theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
 #align polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T
 
 /- warning: polynomial.chebyshev.add_one_mul_T_eq_poly_in_U -> Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_U is a dubious translation:
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(CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.add_one_mul_T_eq_poly_in_U Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_Uₓ'. -/
 theorem add_one_mul_T_eq_poly_in_U (n : ℕ) :
     ((n : R[X]) + 1) * T R (n + 1) = X * U R n - (1 - X ^ 2) * derivative (U R n) :=

1dac236e

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -289,7 +289,7 @@ theorem map_U (f : R →+* S) : ∀ n : ℕ, map f (U R n) = U S n
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HasLiftT.mk.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CoeTCₓ.coe.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Nat.castCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_derivative_eq_U Polynomial.Chebyshev.T_derivative_eq_Uₓ'. -/
 theorem T_derivative_eq_U : ∀ n : ℕ, derivative (T R (n + 1)) = (n + 1) * U R n
   | 0 => by simp only [T_one, U_zero, derivative_X, Nat.cast_zero, zero_add, mul_one]
@@ -320,7 +320,7 @@ theorem T_derivative_eq_U : ∀ n : ℕ, derivative (T R (n + 1)) = (n + 1) * U
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HasLiftT.mk.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CoeTCₓ.coe.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Nat.castCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
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(CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_Tₓ'. -/
 theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
     (1 - X ^ 2) * derivative (T R (n + 1)) = (n + 1) * (T R n - X * T R (n + 1)) :=
@@ -338,7 +338,7 @@ theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HasLiftT.mk.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CoeTCₓ.coe.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Nat.castCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.add_one_mul_T_eq_poly_in_U Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_Uₓ'. -/
 theorem add_one_mul_T_eq_poly_in_U (n : ℕ) :
     ((n : R[X]) + 1) * T R (n + 1) = X * U R n - (1 - X ^ 2) * derivative (U R n) :=

1dac236e

bump to nightly-2023-05-18-03

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

b46e9d53

Diff

@@ -289,7 +289,7 @@ theorem map_U (f : R →+* S) : ∀ n : ℕ, map f (U R n) = U S n
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HasLiftT.mk.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CoeTCₓ.coe.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Nat.castCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))
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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_derivative_eq_U Polynomial.Chebyshev.T_derivative_eq_Uₓ'. -/
 theorem T_derivative_eq_U : ∀ n : ℕ, derivative (T R (n + 1)) = (n + 1) * U R n
   | 0 => by simp only [T_one, U_zero, derivative_X, Nat.cast_zero, zero_add, mul_one]
@@ -320,7 +320,7 @@ theorem T_derivative_eq_U : ∀ n : ℕ, derivative (T R (n + 1)) = (n + 1) * U
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HasLiftT.mk.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CoeTCₓ.coe.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Nat.castCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
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(CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R 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(Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R 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_inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_Tₓ'. -/
 theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
     (1 - X ^ 2) * derivative (T R (n + 1)) = (n + 1) * (T R n - X * T R (n + 1)) :=
@@ -338,7 +338,7 @@ theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
 lean 3 declaration is
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(CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HasLiftT.mk.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CoeTCₓ.coe.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Nat.castCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))))
 but is expected to have type
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_inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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(Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.add_one_mul_T_eq_poly_in_U Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_Uₓ'. -/
 theorem add_one_mul_T_eq_poly_in_U (n : ℕ) :
     ((n : R[X]) + 1) * T R (n + 1) = X * U R n - (1 - X ^ 2) * derivative (U R n) :=

