analysis.special_functions.trigonometric.chebyshev ⟷ Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev

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

@@ -5,7 +5,7 @@ Authors: Johan Commelin
 -/
 import Data.Complex.Exponential
 import Data.Complex.Module
-import Data.Polynomial.AlgebraMap
+import Algebra.Polynomial.AlgebraMap
 import RingTheory.Polynomial.Chebyshev
 
 #align_import analysis.special_functions.trigonometric.chebyshev from "leanprover-community/mathlib"@"fe8d0ff42c3c24d789f491dc2622b6cac3d61564"

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

@@ -3,10 +3,10 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathbin.Data.Complex.Exponential
-import Mathbin.Data.Complex.Module
-import Mathbin.Data.Polynomial.AlgebraMap
-import Mathbin.RingTheory.Polynomial.Chebyshev
+import Data.Complex.Exponential
+import Data.Complex.Module
+import Data.Polynomial.AlgebraMap
+import RingTheory.Polynomial.Chebyshev
 
 #align_import analysis.special_functions.trigonometric.chebyshev from "leanprover-community/mathlib"@"fe8d0ff42c3c24d789f491dc2622b6cac3d61564"
 

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.chebyshev
-! leanprover-community/mathlib commit fe8d0ff42c3c24d789f491dc2622b6cac3d61564
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Complex.Exponential
 import Mathbin.Data.Complex.Module
 import Mathbin.Data.Polynomial.AlgebraMap
 import Mathbin.RingTheory.Polynomial.Chebyshev
 
+#align_import analysis.special_functions.trigonometric.chebyshev from "leanprover-community/mathlib"@"fe8d0ff42c3c24d789f491dc2622b6cac3d61564"
+
 /-!
 # Multiple angle formulas in terms of Chebyshev polynomials
 

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

@@ -30,37 +30,49 @@ open Polynomial
 
 variable {R A : Type _} [CommRing R] [CommRing A] [Algebra R A]
 
+#print Polynomial.Chebyshev.aeval_T /-
 @[simp]
 theorem aeval_T (x : A) (n : ℕ) : aeval x (T R n) = (T A n).eval x := by
   rw [aeval_def, eval₂_eq_eval_map, map_T]
 #align polynomial.chebyshev.aeval_T Polynomial.Chebyshev.aeval_T
+-/
 
+#print Polynomial.Chebyshev.aeval_U /-
 @[simp]
 theorem aeval_U (x : A) (n : ℕ) : aeval x (U R n) = (U A n).eval x := by
   rw [aeval_def, eval₂_eq_eval_map, map_U]
 #align polynomial.chebyshev.aeval_U Polynomial.Chebyshev.aeval_U
+-/
 
+#print Polynomial.Chebyshev.algebraMap_eval_T /-
 @[simp]
 theorem algebraMap_eval_T (x : R) (n : ℕ) :
     algebraMap R A ((T R n).eval x) = (T A n).eval (algebraMap R A x) := by
   rw [← aeval_algebra_map_apply_eq_algebra_map_eval, aeval_T]
 #align polynomial.chebyshev.algebra_map_eval_T Polynomial.Chebyshev.algebraMap_eval_T
+-/
 
+#print Polynomial.Chebyshev.algebraMap_eval_U /-
 @[simp]
 theorem algebraMap_eval_U (x : R) (n : ℕ) :
     algebraMap R A ((U R n).eval x) = (U A n).eval (algebraMap R A x) := by
   rw [← aeval_algebra_map_apply_eq_algebra_map_eval, aeval_U]
 #align polynomial.chebyshev.algebra_map_eval_U Polynomial.Chebyshev.algebraMap_eval_U
+-/
 
+#print Polynomial.Chebyshev.complex_ofReal_eval_T /-
 @[simp, norm_cast]
 theorem complex_ofReal_eval_T : ∀ x n, ((T ℝ n).eval x : ℂ) = (T ℂ n).eval x :=
   @algebraMap_eval_T ℝ ℂ _ _ _
 #align polynomial.chebyshev.complex_of_real_eval_T Polynomial.Chebyshev.complex_ofReal_eval_T
+-/
 
+#print Polynomial.Chebyshev.complex_ofReal_eval_U /-
 @[simp, norm_cast]
 theorem complex_ofReal_eval_U : ∀ x n, ((U ℝ n).eval x : ℂ) = (U ℂ n).eval x :=
   @algebraMap_eval_U ℝ ℂ _ _ _
 #align polynomial.chebyshev.complex_of_real_eval_U Polynomial.Chebyshev.complex_ofReal_eval_U
+-/
 
 /-! ### Complex versions -/
 
@@ -88,6 +100,7 @@ theorem T_complex_cos : ∀ n, (T ℂ n).eval (cos θ) = cos (n * θ)
 #align polynomial.chebyshev.T_complex_cos Polynomial.Chebyshev.T_complex_cos
 -/
 
+#print Polynomial.Chebyshev.U_complex_cos /-
 /-- The `n`-th Chebyshev polynomial of the second kind evaluates on `cos θ` to the
 value `sin ((n + 1) * θ) / sin θ`. -/
 @[simp]
@@ -101,6 +114,7 @@ theorem U_complex_cos (n : ℕ) : (U ℂ n).eval (cos θ) * sin θ = sin ((n + 1
     push_cast
     simp only [add_mul, one_mul]
 #align polynomial.chebyshev.U_complex_cos Polynomial.Chebyshev.U_complex_cos
+-/
 
 end Complex
 
@@ -119,12 +133,14 @@ theorem T_real_cos : (T ℝ n).eval (cos θ) = cos (n * θ) := by exact_mod_cast
 #align polynomial.chebyshev.T_real_cos Polynomial.Chebyshev.T_real_cos
 -/
 