1dac236e

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -95,7 +95,7 @@ theorem T_one : T R 1 = X :=
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (bit0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (instOfNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 2 (instOfNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 2 (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_add_two Polynomial.Chebyshev.T_add_twoₓ'. -/
 @[simp]
 theorem T_add_two (n : ℕ) : T R (n + 2) = 2 * X * T R (n + 1) - T R n := by rw [T]
@@ -105,7 +105,7 @@ theorem T_add_two (n : ℕ) : T R (n + 2) = 2 * X * T R (n + 1) - T R n := by rw
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (bit0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (instOfNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 2 (instOfNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 2 (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_two Polynomial.Chebyshev.T_twoₓ'. -/
 theorem T_two : T R 2 = 2 * X ^ 2 - 1 := by simp only [T, sub_left_inj, sq, mul_assoc]
 #align polynomial.chebyshev.T_two Polynomial.Chebyshev.T_two
@@ -114,7 +114,7 @@ theorem T_two : T R 2 = 2 * X ^ 2 - 1 := by simp only [T, sub_left_inj, sq, mul_
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), (LE.le.{0} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (bit0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), (LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (instOfNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), (LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 2 (instOfNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 2 (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_of_two_le Polynomial.Chebyshev.T_of_two_leₓ'. -/
 theorem T_of_two_le (n : ℕ) (h : 2 ≤ n) : T R n = 2 * X * T R (n - 1) - T R (n - 2) :=
   by
@@ -143,7 +143,7 @@ theorem U_zero : U R 0 = 1 :=
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (bit0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (instOfNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 2 (instOfNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 2 (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.U_one Polynomial.Chebyshev.U_oneₓ'. -/
 @[simp]
 theorem U_one : U R 1 = 2 * X :=
@@ -154,7 +154,7 @@ theorem U_one : U R 1 = 2 * X :=
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (bit0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (instOfNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 2 (instOfNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 2 (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.U_add_two Polynomial.Chebyshev.U_add_twoₓ'. -/
 @[simp]
 theorem U_add_two (n : ℕ) : U R (n + 2) = 2 * X * U R (n + 1) - U R n := by rw [U]
@@ -164,7 +164,7 @@ theorem U_add_two (n : ℕ) : U R (n + 2) = 2 * X * U R (n + 1) - U R n := by rw
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 4 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 4 (bit0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (bit0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 4 (instOfNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 4 (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 4 (instOfNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 4 (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.U_two Polynomial.Chebyshev.U_twoₓ'. -/
 theorem U_two : U R 2 = 4 * X ^ 2 - 1 := by
   simp only [U]
@@ -175,7 +175,7 @@ theorem U_two : U R 2 = 4 * X ^ 2 - 1 := by
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), (LE.le.{0} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (bit0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), (LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (instOfNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), (LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 2 (instOfNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 2 (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.U_of_two_le Polynomial.Chebyshev.U_of_two_leₓ'. -/
 theorem U_of_two_le (n : ℕ) (h : 2 ≤ n) : U R n = 2 * X * U R (n - 1) - U R (n - 2) :=
   by
@@ -212,7 +212,7 @@ theorem T_eq_U_sub_X_mul_U (n : ℕ) : T R (n + 1) = U R (n + 1) - X * U R n :=
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_eq_X_mul_T_sub_pol_U Polynomial.Chebyshev.T_eq_X_mul_T_sub_pol_Uₓ'. -/
 theorem T_eq_X_mul_T_sub_pol_U : ∀ n : ℕ, T R (n + 2) = X * T R (n + 1) - (1 - X ^ 2) * U R n
   | 0 => by
@@ -238,7 +238,7 @@ theorem T_eq_X_mul_T_sub_pol_U : ∀ n : ℕ, T R (n + 2) = X * T R (n + 1) - (1
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.one_sub_X_sq_mul_U_eq_pol_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_U_eq_pol_in_Tₓ'. -/
 theorem one_sub_X_sq_mul_U_eq_pol_in_T (n : ℕ) :
     (1 - X ^ 2) * U R n = X * T R (n + 1) - T R (n + 2) := by
@@ -251,7 +251,7 @@ variable {R S}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (n : Nat), Eq.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f (Polynomial.Chebyshev.T.{u1} R _inst_1 n)) (Polynomial.Chebyshev.T.{u2} S _inst_2 n)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (n : Nat), Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) f (Polynomial.Chebyshev.T.{u2} R _inst_1 n)) (Polynomial.Chebyshev.T.{u1} S _inst_2 n)
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (n : Nat), Eq.{succ u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.map.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) f (Polynomial.Chebyshev.T.{u2} R _inst_1 n)) (Polynomial.Chebyshev.T.{u1} S _inst_2 n)
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.map_T Polynomial.Chebyshev.map_Tₓ'. -/
 @[simp]
 theorem map_T (f : R →+* S) : ∀ n : ℕ, map f (T R n) = T S n
@@ -268,7 +268,7 @@ theorem map_T (f : R →+* S) : ∀ n : ℕ, map f (T R n) = T S n
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (n : Nat), Eq.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (Polynomial.Chebyshev.U.{u2} S _inst_2 n)
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (n : Nat), Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) f (Polynomial.Chebyshev.U.{u2} R _inst_1 n)) (Polynomial.Chebyshev.U.{u1} S _inst_2 n)
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (n : Nat), Eq.{succ u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.map.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) f (Polynomial.Chebyshev.U.{u2} R _inst_1 n)) (Polynomial.Chebyshev.U.{u1} S _inst_2 n)
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.map_U Polynomial.Chebyshev.map_Uₓ'. -/
 @[simp]
 theorem map_U (f : R →+* S) : ∀ n : ℕ, map f (U R n) = U S n
@@ -289,7 +289,7 @@ theorem map_U (f : R →+* S) : ∀ n : ℕ, map f (U R n) = U S n
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HasLiftT.mk.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CoeTCₓ.coe.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Nat.castCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Nat.cast.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) n) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_derivative_eq_U Polynomial.Chebyshev.T_derivative_eq_Uₓ'. -/
 theorem T_derivative_eq_U : ∀ n : ℕ, derivative (T R (n + 1)) = (n + 1) * U R n
   | 0 => by simp only [T_one, U_zero, derivative_X, Nat.cast_zero, zero_add, mul_one]
@@ -320,7 +320,7 @@ theorem T_derivative_eq_U : ∀ n : ℕ, derivative (T R (n + 1)) = (n + 1) * U
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HasLiftT.mk.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CoeTCₓ.coe.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Nat.castCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Nat.cast.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_Tₓ'. -/
 theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
     (1 - X ^ 2) * derivative (T R (n + 1)) = (n + 1) * (T R n - X * T R (n + 1)) :=
@@ -338,7 +338,7 @@ theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HasLiftT.mk.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CoeTCₓ.coe.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Nat.castCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Nat.cast.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R 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+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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(Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n))))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.add_one_mul_T_eq_poly_in_U Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_Uₓ'. -/
 theorem add_one_mul_T_eq_poly_in_U (n : ℕ) :
     ((n : R[X]) + 1) * T R (n + 1) = X * U R n - (1 - X ^ 2) * derivative (U R n) :=
@@ -377,7 +377,7 @@ variable (R)
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (m : Nat) (k : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (bit0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 m)) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m k))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat Nat.hasMul) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) m) k)) (Polynomial.Chebyshev.T.{u1} R _inst_1 k))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (m : Nat) (k : Nat), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (instOfNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 m)) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m k))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) m) k)) (Polynomial.Chebyshev.T.{u1} R _inst_1 k))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (m : Nat) (k : Nat), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 2 (instOfNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 2 (Polynomial.natCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Polynomial.Chebyshev.T.{u1} R _inst_1 m)) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m k))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) m) k)) (Polynomial.Chebyshev.T.{u1} R _inst_1 k))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.mul_T Polynomial.Chebyshev.mul_Tₓ'. -/
 /-- The product of two Chebyshev polynomials is the sum of two other Chebyshev polynomials. -/
 theorem mul_T : ∀ m k, 2 * T R m * T R (m + k) = T R (2 * m + k) + T R k

1dac236e

bump to nightly-2023-03-20-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ec294687917cbc5c73620b4414ae9b5dd9ae1b4

2e1f2c13

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Julian Kuelshammer, Heather Macbeth
 
 ! This file was ported from Lean 3 source module ring_theory.polynomial.chebyshev
-! leanprover-community/mathlib commit d774451114d6045faeb6751c396bea1eb9058946
+! leanprover-community/mathlib commit 1dac236edca9b4b6f5f00b1ad831e35f89472837
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Tactic.LinearCombination
 /-!
 # Chebyshev polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The Chebyshev polynomials are two families of polynomials indexed by `ℕ`,
 with integral coefficients.

d7744511

bump to nightly-2023-03-18-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/02ba8949f486ebecf93fe7460f1ed0564b5e442c

fbf3a71d

Diff

@@ -65,71 +65,124 @@ open Polynomial
 
 variable (R S : Type _) [CommRing R] [CommRing S]
 
+#print Polynomial.Chebyshev.T /-
 /-- `T n` is the `n`-th Chebyshev polynomial of the first kind -/
-noncomputable def t : ℕ → R[X]
+noncomputable def T : ℕ → R[X]
   | 0 => 1
   | 1 => X
   | n + 2 => 2 * X * T (n + 1) - T n
-#align polynomial.chebyshev.T Polynomial.Chebyshev.t
+#align polynomial.chebyshev.T Polynomial.Chebyshev.T
+-/
 
+#print Polynomial.Chebyshev.T_zero /-
 @[simp]
-theorem t_zero : t R 0 = 1 :=
+theorem T_zero : T R 0 = 1 :=
   rfl
-#align polynomial.chebyshev.T_zero Polynomial.Chebyshev.t_zero
+#align polynomial.chebyshev.T_zero Polynomial.Chebyshev.T_zero
+-/
 
+#print Polynomial.Chebyshev.T_one /-
 @[simp]
-theorem t_one : t R 1 = X :=
+theorem T_one : T R 1 = X :=
   rfl
-#align polynomial.chebyshev.T_one Polynomial.Chebyshev.t_one
+#align polynomial.chebyshev.T_one Polynomial.Chebyshev.T_one
+-/
 
+/- warning: polynomial.chebyshev.T_add_two -> Polynomial.Chebyshev.T_add_two is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_add_two Polynomial.Chebyshev.T_add_twoₓ'. -/
 @[simp]
-theorem t_add_two (n : ℕ) : t R (n + 2) = 2 * X * t R (n + 1) - t R n := by rw [T]
-#align polynomial.chebyshev.T_add_two Polynomial.Chebyshev.t_add_two
-
-theorem t_two : t R 2 = 2 * X ^ 2 - 1 := by simp only [T, sub_left_inj, sq, mul_assoc]
-#align polynomial.chebyshev.T_two Polynomial.Chebyshev.t_two
-
-theorem t_of_two_le (n : ℕ) (h : 2 ≤ n) : t R n = 2 * X * t R (n - 1) - t R (n - 2) :=
+theorem T_add_two (n : ℕ) : T R (n + 2) = 2 * X * T R (n + 1) - T R n := by rw [T]
+#align polynomial.chebyshev.T_add_two Polynomial.Chebyshev.T_add_two
+
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+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_two Polynomial.Chebyshev.T_twoₓ'. -/
+theorem T_two : T R 2 = 2 * X ^ 2 - 1 := by simp only [T, sub_left_inj, sq, mul_assoc]
+#align polynomial.chebyshev.T_two Polynomial.Chebyshev.T_two
+
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+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_of_two_le Polynomial.Chebyshev.T_of_two_leₓ'. -/
+theorem T_of_two_le (n : ℕ) (h : 2 ≤ n) : T R n = 2 * X * T R (n - 1) - T R (n - 2) :=
   by
   obtain ⟨n, rfl⟩ := Nat.exists_eq_add_of_le h
   rw [add_comm]
   exact T_add_two R n
-#align polynomial.chebyshev.T_of_two_le Polynomial.Chebyshev.t_of_two_le
+#align polynomial.chebyshev.T_of_two_le Polynomial.Chebyshev.T_of_two_le
 
+#print Polynomial.Chebyshev.U /-
 /-- `U n` is the `n`-th Chebyshev polynomial of the second kind -/
-noncomputable def u : ℕ → R[X]
+noncomputable def U : ℕ → R[X]
   | 0 => 1
   | 1 => 2 * X
   | n + 2 => 2 * X * U (n + 1) - U n
-#align polynomial.chebyshev.U Polynomial.Chebyshev.u
+#align polynomial.chebyshev.U Polynomial.Chebyshev.U
+-/
 
+#print Polynomial.Chebyshev.U_zero /-
 @[simp]
-theorem u_zero : u R 0 = 1 :=
+theorem U_zero : U R 0 = 1 :=
   rfl
-#align polynomial.chebyshev.U_zero Polynomial.Chebyshev.u_zero
+#align polynomial.chebyshev.U_zero Polynomial.Chebyshev.U_zero
+-/
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.U_one Polynomial.Chebyshev.U_oneₓ'. -/
 @[simp]
-theorem u_one : u R 1 = 2 * X :=
+theorem U_one : U R 1 = 2 * X :=
   rfl
-#align polynomial.chebyshev.U_one Polynomial.Chebyshev.u_one
-
+#align polynomial.chebyshev.U_one Polynomial.Chebyshev.U_one
+
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+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.U_add_two Polynomial.Chebyshev.U_add_twoₓ'. -/
 @[simp]
-theorem u_add_two (n : ℕ) : u R (n + 2) = 2 * X * u R (n + 1) - u R n := by rw [U]
-#align polynomial.chebyshev.U_add_two Polynomial.Chebyshev.u_add_two
-
-theorem u_two : u R 2 = 4 * X ^ 2 - 1 := by
+theorem U_add_two (n : ℕ) : U R (n + 2) = 2 * X * U R (n + 1) - U R n := by rw [U]
+#align polynomial.chebyshev.U_add_two Polynomial.Chebyshev.U_add_two
+
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+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.U_two Polynomial.Chebyshev.U_twoₓ'. -/
+theorem U_two : U R 2 = 4 * X ^ 2 - 1 := by
   simp only [U]
   ring
-#align polynomial.chebyshev.U_two Polynomial.Chebyshev.u_two
-
-theorem u_of_two_le (n : ℕ) (h : 2 ≤ n) : u R n = 2 * X * u R (n - 1) - u R (n - 2) :=
+#align polynomial.chebyshev.U_two Polynomial.Chebyshev.U_two
+
+/- warning: polynomial.chebyshev.U_of_two_le -> Polynomial.Chebyshev.U_of_two_le is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (n : Nat), (LE.le.{0} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.U.{u1} R _inst_1 n) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 2 (bit0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Polynomial.Chebyshev.U.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.U_of_two_le Polynomial.Chebyshev.U_of_two_leₓ'. -/
+theorem U_of_two_le (n : ℕ) (h : 2 ≤ n) : U R n = 2 * X * U R (n - 1) - U R (n - 2) :=
   by
   obtain ⟨n, rfl⟩ := Nat.exists_eq_add_of_le h
   rw [add_comm]
   exact U_add_two R n
-#align polynomial.chebyshev.U_of_two_le Polynomial.Chebyshev.u_of_two_le
+#align polynomial.chebyshev.U_of_two_le Polynomial.Chebyshev.U_of_two_le
 
-theorem u_eq_x_mul_u_add_t : ∀ n : ℕ, u R (n + 1) = X * u R n + t R (n + 1)
+#print Polynomial.Chebyshev.U_eq_X_mul_U_add_T /-
+theorem U_eq_X_mul_U_add_T : ∀ n : ℕ, U R (n + 1) = X * U R n + T R (n + 1)
   | 0 => by
     simp only [U_zero, U_one, T_one]
     ring
@@ -138,18 +191,27 @@ theorem u_eq_x_mul_u_add_t : ∀ n : ℕ, u R (n + 1) = X * u R n + t R (n + 1)
     ring
   | n + 2 =>
     calc
-      u R (n + 2 + 1) = 2 * X * (X * u R (n + 1) + t R (n + 2)) - (X * u R n + t R (n + 1)) := by
+      U R (n + 2 + 1) = 2 * X * (X * U R (n + 1) + T R (n + 2)) - (X * U R n + T R (n + 1)) := by
         simp only [U_add_two, U_eq_X_mul_U_add_T n, U_eq_X_mul_U_add_T (n + 1)]
-      _ = X * (2 * X * u R (n + 1) - u R n) + (2 * X * t R (n + 2) - t R (n + 1)) := by ring
-      _ = X * u R (n + 2) + t R (n + 2 + 1) := by simp only [U_add_two, T_add_two]
+      _ = X * (2 * X * U R (n + 1) - U R n) + (2 * X * T R (n + 2) - T R (n + 1)) := by ring
+      _ = X * U R (n + 2) + T R (n + 2 + 1) := by simp only [U_add_two, T_add_two]
       
-#align polynomial.chebyshev.U_eq_X_mul_U_add_T Polynomial.Chebyshev.u_eq_x_mul_u_add_t
+#align polynomial.chebyshev.U_eq_X_mul_U_add_T Polynomial.Chebyshev.U_eq_X_mul_U_add_T
+-/
 