+#print Polynomial.Chebyshev.U_real_cos /-
 /-- The `n`-th Chebyshev polynomial of the second kind evaluates on `cos θ` to the
 value `sin ((n + 1) * θ) / sin θ`. -/
 @[simp]
 theorem U_real_cos : (U ℝ n).eval (cos θ) * sin θ = sin ((n + 1) * θ) := by
   exact_mod_cast U_complex_cos θ n
 #align polynomial.chebyshev.U_real_cos Polynomial.Chebyshev.U_real_cos
+-/
 
 end Real
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -53,14 +53,14 @@ theorem algebraMap_eval_U (x : R) (n : ℕ) :
 #align polynomial.chebyshev.algebra_map_eval_U Polynomial.Chebyshev.algebraMap_eval_U
 
 @[simp, norm_cast]
-theorem complex_of_real_eval_T : ∀ x n, ((T ℝ n).eval x : ℂ) = (T ℂ n).eval x :=
+theorem complex_ofReal_eval_T : ∀ x n, ((T ℝ n).eval x : ℂ) = (T ℂ n).eval x :=
   @algebraMap_eval_T ℝ ℂ _ _ _
-#align polynomial.chebyshev.complex_of_real_eval_T Polynomial.Chebyshev.complex_of_real_eval_T
+#align polynomial.chebyshev.complex_of_real_eval_T Polynomial.Chebyshev.complex_ofReal_eval_T
 
 @[simp, norm_cast]
-theorem complex_of_real_eval_U : ∀ x n, ((U ℝ n).eval x : ℂ) = (U ℂ n).eval x :=
+theorem complex_ofReal_eval_U : ∀ x n, ((U ℝ n).eval x : ℂ) = (U ℂ n).eval x :=
   @algebraMap_eval_U ℝ ℂ _ _ _
-#align polynomial.chebyshev.complex_of_real_eval_U Polynomial.Chebyshev.complex_of_real_eval_U
+#align polynomial.chebyshev.complex_of_real_eval_U Polynomial.Chebyshev.complex_ofReal_eval_U
 
 /-! ### Complex versions -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -30,19 +30,15 @@ open Polynomial
 
 variable {R A : Type _} [CommRing R] [CommRing A] [Algebra R A]
 
-#print Polynomial.Chebyshev.aeval_T /-
 @[simp]
 theorem aeval_T (x : A) (n : ℕ) : aeval x (T R n) = (T A n).eval x := by
   rw [aeval_def, eval₂_eq_eval_map, map_T]
 #align polynomial.chebyshev.aeval_T Polynomial.Chebyshev.aeval_T
--/
 
-#print Polynomial.Chebyshev.aeval_U /-
 @[simp]
 theorem aeval_U (x : A) (n : ℕ) : aeval x (U R n) = (U A n).eval x := by
   rw [aeval_def, eval₂_eq_eval_map, map_U]
 #align polynomial.chebyshev.aeval_U Polynomial.Chebyshev.aeval_U
--/
 
 @[simp]
 theorem algebraMap_eval_T (x : R) (n : ℕ) :

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

@@ -44,47 +44,23 @@ theorem aeval_U (x : A) (n : ℕ) : aeval x (U R n) = (U A n).eval x := by
 #align polynomial.chebyshev.aeval_U Polynomial.Chebyshev.aeval_U
 -/
 
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 @[simp]
 theorem algebraMap_eval_T (x : R) (n : ℕ) :
     algebraMap R A ((T R n).eval x) = (T A n).eval (algebraMap R A x) := by
   rw [← aeval_algebra_map_apply_eq_algebra_map_eval, aeval_T]
 #align polynomial.chebyshev.algebra_map_eval_T Polynomial.Chebyshev.algebraMap_eval_T
 
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 @[simp]
 theorem algebraMap_eval_U (x : R) (n : ℕ) :
     algebraMap R A ((U R n).eval x) = (U A n).eval (algebraMap R A x) := by
   rw [← aeval_algebra_map_apply_eq_algebra_map_eval, aeval_U]
 #align polynomial.chebyshev.algebra_map_eval_U Polynomial.Chebyshev.algebraMap_eval_U
 
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 @[simp, norm_cast]
 theorem complex_of_real_eval_T : ∀ x n, ((T ℝ n).eval x : ℂ) = (T ℂ n).eval x :=
   @algebraMap_eval_T ℝ ℂ _ _ _
 #align polynomial.chebyshev.complex_of_real_eval_T Polynomial.Chebyshev.complex_of_real_eval_T
 
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 @[simp, norm_cast]
 theorem complex_of_real_eval_U : ∀ x n, ((U ℝ n).eval x : ℂ) = (U ℂ n).eval x :=
   @algebraMap_eval_U ℝ ℂ _ _ _
@@ -116,12 +92,6 @@ theorem T_complex_cos : ∀ n, (T ℂ n).eval (cos θ) = cos (n * θ)
 #align polynomial.chebyshev.T_complex_cos Polynomial.Chebyshev.T_complex_cos
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.U_complex_cos Polynomial.Chebyshev.U_complex_cosₓ'. -/
 /-- The `n`-th Chebyshev polynomial of the second kind evaluates on `cos θ` to the
 value `sin ((n + 1) * θ) / sin θ`. -/
 @[simp]
@@ -153,12 +123,6 @@ theorem T_real_cos : (T ℝ n).eval (cos θ) = cos (n * θ) := by exact_mod_cast
 #align polynomial.chebyshev.T_real_cos Polynomial.Chebyshev.T_real_cos
 -/
 