-theorem t_eq_u_sub_x_mul_u (n : ℕ) : t R (n + 1) = u R (n + 1) - X * u R n := by
+#print Polynomial.Chebyshev.T_eq_U_sub_X_mul_U /-
+theorem T_eq_U_sub_X_mul_U (n : ℕ) : T R (n + 1) = U R (n + 1) - X * U R n := by
   rw [U_eq_X_mul_U_add_T, add_comm (X * U R n), add_sub_cancel]
-#align polynomial.chebyshev.T_eq_U_sub_X_mul_U Polynomial.Chebyshev.t_eq_u_sub_x_mul_u
+#align polynomial.chebyshev.T_eq_U_sub_X_mul_U Polynomial.Chebyshev.T_eq_U_sub_X_mul_U
+-/
 
-theorem t_eq_x_mul_t_sub_pol_u : ∀ n : ℕ, t R (n + 2) = X * t R (n + 1) - (1 - X ^ 2) * u R n
+/- warning: polynomial.chebyshev.T_eq_X_mul_T_sub_pol_U -> Polynomial.Chebyshev.T_eq_X_mul_T_sub_pol_U is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_eq_X_mul_T_sub_pol_U Polynomial.Chebyshev.T_eq_X_mul_T_sub_pol_Uₓ'. -/
+theorem T_eq_X_mul_T_sub_pol_U : ∀ n : ℕ, T R (n + 2) = X * T R (n + 1) - (1 - X ^ 2) * U R n
   | 0 => by
     simp only [T_one, T_two, U_zero]
     ring
@@ -158,26 +220,38 @@ theorem t_eq_x_mul_t_sub_pol_u : ∀ n : ℕ, t R (n + 2) = X * t R (n + 1) - (1
     ring
   | n + 2 =>
     calc
-      t R (n + 2 + 2) = 2 * X * t R (n + 2 + 1) - t R (n + 2) := t_add_two _ _
+      T R (n + 2 + 2) = 2 * X * T R (n + 2 + 1) - T R (n + 2) := T_add_two _ _
       _ =
-          2 * X * (X * t R (n + 2) - (1 - X ^ 2) * u R (n + 1)) -
-            (X * t R (n + 1) - (1 - X ^ 2) * u R n) :=
+          2 * X * (X * T R (n + 2) - (1 - X ^ 2) * U R (n + 1)) -
+            (X * T R (n + 1) - (1 - X ^ 2) * U R n) :=
         by simp only [T_eq_X_mul_T_sub_pol_U]
-      _ = X * (2 * X * t R (n + 2) - t R (n + 1)) - (1 - X ^ 2) * (2 * X * u R (n + 1) - u R n) :=
+      _ = X * (2 * X * T R (n + 2) - T R (n + 1)) - (1 - X ^ 2) * (2 * X * U R (n + 1) - U R n) :=
         by ring
-      _ = X * t R (n + 2 + 1) - (1 - X ^ 2) * u R (n + 2) := by rw [T_add_two _ (n + 1), U_add_two]
+      _ = X * T R (n + 2 + 1) - (1 - X ^ 2) * U R (n + 2) := by rw [T_add_two _ (n + 1), U_add_two]
       
-#align polynomial.chebyshev.T_eq_X_mul_T_sub_pol_U Polynomial.Chebyshev.t_eq_x_mul_t_sub_pol_u
-
-theorem one_sub_x_sq_mul_u_eq_pol_in_t (n : ℕ) :
-    (1 - X ^ 2) * u R n = X * t R (n + 1) - t R (n + 2) := by
+#align polynomial.chebyshev.T_eq_X_mul_T_sub_pol_U Polynomial.Chebyshev.T_eq_X_mul_T_sub_pol_U
+
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+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.one_sub_X_sq_mul_U_eq_pol_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_U_eq_pol_in_Tₓ'. -/
+theorem one_sub_X_sq_mul_U_eq_pol_in_T (n : ℕ) :
+    (1 - X ^ 2) * U R n = X * T R (n + 1) - T R (n + 2) := by
   rw [T_eq_X_mul_T_sub_pol_U, ← sub_add, sub_self, zero_add]
-#align polynomial.chebyshev.one_sub_X_sq_mul_U_eq_pol_in_T Polynomial.Chebyshev.one_sub_x_sq_mul_u_eq_pol_in_t
+#align polynomial.chebyshev.one_sub_X_sq_mul_U_eq_pol_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_U_eq_pol_in_T
 
 variable {R S}
 
+/- warning: polynomial.chebyshev.map_T -> Polynomial.Chebyshev.map_T is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (n : Nat), Eq.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f (Polynomial.Chebyshev.T.{u1} R _inst_1 n)) (Polynomial.Chebyshev.T.{u2} S _inst_2 n)
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (n : Nat), Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) f (Polynomial.Chebyshev.T.{u2} R _inst_1 n)) (Polynomial.Chebyshev.T.{u1} S _inst_2 n)
+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.map_T Polynomial.Chebyshev.map_Tₓ'. -/
 @[simp]
-theorem map_t (f : R →+* S) : ∀ n : ℕ, map f (t R n) = t S n
+theorem map_T (f : R →+* S) : ∀ n : ℕ, map f (T R n) = T S n
   | 0 => by simp only [T_zero, Polynomial.map_one]
   | 1 => by simp only [T_one, map_X]
   | n + 2 =>
@@ -185,10 +259,16 @@ theorem map_t (f : R →+* S) : ∀ n : ℕ, map f (t R n) = t S n
     simp only [T_add_two, Polynomial.map_mul, Polynomial.map_sub, map_X, bit0, Polynomial.map_add,
       Polynomial.map_one]
     rw [map_T (n + 1), map_T n]
-#align polynomial.chebyshev.map_T Polynomial.Chebyshev.map_t
-
+#align polynomial.chebyshev.map_T Polynomial.Chebyshev.map_T
+
+/- warning: polynomial.chebyshev.map_U -> Polynomial.Chebyshev.map_U is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (n : Nat), Eq.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f (Polynomial.Chebyshev.U.{u1} R _inst_1 n)) (Polynomial.Chebyshev.U.{u2} S _inst_2 n)
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (n : Nat), Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) f (Polynomial.Chebyshev.U.{u2} R _inst_1 n)) (Polynomial.Chebyshev.U.{u1} S _inst_2 n)
+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.map_U Polynomial.Chebyshev.map_Uₓ'. -/
 @[simp]
-theorem map_u (f : R →+* S) : ∀ n : ℕ, map f (u R n) = u S n
+theorem map_U (f : R →+* S) : ∀ n : ℕ, map f (U R n) = U S n
   | 0 => by simp only [U_zero, Polynomial.map_one]
   | 1 =>
     by
@@ -200,9 +280,15 @@ theorem map_u (f : R →+* S) : ∀ n : ℕ, map f (u R n) = u S n
     simp only [U_add_two, Polynomial.map_mul, Polynomial.map_sub, map_X, bit0, Polynomial.map_add,
       Polynomial.map_one]
     rw [map_U (n + 1), map_U n]
-#align polynomial.chebyshev.map_U Polynomial.Chebyshev.map_u
-
-theorem t_derivative_eq_u : ∀ n : ℕ, derivative (t R (n + 1)) = (n + 1) * u R n
+#align polynomial.chebyshev.map_U Polynomial.Chebyshev.map_U
+
+/- warning: polynomial.chebyshev.T_derivative_eq_U -> Polynomial.Chebyshev.T_derivative_eq_U is a dubious translation:
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n))
+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.T_derivative_eq_U Polynomial.Chebyshev.T_derivative_eq_Uₓ'. -/
+theorem T_derivative_eq_U : ∀ n : ℕ, derivative (T R (n + 1)) = (n + 1) * U R n
   | 0 => by simp only [T_one, U_zero, derivative_X, Nat.cast_zero, zero_add, mul_one]
   | 1 =>
     by
@@ -211,36 +297,48 @@ theorem t_derivative_eq_u : ∀ n : ℕ, derivative (t R (n + 1)) = (n + 1) * u
     norm_num
   | n + 2 =>
     calc
-      derivative (t R (n + 2 + 1)) =
-          2 * t R (n + 2) + 2 * X * derivative (t R (n + 1 + 1)) - derivative (t R (n + 1)) :=
+      derivative (T R (n + 2 + 1)) =
+          2 * T R (n + 2) + 2 * X * derivative (T R (n + 1 + 1)) - derivative (T R (n + 1)) :=
         by
         simp only [T_add_two _ (n + 1), derivative_sub, derivative_mul, derivative_X,
           derivative_bit0, derivative_one, bit0_zero, MulZeroClass.zero_mul, zero_add, mul_one]
       _ =
-          2 * (u R (n + 1 + 1) - X * u R (n + 1)) + 2 * X * ((n + 1 + 1) * u R (n + 1)) -
-            (n + 1) * u R n :=
+          2 * (U R (n + 1 + 1) - X * U R (n + 1)) + 2 * X * ((n + 1 + 1) * U R (n + 1)) -
+            (n + 1) * U R n :=
         by rw_mod_cast [T_derivative_eq_U, T_derivative_eq_U, T_eq_U_sub_X_mul_U]
-      _ = (n + 1) * (2 * X * u R (n + 1) - u R n) + 2 * u R (n + 2) := by ring
-      _ = (n + 1) * u R (n + 2) + 2 * u R (n + 2) := by rw [U_add_two]
-      _ = (n + 2 + 1) * u R (n + 2) := by ring
-      _ = (↑(n + 2) + 1) * u R (n + 2) := by norm_cast
+      _ = (n + 1) * (2 * X * U R (n + 1) - U R n) + 2 * U R (n + 2) := by ring
+      _ = (n + 1) * U R (n + 2) + 2 * U R (n + 2) := by rw [U_add_two]
+      _ = (n + 2 + 1) * U R (n + 2) := by ring
+      _ = (↑(n + 2) + 1) * U R (n + 2) := by norm_cast
       
-#align polynomial.chebyshev.T_derivative_eq_U Polynomial.Chebyshev.t_derivative_eq_u
-
-theorem one_sub_x_sq_mul_derivative_t_eq_poly_in_t (n : ℕ) :
-    (1 - X ^ 2) * derivative (t R (n + 1)) = (n + 1) * (t R n - X * t R (n + 1)) :=
+#align polynomial.chebyshev.T_derivative_eq_U Polynomial.Chebyshev.T_derivative_eq_U
+
+/- warning: polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T -> Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T is a dubious translation:
+lean 3 declaration is
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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.derivative.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HasLiftT.mk.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CoeTCₓ.coe.{1, succ u1} Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Nat.castCoe.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.natCast.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 n) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.Chebyshev.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_Tₓ'. -/
+theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
+    (1 - X ^ 2) * derivative (T R (n + 1)) = (n + 1) * (T R n - X * T R (n + 1)) :=
   calc
-    (1 - X ^ 2) * derivative (t R (n + 1)) = (1 - X ^ 2) * ((n + 1) * u R n) := by
+    (1 - X ^ 2) * derivative (T R (n + 1)) = (1 - X ^ 2) * ((n + 1) * U R n) := by
       rw [T_derivative_eq_U]
-    _ = (n + 1) * ((1 - X ^ 2) * u R n) := by ring
-    _ = (n + 1) * (X * t R (n + 1) - (2 * X * t R (n + 1) - t R n)) := by
+    _ = (n + 1) * ((1 - X ^ 2) * U R n) := by ring
+    _ = (n + 1) * (X * T R (n + 1) - (2 * X * T R (n + 1) - T R n)) := by
       rw [one_sub_X_sq_mul_U_eq_pol_in_T, T_add_two]
-    _ = (n + 1) * (t R n - X * t R (n + 1)) := by ring
+    _ = (n + 1) * (T R n - X * T R (n + 1)) := by ring
     
-#align polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T Polynomial.Chebyshev.one_sub_x_sq_mul_derivative_t_eq_poly_in_t
-
-theorem add_one_mul_t_eq_poly_in_u (n : ℕ) :
-    ((n : R[X]) + 1) * t R (n + 1) = X * u R n - (1 - X ^ 2) * derivative (u R n) :=
+#align polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T
+
+/- warning: polynomial.chebyshev.add_one_mul_T_eq_poly_in_U -> Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_U is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.add_one_mul_T_eq_poly_in_U Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_Uₓ'. -/
+theorem add_one_mul_T_eq_poly_in_U (n : ℕ) :
+    ((n : R[X]) + 1) * T R (n + 1) = X * U R n - (1 - X ^ 2) * derivative (U R n) :=
   by
   have h :
     derivative (T R (n + 2)) =
@@ -268,12 +366,18 @@ theorem add_one_mul_t_eq_poly_in_u (n : ℕ) :
       by rw [h]
     _ = X * U R n - (1 - X ^ 2) * derivative (U R n) := by ring
     
-#align polynomial.chebyshev.add_one_mul_T_eq_poly_in_U Polynomial.Chebyshev.add_one_mul_t_eq_poly_in_u
+#align polynomial.chebyshev.add_one_mul_T_eq_poly_in_U Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_U
 
 variable (R)
 
+/- warning: polynomial.chebyshev.mul_T -> Polynomial.Chebyshev.mul_T is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.mul_T Polynomial.Chebyshev.mul_Tₓ'. -/
 /-- The product of two Chebyshev polynomials is the sum of two other Chebyshev polynomials. -/
-theorem mul_t : ∀ m k, 2 * t R m * t R (m + k) = t R (2 * m + k) + t R k
+theorem mul_T : ∀ m k, 2 * T R m * T R (m + k) = T R (2 * m + k) + T R k
   | 0 => by simp [two_mul, add_mul]
   | 1 => by simp [add_comm]
   | m + 2 => by
@@ -303,10 +407,11 @@ theorem mul_t : ∀ m k, 2 * t R m * t R (m + k) = t R (2 * m + k) + t R k
     have h₃ := T_add_two R k
     -- the desired identity is an appropriate linear combination of H₁, H₂, h₁, h₂, h₃
     linear_combination 2 * T R (m + k + 2) * h₁ + 2 * X * H₁ - H₂ - h₂ - h₃
-#align polynomial.chebyshev.mul_T Polynomial.Chebyshev.mul_t
+#align polynomial.chebyshev.mul_T Polynomial.Chebyshev.mul_T
 