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 /-- The `n`-th Chebyshev polynomial of the second kind evaluates on `cos θ` to the
 value `sin ((n + 1) * θ) / sin θ`. -/
 @[simp]

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

@@ -110,10 +110,7 @@ theorem T_complex_cos : ∀ n, (T ℂ n).eval (cos θ) = cos (n * θ)
     by
     simp only [eval_X, eval_one, T_add_two, eval_sub, eval_bit0, Nat.cast_succ, eval_mul]
     rw [T_complex_cos (n + 1), T_complex_cos n]
-    have aux : sin θ * sin θ = 1 - cos θ * cos θ :=
-      by
-      rw [← sin_sq_add_cos_sq θ]
-      ring
+    have aux : sin θ * sin θ = 1 - cos θ * cos θ := by rw [← sin_sq_add_cos_sq θ]; ring
     simp only [Nat.cast_add, Nat.cast_one, add_mul, cos_add, one_mul, sin_add, mul_assoc, aux]
     ring
 #align polynomial.chebyshev.T_complex_cos Polynomial.Chebyshev.T_complex_cos

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -48,7 +48,7 @@ theorem aeval_U (x : A) (n : ℕ) : aeval x (U R n) = (U A n).eval x := by
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x (Polynomial.Chebyshev.T.{u1} R _inst_1 n))) (Polynomial.eval.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.T.{u2} A _inst_2 n))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x (Polynomial.Chebyshev.T.{u1} R _inst_1 n))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x (Polynomial.Chebyshev.T.{u1} R _inst_1 n))) (Polynomial.eval.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.T.{u2} A _inst_2 n))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x (Polynomial.Chebyshev.T.{u1} R _inst_1 n))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x (Polynomial.Chebyshev.T.{u1} R _inst_1 n))) (Polynomial.eval.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) x) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.T.{u2} A _inst_2 n))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.algebra_map_eval_T Polynomial.Chebyshev.algebraMap_eval_Tₓ'. -/
 @[simp]
 theorem algebraMap_eval_T (x : R) (n : ℕ) :
@@ -60,7 +60,7 @@ theorem algebraMap_eval_T (x : R) (n : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x (Polynomial.Chebyshev.U.{u1} R _inst_1 n))) (Polynomial.eval.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.U.{u2} A _inst_2 n))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x (Polynomial.Chebyshev.U.{u1} R _inst_1 n))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x (Polynomial.Chebyshev.U.{u1} R _inst_1 n))) (Polynomial.eval.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.U.{u2} A _inst_2 n))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x (Polynomial.Chebyshev.U.{u1} R _inst_1 n))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x (Polynomial.Chebyshev.U.{u1} R _inst_1 n))) (Polynomial.eval.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) x) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.U.{u2} A _inst_2 n))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.algebra_map_eval_U Polynomial.Chebyshev.algebraMap_eval_Uₓ'. -/
 @[simp]
 theorem algebraMap_eval_U (x : R) (n : ℕ) :

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

@@ -48,7 +48,7 @@ theorem aeval_U (x : A) (n : ℕ) : aeval x (U R n) = (U A n).eval x := by
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x (Polynomial.Chebyshev.T.{u1} R _inst_1 n))) (Polynomial.eval.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.T.{u2} A _inst_2 n))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x (Polynomial.Chebyshev.T.{u1} R _inst_1 n))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x (Polynomial.Chebyshev.T.{u1} R _inst_1 n))) (Polynomial.eval.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.T.{u2} A _inst_2 n))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x (Polynomial.Chebyshev.T.{u1} R _inst_1 n))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x (Polynomial.Chebyshev.T.{u1} R _inst_1 n))) (Polynomial.eval.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.T.{u2} A _inst_2 n))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.algebra_map_eval_T Polynomial.Chebyshev.algebraMap_eval_Tₓ'. -/
 @[simp]
 theorem algebraMap_eval_T (x : R) (n : ℕ) :
@@ -60,7 +60,7 @@ theorem algebraMap_eval_T (x : R) (n : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x (Polynomial.Chebyshev.U.{u1} R _inst_1 n))) (Polynomial.eval.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.U.{u2} A _inst_2 n))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x (Polynomial.Chebyshev.U.{u1} R _inst_1 n))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x (Polynomial.Chebyshev.U.{u1} R _inst_1 n))) (Polynomial.eval.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.U.{u2} A _inst_2 n))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x (Polynomial.Chebyshev.U.{u1} R _inst_1 n))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x (Polynomial.Chebyshev.U.{u1} R _inst_1 n))) (Polynomial.eval.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.U.{u2} A _inst_2 n))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.algebra_map_eval_U Polynomial.Chebyshev.algebraMap_eval_Uₓ'. -/
 @[simp]
 theorem algebraMap_eval_U (x : R) (n : ℕ) :
@@ -72,7 +72,7 @@ theorem algebraMap_eval_U (x : R) (n : ℕ) :
 lean 3 declaration is
   forall (x : Real) (n : Nat), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Polynomial.eval.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) x (Polynomial.Chebyshev.T.{0} Real Real.commRing n))) (Polynomial.eval.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex Complex.commRing)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) (Polynomial.Chebyshev.T.{0} Complex Complex.commRing n))
 but is expected to have type
-  forall (x : Real) (n : Nat), Eq.{1} Complex (Complex.ofReal' (Polynomial.eval.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) x (Polynomial.Chebyshev.T.{0} Real Real.commRing n))) (Polynomial.eval.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex Complex.commRing)) (Complex.ofReal' x) (Polynomial.Chebyshev.T.{0} Complex Complex.commRing n))
+  forall (x : Real) (n : Nat), Eq.{1} Complex (Complex.ofReal' (Polynomial.eval.{0} Real (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing)) x (Polynomial.Chebyshev.T.{0} Real Real.commRing n))) (Polynomial.eval.{0} Complex (CommSemiring.toSemiring.{0} Complex (CommRing.toCommSemiring.{0} Complex Complex.commRing)) (Complex.ofReal' x) (Polynomial.Chebyshev.T.{0} Complex Complex.commRing n))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.complex_of_real_eval_T Polynomial.Chebyshev.complex_of_real_eval_Tₓ'. -/
 @[simp, norm_cast]
 theorem complex_of_real_eval_T : ∀ x n, ((T ℝ n).eval x : ℂ) = (T ℂ n).eval x :=
@@ -83,7 +83,7 @@ theorem complex_of_real_eval_T : ∀ x n, ((T ℝ n).eval x : ℂ) = (T ℂ n).e
 lean 3 declaration is
   forall (x : Real) (n : Nat), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Polynomial.eval.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) x (Polynomial.Chebyshev.U.{0} Real Real.commRing n))) (Polynomial.eval.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex Complex.commRing)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) (Polynomial.Chebyshev.U.{0} Complex Complex.commRing n))
 but is expected to have type
-  forall (x : Real) (n : Nat), Eq.{1} Complex (Complex.ofReal' (Polynomial.eval.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) x (Polynomial.Chebyshev.U.{0} Real Real.commRing n))) (Polynomial.eval.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex Complex.commRing)) (Complex.ofReal' x) (Polynomial.Chebyshev.U.{0} Complex Complex.commRing n))
+  forall (x : Real) (n : Nat), Eq.{1} Complex (Complex.ofReal' (Polynomial.eval.{0} Real (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing)) x (Polynomial.Chebyshev.U.{0} Real Real.commRing n))) (Polynomial.eval.{0} Complex (CommSemiring.toSemiring.{0} Complex (CommRing.toCommSemiring.{0} Complex Complex.commRing)) (Complex.ofReal' x) (Polynomial.Chebyshev.U.{0} Complex Complex.commRing n))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.complex_of_real_eval_U Polynomial.Chebyshev.complex_of_real_eval_Uₓ'. -/
 @[simp, norm_cast]
 theorem complex_of_real_eval_U : ∀ x n, ((U ℝ n).eval x : ℂ) = (U ℂ n).eval x :=
@@ -123,7 +123,7 @@ theorem T_complex_cos : ∀ n, (T ℂ n).eval (cos θ) = cos (n * θ)
 lean 3 declaration is
   forall (θ : Complex) (n : Nat), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (Polynomial.eval.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex Complex.commRing)) (Complex.cos θ) (Polynomial.Chebyshev.U.{0} Complex Complex.commRing n)) (Complex.sin θ)) (Complex.sin (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) θ))
 but is expected to have type
-  forall (θ : Complex) (n : Nat), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Polynomial.eval.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex Complex.commRing)) (Complex.cos θ) (Polynomial.Chebyshev.U.{0} Complex Complex.commRing n)) (Complex.sin θ)) (Complex.sin (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) θ))
+  forall (θ : Complex) (n : Nat), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Polynomial.eval.{0} Complex (CommSemiring.toSemiring.{0} Complex (CommRing.toCommSemiring.{0} Complex Complex.commRing)) (Complex.cos θ) (Polynomial.Chebyshev.U.{0} Complex Complex.commRing n)) (Complex.sin θ)) (Complex.sin (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Nat.cast.{0} Complex (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) n) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) θ))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.U_complex_cos Polynomial.Chebyshev.U_complex_cosₓ'. -/
 /-- The `n`-th Chebyshev polynomial of the second kind evaluates on `cos θ` to the
 value `sin ((n + 1) * θ) / sin θ`. -/
@@ -160,7 +160,7 @@ theorem T_real_cos : (T ℝ n).eval (cos θ) = cos (n * θ) := by exact_mod_cast
 lean 3 declaration is
   forall (θ : Real) (n : Nat), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Polynomial.eval.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Real.cos θ) (Polynomial.Chebyshev.U.{0} Real Real.commRing n)) (Real.sin θ)) (Real.sin (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) θ))
 but is expected to have type
-  forall (θ : Real) (n : Nat), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Polynomial.eval.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Real.cos θ) (Polynomial.Chebyshev.U.{0} Real Real.commRing n)) (Real.sin θ)) (Real.sin (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Nat.cast.{0} Real Real.natCast n) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) θ))
+  forall (θ : Real) (n : Nat), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Polynomial.eval.{0} Real (CommSemiring.toSemiring.{0} Real (CommRing.toCommSemiring.{0} Real Real.commRing)) (Real.cos θ) (Polynomial.Chebyshev.U.{0} Real Real.commRing n)) (Real.sin θ)) (Real.sin (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Nat.cast.{0} Real Real.natCast n) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) θ))
 Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.U_real_cos Polynomial.Chebyshev.U_real_cosₓ'. -/
 /-- The `n`-th Chebyshev polynomial of the second kind evaluates on `cos θ` to the
 value `sin ((n + 1) * θ) / sin θ`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.chebyshev
-! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
+! leanprover-community/mathlib commit fe8d0ff42c3c24d789f491dc2622b6cac3d61564
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.RingTheory.Polynomial.Chebyshev
 /-!
 # Multiple angle formulas in terms of Chebyshev polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file gives the trigonometric characterizations of Chebyshev polynomials, for both the real
 (`real.cos`) and complex (`complex.cos`) cosine.
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -27,37 +27,65 @@ open Polynomial
 
 variable {R A : Type _} [CommRing R] [CommRing A] [Algebra R A]
 