+#print Polynomial.Chebyshev.T_mul /-
 /-- The `(m * n)`-th Chebyshev polynomial is the composition of the `m`-th and `n`-th -/
-theorem t_mul : ∀ m n, t R (m * n) = (t R m).comp (t R n)
+theorem T_mul : ∀ m n, T R (m * n) = (T R m).comp (T R n)
   | 0 => by simp
   | 1 => by simp
   | m + 2 => by
@@ -314,7 +419,8 @@ theorem t_mul : ∀ m n, t R (m * n) = (t R m).comp (t R n)
     have : 2 * T R n * T R ((m + 1) * n) = T R ((m + 2) * n) + T R (m * n) := by
       convert mul_T R n (m * n) <;> ring
     simp [this, T_mul m, ← T_mul (m + 1)]
-#align polynomial.chebyshev.T_mul Polynomial.Chebyshev.t_mul
+#align polynomial.chebyshev.T_mul Polynomial.Chebyshev.T_mul
+-/
 
 end Polynomial.Chebyshev

d7744511

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -215,7 +215,7 @@ theorem t_derivative_eq_u : ∀ n : ℕ, derivative (t R (n + 1)) = (n + 1) * u
           2 * t R (n + 2) + 2 * X * derivative (t R (n + 1 + 1)) - derivative (t R (n + 1)) :=
         by
         simp only [T_add_two _ (n + 1), derivative_sub, derivative_mul, derivative_X,
-          derivative_bit0, derivative_one, bit0_zero, zero_mul, zero_add, mul_one]
+          derivative_bit0, derivative_one, bit0_zero, MulZeroClass.zero_mul, zero_add, mul_one]
       _ =
           2 * (u R (n + 1 + 1) - X * u R (n + 1)) + 2 * X * ((n + 1 + 1) * u R (n + 1)) -
             (n + 1) * u R n :=

d7744511

bump to nightly-2023-03-08-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

422cc012

Diff

@@ -68,8 +68,8 @@ variable (R S : Type _) [CommRing R] [CommRing S]
 /-- `T n` is the `n`-th Chebyshev polynomial of the first kind -/
 noncomputable def t : ℕ → R[X]
   | 0 => 1
-  | 1 => x
-  | n + 2 => 2 * x * T (n + 1) - T n
+  | 1 => X
+  | n + 2 => 2 * X * T (n + 1) - T n
 #align polynomial.chebyshev.T Polynomial.Chebyshev.t
 
 @[simp]
@@ -78,18 +78,18 @@ theorem t_zero : t R 0 = 1 :=
 #align polynomial.chebyshev.T_zero Polynomial.Chebyshev.t_zero
 
 @[simp]
-theorem t_one : t R 1 = x :=
+theorem t_one : t R 1 = X :=
   rfl
 #align polynomial.chebyshev.T_one Polynomial.Chebyshev.t_one
 
 @[simp]
-theorem t_add_two (n : ℕ) : t R (n + 2) = 2 * x * t R (n + 1) - t R n := by rw [T]
+theorem t_add_two (n : ℕ) : t R (n + 2) = 2 * X * t R (n + 1) - t R n := by rw [T]
 #align polynomial.chebyshev.T_add_two Polynomial.Chebyshev.t_add_two
 
-theorem t_two : t R 2 = 2 * x ^ 2 - 1 := by simp only [T, sub_left_inj, sq, mul_assoc]
+theorem t_two : t R 2 = 2 * X ^ 2 - 1 := by simp only [T, sub_left_inj, sq, mul_assoc]
 #align polynomial.chebyshev.T_two Polynomial.Chebyshev.t_two
 
-theorem t_of_two_le (n : ℕ) (h : 2 ≤ n) : t R n = 2 * x * t R (n - 1) - t R (n - 2) :=
+theorem t_of_two_le (n : ℕ) (h : 2 ≤ n) : t R n = 2 * X * t R (n - 1) - t R (n - 2) :=
   by
   obtain ⟨n, rfl⟩ := Nat.exists_eq_add_of_le h
   rw [add_comm]
@@ -99,8 +99,8 @@ theorem t_of_two_le (n : ℕ) (h : 2 ≤ n) : t R n = 2 * x * t R (n - 1) - t R
 /-- `U n` is the `n`-th Chebyshev polynomial of the second kind -/
 noncomputable def u : ℕ → R[X]
   | 0 => 1
-  | 1 => 2 * x
-  | n + 2 => 2 * x * U (n + 1) - U n
+  | 1 => 2 * X
+  | n + 2 => 2 * X * U (n + 1) - U n
 #align polynomial.chebyshev.U Polynomial.Chebyshev.u
 
 @[simp]
@@ -109,27 +109,27 @@ theorem u_zero : u R 0 = 1 :=
 #align polynomial.chebyshev.U_zero Polynomial.Chebyshev.u_zero
 
 @[simp]
-theorem u_one : u R 1 = 2 * x :=
+theorem u_one : u R 1 = 2 * X :=
   rfl
 #align polynomial.chebyshev.U_one Polynomial.Chebyshev.u_one
 
 @[simp]
-theorem u_add_two (n : ℕ) : u R (n + 2) = 2 * x * u R (n + 1) - u R n := by rw [U]
+theorem u_add_two (n : ℕ) : u R (n + 2) = 2 * X * u R (n + 1) - u R n := by rw [U]
 #align polynomial.chebyshev.U_add_two Polynomial.Chebyshev.u_add_two
 
-theorem u_two : u R 2 = 4 * x ^ 2 - 1 := by
+theorem u_two : u R 2 = 4 * X ^ 2 - 1 := by
   simp only [U]
   ring
 #align polynomial.chebyshev.U_two Polynomial.Chebyshev.u_two
 
-theorem u_of_two_le (n : ℕ) (h : 2 ≤ n) : u R n = 2 * x * u R (n - 1) - u R (n - 2) :=
+theorem u_of_two_le (n : ℕ) (h : 2 ≤ n) : u R n = 2 * X * u R (n - 1) - u R (n - 2) :=
   by
   obtain ⟨n, rfl⟩ := Nat.exists_eq_add_of_le h
   rw [add_comm]
   exact U_add_two R n
 #align polynomial.chebyshev.U_of_two_le Polynomial.Chebyshev.u_of_two_le
 