+#print Polynomial.Chebyshev.aeval_T /-
 @[simp]
-theorem aeval_t (x : A) (n : ℕ) : aeval x (T R n) = (T A n).eval x := by
+theorem aeval_T (x : A) (n : ℕ) : aeval x (T R n) = (T A n).eval x := by
   rw [aeval_def, eval₂_eq_eval_map, map_T]
-#align polynomial.chebyshev.aeval_T Polynomial.Chebyshev.aeval_t
+#align polynomial.chebyshev.aeval_T Polynomial.Chebyshev.aeval_T
+-/
 
+#print Polynomial.Chebyshev.aeval_U /-
 @[simp]
-theorem aeval_u (x : A) (n : ℕ) : aeval x (U R n) = (U A n).eval x := by
+theorem aeval_U (x : A) (n : ℕ) : aeval x (U R n) = (U A n).eval x := by
   rw [aeval_def, eval₂_eq_eval_map, map_U]
-#align polynomial.chebyshev.aeval_U Polynomial.Chebyshev.aeval_u
+#align polynomial.chebyshev.aeval_U Polynomial.Chebyshev.aeval_U
+-/
 
+/- warning: polynomial.chebyshev.algebra_map_eval_T -> Polynomial.Chebyshev.algebraMap_eval_T is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x (Polynomial.Chebyshev.T.{u1} R _inst_1 n))) (Polynomial.eval.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.T.{u2} A _inst_2 n))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x (Polynomial.Chebyshev.T.{u1} R _inst_1 n))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.T.{u2} A _inst_2 n))
+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.algebra_map_eval_T Polynomial.Chebyshev.algebraMap_eval_Tₓ'. -/
 @[simp]
-theorem algebraMap_eval_t (x : R) (n : ℕ) :
+theorem algebraMap_eval_T (x : R) (n : ℕ) :
     algebraMap R A ((T R n).eval x) = (T A n).eval (algebraMap R A x) := by
   rw [← aeval_algebra_map_apply_eq_algebra_map_eval, aeval_T]
-#align polynomial.chebyshev.algebra_map_eval_T Polynomial.Chebyshev.algebraMap_eval_t
-
+#align polynomial.chebyshev.algebra_map_eval_T Polynomial.Chebyshev.algebraMap_eval_T
+
+/- warning: polynomial.chebyshev.algebra_map_eval_U -> Polynomial.Chebyshev.algebraMap_eval_U is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x (Polynomial.Chebyshev.U.{u1} R _inst_1 n))) (Polynomial.eval.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.U.{u2} A _inst_2 n))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] (x : R) (n : Nat), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x (Polynomial.Chebyshev.U.{u1} R _inst_1 n))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) x) (Polynomial.Chebyshev.U.{u2} A _inst_2 n))
+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.algebra_map_eval_U Polynomial.Chebyshev.algebraMap_eval_Uₓ'. -/
 @[simp]
-theorem algebraMap_eval_u (x : R) (n : ℕ) :
+theorem algebraMap_eval_U (x : R) (n : ℕ) :
     algebraMap R A ((U R n).eval x) = (U A n).eval (algebraMap R A x) := by
   rw [← aeval_algebra_map_apply_eq_algebra_map_eval, aeval_U]
-#align polynomial.chebyshev.algebra_map_eval_U Polynomial.Chebyshev.algebraMap_eval_u
-
+#align polynomial.chebyshev.algebra_map_eval_U Polynomial.Chebyshev.algebraMap_eval_U
+
+/- warning: polynomial.chebyshev.complex_of_real_eval_T -> Polynomial.Chebyshev.complex_of_real_eval_T is a dubious translation:
+lean 3 declaration is
+  forall (x : Real) (n : Nat), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Polynomial.eval.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) x (Polynomial.Chebyshev.T.{0} Real Real.commRing n))) (Polynomial.eval.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex Complex.commRing)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) (Polynomial.Chebyshev.T.{0} Complex Complex.commRing n))
+but is expected to have type
+  forall (x : Real) (n : Nat), Eq.{1} Complex (Complex.ofReal' (Polynomial.eval.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) x (Polynomial.Chebyshev.T.{0} Real Real.commRing n))) (Polynomial.eval.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex Complex.commRing)) (Complex.ofReal' x) (Polynomial.Chebyshev.T.{0} Complex Complex.commRing n))
+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.complex_of_real_eval_T Polynomial.Chebyshev.complex_of_real_eval_Tₓ'. -/
 @[simp, norm_cast]
-theorem complex_of_real_eval_t : ∀ x n, ((T ℝ n).eval x : ℂ) = (T ℂ n).eval x :=
-  @algebraMap_eval_t ℝ ℂ _ _ _
-#align polynomial.chebyshev.complex_of_real_eval_T Polynomial.Chebyshev.complex_of_real_eval_t
-
+theorem complex_of_real_eval_T : ∀ x n, ((T ℝ n).eval x : ℂ) = (T ℂ n).eval x :=
+  @algebraMap_eval_T ℝ ℂ _ _ _
+#align polynomial.chebyshev.complex_of_real_eval_T Polynomial.Chebyshev.complex_of_real_eval_T
+
+/- warning: polynomial.chebyshev.complex_of_real_eval_U -> Polynomial.Chebyshev.complex_of_real_eval_U is a dubious translation:
+lean 3 declaration is
+  forall (x : Real) (n : Nat), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Polynomial.eval.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) x (Polynomial.Chebyshev.U.{0} Real Real.commRing n))) (Polynomial.eval.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex Complex.commRing)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) (Polynomial.Chebyshev.U.{0} Complex Complex.commRing n))
+but is expected to have type
+  forall (x : Real) (n : Nat), Eq.{1} Complex (Complex.ofReal' (Polynomial.eval.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) x (Polynomial.Chebyshev.U.{0} Real Real.commRing n))) (Polynomial.eval.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex Complex.commRing)) (Complex.ofReal' x) (Polynomial.Chebyshev.U.{0} Complex Complex.commRing n))
+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.complex_of_real_eval_U Polynomial.Chebyshev.complex_of_real_eval_Uₓ'. -/
 @[simp, norm_cast]
-theorem complex_of_real_eval_u : ∀ x n, ((U ℝ n).eval x : ℂ) = (U ℂ n).eval x :=
-  @algebraMap_eval_u ℝ ℂ _ _ _
-#align polynomial.chebyshev.complex_of_real_eval_U Polynomial.Chebyshev.complex_of_real_eval_u
+theorem complex_of_real_eval_U : ∀ x n, ((U ℝ n).eval x : ℂ) = (U ℂ n).eval x :=
+  @algebraMap_eval_U ℝ ℂ _ _ _
+#align polynomial.chebyshev.complex_of_real_eval_U Polynomial.Chebyshev.complex_of_real_eval_U
 
 /-! ### Complex versions -/
 
@@ -68,10 +96,11 @@ open Complex
 
 variable (θ : ℂ)
 
+#print Polynomial.Chebyshev.T_complex_cos /-
 /-- The `n`-th Chebyshev polynomial of the first kind evaluates on `cos θ` to the
 value `cos (n * θ)`. -/
 @[simp]
-theorem t_complex_cos : ∀ n, (T ℂ n).eval (cos θ) = cos (n * θ)
+theorem T_complex_cos : ∀ n, (T ℂ n).eval (cos θ) = cos (n * θ)
   | 0 => by simp only [T_zero, eval_one, Nat.cast_zero, MulZeroClass.zero_mul, cos_zero]
   | 1 => by simp only [eval_X, one_mul, T_one, Nat.cast_one]
   | n + 2 =>
@@ -84,12 +113,19 @@ theorem t_complex_cos : ∀ n, (T ℂ n).eval (cos θ) = cos (n * θ)
       ring
     simp only [Nat.cast_add, Nat.cast_one, add_mul, cos_add, one_mul, sin_add, mul_assoc, aux]
     ring
-#align polynomial.chebyshev.T_complex_cos Polynomial.Chebyshev.t_complex_cos
+#align polynomial.chebyshev.T_complex_cos Polynomial.Chebyshev.T_complex_cos
+-/
 
+/- warning: polynomial.chebyshev.U_complex_cos -> Polynomial.Chebyshev.U_complex_cos is a dubious translation:
+lean 3 declaration is
+  forall (θ : Complex) (n : Nat), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (Polynomial.eval.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex Complex.commRing)) (Complex.cos θ) (Polynomial.Chebyshev.U.{0} Complex Complex.commRing n)) (Complex.sin θ)) (Complex.sin (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) θ))
+but is expected to have type
+  forall (θ : Complex) (n : Nat), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Polynomial.eval.{0} Complex (Ring.toSemiring.{0} Complex (CommRing.toRing.{0} Complex Complex.commRing)) (Complex.cos θ) (Polynomial.Chebyshev.U.{0} Complex Complex.commRing n)) (Complex.sin θ)) (Complex.sin (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) θ))
+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.U_complex_cos Polynomial.Chebyshev.U_complex_cosₓ'. -/
 /-- The `n`-th Chebyshev polynomial of the second kind evaluates on `cos θ` to the
 value `sin ((n + 1) * θ) / sin θ`. -/
 @[simp]
-theorem u_complex_cos (n : ℕ) : (U ℂ n).eval (cos θ) * sin θ = sin ((n + 1) * θ) :=
+theorem U_complex_cos (n : ℕ) : (U ℂ n).eval (cos θ) * sin θ = sin ((n + 1) * θ) :=
   by
   induction' n with d hd
   · simp only [U_zero, Nat.cast_zero, eval_one, mul_one, zero_add, one_mul]
@@ -98,7 +134,7 @@ theorem u_complex_cos (n : ℕ) : (U ℂ n).eval (cos θ) * sin θ = sin ((n + 1
     conv_rhs => rw [sin_add, mul_comm]
     push_cast
     simp only [add_mul, one_mul]
-#align polynomial.chebyshev.U_complex_cos Polynomial.Chebyshev.u_complex_cos
+#align polynomial.chebyshev.U_complex_cos Polynomial.Chebyshev.U_complex_cos
 
 end Complex
 
@@ -109,18 +145,26 @@ open Real
 
 variable (θ : ℝ) (n : ℕ)
 