-theorem u_eq_x_mul_u_add_t : ∀ n : ℕ, u R (n + 1) = x * u R n + t R (n + 1)
+theorem u_eq_x_mul_u_add_t : ∀ n : ℕ, u R (n + 1) = X * u R n + t R (n + 1)
   | 0 => by
     simp only [U_zero, U_one, T_one]
     ring
@@ -138,18 +138,18 @@ theorem u_eq_x_mul_u_add_t : ∀ n : ℕ, u R (n + 1) = x * u R n + t R (n + 1)
     ring
   | n + 2 =>
     calc
-      u R (n + 2 + 1) = 2 * x * (x * u R (n + 1) + t R (n + 2)) - (x * u R n + t R (n + 1)) := by
+      u R (n + 2 + 1) = 2 * X * (X * u R (n + 1) + t R (n + 2)) - (X * u R n + t R (n + 1)) := by
         simp only [U_add_two, U_eq_X_mul_U_add_T n, U_eq_X_mul_U_add_T (n + 1)]
-      _ = x * (2 * x * u R (n + 1) - u R n) + (2 * x * t R (n + 2) - t R (n + 1)) := by ring
-      _ = x * u R (n + 2) + t R (n + 2 + 1) := by simp only [U_add_two, T_add_two]
+      _ = X * (2 * X * u R (n + 1) - u R n) + (2 * X * t R (n + 2) - t R (n + 1)) := by ring
+      _ = X * u R (n + 2) + t R (n + 2 + 1) := by simp only [U_add_two, T_add_two]
       
 #align polynomial.chebyshev.U_eq_X_mul_U_add_T Polynomial.Chebyshev.u_eq_x_mul_u_add_t
 
-theorem t_eq_u_sub_x_mul_u (n : ℕ) : t R (n + 1) = u R (n + 1) - x * u R n := by
+theorem t_eq_u_sub_x_mul_u (n : ℕ) : t R (n + 1) = u R (n + 1) - X * u R n := by
   rw [U_eq_X_mul_U_add_T, add_comm (X * U R n), add_sub_cancel]
 #align polynomial.chebyshev.T_eq_U_sub_X_mul_U Polynomial.Chebyshev.t_eq_u_sub_x_mul_u
 
-theorem t_eq_x_mul_t_sub_pol_u : ∀ n : ℕ, t R (n + 2) = x * t R (n + 1) - (1 - x ^ 2) * u R n
+theorem t_eq_x_mul_t_sub_pol_u : ∀ n : ℕ, t R (n + 2) = X * t R (n + 1) - (1 - X ^ 2) * u R n
   | 0 => by
     simp only [T_one, T_two, U_zero]
     ring
@@ -158,19 +158,19 @@ theorem t_eq_x_mul_t_sub_pol_u : ∀ n : ℕ, t R (n + 2) = x * t R (n + 1) - (1
     ring
   | n + 2 =>
     calc
-      t R (n + 2 + 2) = 2 * x * t R (n + 2 + 1) - t R (n + 2) := t_add_two _ _
+      t R (n + 2 + 2) = 2 * X * t R (n + 2 + 1) - t R (n + 2) := t_add_two _ _
       _ =
-          2 * x * (x * t R (n + 2) - (1 - x ^ 2) * u R (n + 1)) -
-            (x * t R (n + 1) - (1 - x ^ 2) * u R n) :=
+          2 * X * (X * t R (n + 2) - (1 - X ^ 2) * u R (n + 1)) -
+            (X * t R (n + 1) - (1 - X ^ 2) * u R n) :=
         by simp only [T_eq_X_mul_T_sub_pol_U]
-      _ = x * (2 * x * t R (n + 2) - t R (n + 1)) - (1 - x ^ 2) * (2 * x * u R (n + 1) - u R n) :=
+      _ = X * (2 * X * t R (n + 2) - t R (n + 1)) - (1 - X ^ 2) * (2 * X * u R (n + 1) - u R n) :=
         by ring
-      _ = x * t R (n + 2 + 1) - (1 - x ^ 2) * u R (n + 2) := by rw [T_add_two _ (n + 1), U_add_two]
+      _ = X * t R (n + 2 + 1) - (1 - X ^ 2) * u R (n + 2) := by rw [T_add_two _ (n + 1), U_add_two]
       
 #align polynomial.chebyshev.T_eq_X_mul_T_sub_pol_U Polynomial.Chebyshev.t_eq_x_mul_t_sub_pol_u
 
 theorem one_sub_x_sq_mul_u_eq_pol_in_t (n : ℕ) :
-    (1 - x ^ 2) * u R n = x * t R (n + 1) - t R (n + 2) := by
+    (1 - X ^ 2) * u R n = X * t R (n + 1) - t R (n + 2) := by
   rw [T_eq_X_mul_T_sub_pol_U, ← sub_add, sub_self, zero_add]
 #align polynomial.chebyshev.one_sub_X_sq_mul_U_eq_pol_in_T Polynomial.Chebyshev.one_sub_x_sq_mul_u_eq_pol_in_t
 
@@ -212,15 +212,15 @@ theorem t_derivative_eq_u : ∀ n : ℕ, derivative (t R (n + 1)) = (n + 1) * u
   | n + 2 =>
     calc
       derivative (t R (n + 2 + 1)) =
-          2 * t R (n + 2) + 2 * x * derivative (t R (n + 1 + 1)) - derivative (t R (n + 1)) :=
+          2 * t R (n + 2) + 2 * X * derivative (t R (n + 1 + 1)) - derivative (t R (n + 1)) :=
         by
         simp only [T_add_two _ (n + 1), derivative_sub, derivative_mul, derivative_X,
           derivative_bit0, derivative_one, bit0_zero, zero_mul, zero_add, mul_one]
       _ =
-          2 * (u R (n + 1 + 1) - x * u R (n + 1)) + 2 * x * ((n + 1 + 1) * u R (n + 1)) -
+          2 * (u R (n + 1 + 1) - X * u R (n + 1)) + 2 * X * ((n + 1 + 1) * u R (n + 1)) -
             (n + 1) * u R n :=
         by rw_mod_cast [T_derivative_eq_U, T_derivative_eq_U, T_eq_U_sub_X_mul_U]
-      _ = (n + 1) * (2 * x * u R (n + 1) - u R n) + 2 * u R (n + 2) := by ring
+      _ = (n + 1) * (2 * X * u R (n + 1) - u R n) + 2 * u R (n + 2) := by ring
       _ = (n + 1) * u R (n + 2) + 2 * u R (n + 2) := by rw [U_add_two]
       _ = (n + 2 + 1) * u R (n + 2) := by ring
       _ = (↑(n + 2) + 1) * u R (n + 2) := by norm_cast
@@ -228,19 +228,19 @@ theorem t_derivative_eq_u : ∀ n : ℕ, derivative (t R (n + 1)) = (n + 1) * u
 #align polynomial.chebyshev.T_derivative_eq_U Polynomial.Chebyshev.t_derivative_eq_u
 
 theorem one_sub_x_sq_mul_derivative_t_eq_poly_in_t (n : ℕ) :
-    (1 - x ^ 2) * derivative (t R (n + 1)) = (n + 1) * (t R n - x * t R (n + 1)) :=
+    (1 - X ^ 2) * derivative (t R (n + 1)) = (n + 1) * (t R n - X * t R (n + 1)) :=
   calc
-    (1 - x ^ 2) * derivative (t R (n + 1)) = (1 - x ^ 2) * ((n + 1) * u R n) := by
+    (1 - X ^ 2) * derivative (t R (n + 1)) = (1 - X ^ 2) * ((n + 1) * u R n) := by
       rw [T_derivative_eq_U]
-    _ = (n + 1) * ((1 - x ^ 2) * u R n) := by ring
-    _ = (n + 1) * (x * t R (n + 1) - (2 * x * t R (n + 1) - t R n)) := by
+    _ = (n + 1) * ((1 - X ^ 2) * u R n) := by ring
+    _ = (n + 1) * (X * t R (n + 1) - (2 * X * t R (n + 1) - t R n)) := by
       rw [one_sub_X_sq_mul_U_eq_pol_in_T, T_add_two]
-    _ = (n + 1) * (t R n - x * t R (n + 1)) := by ring
+    _ = (n + 1) * (t R n - X * t R (n + 1)) := by ring
     