+#print Polynomial.Chebyshev.T_real_cos /-
 /-- The `n`-th Chebyshev polynomial of the first kind evaluates on `cos θ` to the
 value `cos (n * θ)`. -/
 @[simp]
-theorem t_real_cos : (T ℝ n).eval (cos θ) = cos (n * θ) := by exact_mod_cast T_complex_cos θ n
-#align polynomial.chebyshev.T_real_cos Polynomial.Chebyshev.t_real_cos
+theorem T_real_cos : (T ℝ n).eval (cos θ) = cos (n * θ) := by exact_mod_cast T_complex_cos θ n
+#align polynomial.chebyshev.T_real_cos Polynomial.Chebyshev.T_real_cos
+-/
 
+/- warning: polynomial.chebyshev.U_real_cos -> Polynomial.Chebyshev.U_real_cos is a dubious translation:
+lean 3 declaration is
+  forall (θ : Real) (n : Nat), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Polynomial.eval.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Real.cos θ) (Polynomial.Chebyshev.U.{0} Real Real.commRing n)) (Real.sin θ)) (Real.sin (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) θ))
+but is expected to have type
+  forall (θ : Real) (n : Nat), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Polynomial.eval.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)) (Real.cos θ) (Polynomial.Chebyshev.U.{0} Real Real.commRing n)) (Real.sin θ)) (Real.sin (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Nat.cast.{0} Real Real.natCast n) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) θ))
+Case conversion may be inaccurate. Consider using '#align polynomial.chebyshev.U_real_cos Polynomial.Chebyshev.U_real_cosₓ'. -/
 /-- The `n`-th Chebyshev polynomial of the second kind evaluates on `cos θ` to the
 value `sin ((n + 1) * θ) / sin θ`. -/
 @[simp]
-theorem u_real_cos : (U ℝ n).eval (cos θ) * sin θ = sin ((n + 1) * θ) := by
+theorem U_real_cos : (U ℝ n).eval (cos θ) * sin θ = sin ((n + 1) * θ) := by
   exact_mod_cast U_complex_cos θ n
-#align polynomial.chebyshev.U_real_cos Polynomial.Chebyshev.u_real_cos
+#align polynomial.chebyshev.U_real_cos Polynomial.Chebyshev.U_real_cos
 
 end Real
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.chebyshev
-! leanprover-community/mathlib commit 7aebb349fbbbf07c1b6e3867451b354730dc7799
+! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Analysis.Complex.Basic
 import Mathbin.Data.Complex.Exponential
+import Mathbin.Data.Complex.Module
 import Mathbin.Data.Polynomial.AlgebraMap
 import Mathbin.RingTheory.Polynomial.Chebyshev
 

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

@@ -28,34 +28,34 @@ open Polynomial
 variable {R A : Type _} [CommRing R] [CommRing A] [Algebra R A]
 
 @[simp]
-theorem aeval_t (x : A) (n : ℕ) : aeval x (t R n) = (t A n).eval x := by
+theorem aeval_t (x : A) (n : ℕ) : aeval x (T R n) = (T A n).eval x := by
   rw [aeval_def, eval₂_eq_eval_map, map_T]
 #align polynomial.chebyshev.aeval_T Polynomial.Chebyshev.aeval_t
 
 @[simp]
-theorem aeval_u (x : A) (n : ℕ) : aeval x (u R n) = (u A n).eval x := by
+theorem aeval_u (x : A) (n : ℕ) : aeval x (U R n) = (U A n).eval x := by
   rw [aeval_def, eval₂_eq_eval_map, map_U]
 #align polynomial.chebyshev.aeval_U Polynomial.Chebyshev.aeval_u
 
 @[simp]
 theorem algebraMap_eval_t (x : R) (n : ℕ) :
-    algebraMap R A ((t R n).eval x) = (t A n).eval (algebraMap R A x) := by
+    algebraMap R A ((T R n).eval x) = (T A n).eval (algebraMap R A x) := by
   rw [← aeval_algebra_map_apply_eq_algebra_map_eval, aeval_T]
 #align polynomial.chebyshev.algebra_map_eval_T Polynomial.Chebyshev.algebraMap_eval_t
 
 @[simp]
 theorem algebraMap_eval_u (x : R) (n : ℕ) :
-    algebraMap R A ((u R n).eval x) = (u A n).eval (algebraMap R A x) := by
+    algebraMap R A ((U R n).eval x) = (U A n).eval (algebraMap R A x) := by
   rw [← aeval_algebra_map_apply_eq_algebra_map_eval, aeval_U]
 #align polynomial.chebyshev.algebra_map_eval_U Polynomial.Chebyshev.algebraMap_eval_u
 
 @[simp, norm_cast]
-theorem complex_of_real_eval_t : ∀ x n, ((t ℝ n).eval x : ℂ) = (t ℂ n).eval x :=
+theorem complex_of_real_eval_t : ∀ x n, ((T ℝ n).eval x : ℂ) = (T ℂ n).eval x :=
   @algebraMap_eval_t ℝ ℂ _ _ _
 #align polynomial.chebyshev.complex_of_real_eval_T Polynomial.Chebyshev.complex_of_real_eval_t
 