 #align polynomial.chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T Polynomial.Chebyshev.one_sub_x_sq_mul_derivative_t_eq_poly_in_t
 
 theorem add_one_mul_t_eq_poly_in_u (n : ℕ) :
-    ((n : R[X]) + 1) * t R (n + 1) = x * u R n - (1 - x ^ 2) * derivative (u R n) :=
+    ((n : R[X]) + 1) * t R (n + 1) = X * u R n - (1 - X ^ 2) * derivative (u R n) :=
   by
   have h :
     derivative (T R (n + 2)) =

d7744511

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

d7744511

chore: Rename nat_cast/int_cast/rat_cast to natCast/intCast/ratCast (#11486)

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

145460b9

Diff

@@ -215,7 +215,7 @@ theorem add_one_mul_T_eq_poly_in_U (n : ℕ) :
     conv_lhs => rw [T_eq_X_mul_T_sub_pol_U]
     simp only [derivative_sub, derivative_mul, derivative_X, derivative_one, derivative_X_pow,
       one_mul, T_derivative_eq_U]
-    rw [T_eq_U_sub_X_mul_U, C_eq_nat_cast]
+    rw [T_eq_U_sub_X_mul_U, C_eq_natCast]
     ring
   calc
     ((n : R[X]) + 1) * T R (n + 1) =

d7744511

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

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

56e439ec

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Julian Kuelshammer, Heather Macbeth
 -/
-import Mathlib.Data.Polynomial.Derivative
+import Mathlib.Algebra.Polynomial.Derivative
 import Mathlib.Tactic.LinearCombination
 
 #align_import ring_theory.polynomial.chebyshev from "leanprover-community/mathlib"@"d774451114d6045faeb6751c396bea1eb9058946"

d7744511

chore: Rename mul-div cancellation lemmas (#11530)

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

4ea4a86a

Diff

@@ -133,7 +133,7 @@ theorem U_eq_X_mul_U_add_T : ∀ n : ℕ, U R (n + 1) = X * U R n + T R (n + 1)
 #align polynomial.chebyshev.U_eq_X_mul_U_add_T Polynomial.Chebyshev.U_eq_X_mul_U_add_T
 
 theorem T_eq_U_sub_X_mul_U (n : ℕ) : T R (n + 1) = U R (n + 1) - X * U R n := by
-  rw [U_eq_X_mul_U_add_T, add_comm (X * U R n), add_sub_cancel]
+  rw [U_eq_X_mul_U_add_T, add_comm (X * U R n), add_sub_cancel_right]
 #align polynomial.chebyshev.T_eq_U_sub_X_mul_U Polynomial.Chebyshev.T_eq_U_sub_X_mul_U
 
 theorem T_eq_X_mul_T_sub_pol_U : ∀ n : ℕ, T R (n + 2) = X * T R (n + 1) - (1 - X ^ 2) * U R n

d7744511

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

@@ -61,7 +61,7 @@ open Polynomial
 
 open Polynomial
 
-variable (R S : Type _) [CommRing R] [CommRing S]
+variable (R S : Type*) [CommRing R] [CommRing S]
 
 /-- `T n` is the `n`-th Chebyshev polynomial of the first kind -/
 noncomputable def T : ℕ → R[X]

d7744511

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Julian Kuelshammer, Heather Macbeth
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.chebyshev
-! leanprover-community/mathlib commit d774451114d6045faeb6751c396bea1eb9058946
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Polynomial.Derivative
 import Mathlib.Tactic.LinearCombination
 
+#align_import ring_theory.polynomial.chebyshev from "leanprover-community/mathlib"@"d774451114d6045faeb6751c396bea1eb9058946"
+
 /-!
 # Chebyshev polynomials

d7744511

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -187,11 +187,10 @@ theorem T_derivative_eq_U : ∀ n : ℕ, derivative (T R (n + 1)) = (n + 1) * U
   | n + 2 =>
     calc
       derivative (T R (n + 2 + 1)) =
-          2 * T R (n + 2) + 2 * X * derivative (T R (n + 1 + 1)) - derivative (T R (n + 1)) :=
-        by
-          rw [T_add_two _ (n + 1), derivative_sub, derivative_mul, derivative_mul, derivative_X,
-            derivative_ofNat]
-          ring_nf
+          2 * T R (n + 2) + 2 * X * derivative (T R (n + 1 + 1)) - derivative (T R (n + 1)) := by
+        rw [T_add_two _ (n + 1), derivative_sub, derivative_mul, derivative_mul, derivative_X,
+          derivative_ofNat]
+        ring_nf
       _ = 2 * (U R (n + 1 + 1) - X * U R (n + 1)) + 2 * X * (((n + 1 + 1) : R[X]) * U R (n + 1))
           - ((n + 1) : R[X]) * U R n := by
         rw_mod_cast [T_derivative_eq_U (n + 1), T_derivative_eq_U n, T_eq_U_sub_X_mul_U _ (n + 1)]
@@ -214,11 +213,8 @@ theorem one_sub_X_sq_mul_derivative_T_eq_poly_in_T (n : ℕ) :
 
 theorem add_one_mul_T_eq_poly_in_U (n : ℕ) :
     ((n : R[X]) + 1) * T R (n + 1) = X * U R n - (1 - X ^ 2) * derivative (U R n) := by
-  have h :
-    derivative (T R (n + 2)) =
-      U R (n + 1) - X * U R n + X * derivative (T R (n + 1)) + 2 * X * U R n -
-        (1 - X ^ 2) * derivative (U R n) :=
-    by
+  have h : derivative (T R (n + 2)) = U R (n + 1) - X * U R n + X * derivative (T R (n + 1)) +
+      2 * X * U R n - (1 - X ^ 2) * derivative (U R n) := by
     conv_lhs => rw [T_eq_X_mul_T_sub_pol_U]
     simp only [derivative_sub, derivative_mul, derivative_X, derivative_one, derivative_X_pow,
       one_mul, T_derivative_eq_U]

d7744511

feat: port RingTheory.Polynomial.Chebyshev (#2880)

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: int-y1 <jason_yuen2007@hotmail.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

8037968d

`ring_theory.polynomial.chebyshev` ⟷ `Mathlib.RingTheory.Polynomial.Chebyshev`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 396

ring_theory.polynomial.chebyshev ⟷ Mathlib.RingTheory.Polynomial.Chebyshev

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 396

`ring_theory.polynomial.chebyshev` ⟷ `Mathlib.RingTheory.Polynomial.Chebyshev`