 @[simp, norm_cast]
-theorem complex_of_real_eval_u : ∀ x n, ((u ℝ n).eval x : ℂ) = (u ℂ n).eval x :=
+theorem complex_of_real_eval_u : ∀ x n, ((U ℝ n).eval x : ℂ) = (U ℂ n).eval x :=
   @algebraMap_eval_u ℝ ℂ _ _ _
 #align polynomial.chebyshev.complex_of_real_eval_U Polynomial.Chebyshev.complex_of_real_eval_u
 
@@ -71,7 +71,7 @@ variable (θ : ℂ)
 /-- The `n`-th Chebyshev polynomial of the first kind evaluates on `cos θ` to the
 value `cos (n * θ)`. -/
 @[simp]
-theorem t_complex_cos : ∀ n, (t ℂ n).eval (cos θ) = cos (n * θ)
+theorem t_complex_cos : ∀ n, (T ℂ n).eval (cos θ) = cos (n * θ)
   | 0 => by simp only [T_zero, eval_one, Nat.cast_zero, MulZeroClass.zero_mul, cos_zero]
   | 1 => by simp only [eval_X, one_mul, T_one, Nat.cast_one]
   | n + 2 =>
@@ -89,7 +89,7 @@ theorem t_complex_cos : ∀ n, (t ℂ n).eval (cos θ) = cos (n * θ)
 /-- The `n`-th Chebyshev polynomial of the second kind evaluates on `cos θ` to the
 value `sin ((n + 1) * θ) / sin θ`. -/
 @[simp]
-theorem u_complex_cos (n : ℕ) : (u ℂ n).eval (cos θ) * sin θ = sin ((n + 1) * θ) :=
+theorem u_complex_cos (n : ℕ) : (U ℂ n).eval (cos θ) * sin θ = sin ((n + 1) * θ) :=
   by
   induction' n with d hd
   · simp only [U_zero, Nat.cast_zero, eval_one, mul_one, zero_add, one_mul]
@@ -112,13 +112,13 @@ variable (θ : ℝ) (n : ℕ)
 /-- The `n`-th Chebyshev polynomial of the first kind evaluates on `cos θ` to the
 value `cos (n * θ)`. -/
 @[simp]
-theorem t_real_cos : (t ℝ n).eval (cos θ) = cos (n * θ) := by exact_mod_cast T_complex_cos θ n
+theorem t_real_cos : (T ℝ n).eval (cos θ) = cos (n * θ) := by exact_mod_cast T_complex_cos θ n
 #align polynomial.chebyshev.T_real_cos Polynomial.Chebyshev.t_real_cos
 
 /-- The `n`-th Chebyshev polynomial of the second kind evaluates on `cos θ` to the
 value `sin ((n + 1) * θ) / sin θ`. -/
 @[simp]
-theorem u_real_cos : (u ℝ n).eval (cos θ) * sin θ = sin ((n + 1) * θ) := by
+theorem u_real_cos : (U ℝ n).eval (cos θ) * sin θ = sin ((n + 1) * θ) := by
   exact_mod_cast U_complex_cos θ n
 #align polynomial.chebyshev.U_real_cos Polynomial.Chebyshev.u_real_cos
 

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

@@ -72,7 +72,7 @@ variable (θ : ℂ)
 value `cos (n * θ)`. -/
 @[simp]
 theorem t_complex_cos : ∀ n, (t ℂ n).eval (cos θ) = cos (n * θ)
-  | 0 => by simp only [T_zero, eval_one, Nat.cast_zero, zero_mul, cos_zero]
+  | 0 => by simp only [T_zero, eval_one, Nat.cast_zero, MulZeroClass.zero_mul, cos_zero]
   | 1 => by simp only [eval_X, one_mul, T_one, Nat.cast_one]
   | n + 2 =>
     by

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

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.

@@ -77,7 +77,7 @@ theorem T_complex_cos : ∀ n, (T ℂ n).eval (cos θ) = cos (n * θ)
   | n + 2 => by
     -- Porting note: partially rewrote proof for lean4 numerals.
     have : (2 : ℂ[X]) = (2 : ℕ) := by norm_num
-    simp only [this, eval_X, eval_one, T_add_two, eval_sub, eval_mul, eval_nat_cast]
+    simp only [this, eval_X, eval_one, T_add_two, eval_sub, eval_mul, eval_natCast]
     simp only [Nat.cast_ofNat, Nat.cast_add]
     rw [T_complex_cos (n + 1), T_complex_cos n]
     simp only [Nat.cast_add, Nat.cast_one, add_mul, cos_add, one_mul, mul_assoc, sin_two_mul,

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
+import Mathlib.Algebra.Polynomial.AlgebraMap
 import Mathlib.Data.Complex.Exponential
 import Mathlib.Data.Complex.Module
-import Mathlib.Data.Polynomial.AlgebraMap
 import Mathlib.RingTheory.Polynomial.Chebyshev
 
 #align_import analysis.special_functions.trigonometric.chebyshev from "leanprover-community/mathlib"@"2c1d8ca2812b64f88992a5294ea3dba144755cd1"

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

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

@@ -114,14 +114,14 @@ variable (θ : ℝ) (n : ℕ)
 /-- The `n`-th Chebyshev polynomial of the first kind evaluates on `cos θ` to the
 value `cos (n * θ)`. -/
 @[simp]
-theorem T_real_cos : (T ℝ n).eval (cos θ) = cos (n * θ) := by exact_mod_cast T_complex_cos θ n
+theorem T_real_cos : (T ℝ n).eval (cos θ) = cos (n * θ) := mod_cast T_complex_cos θ n
 #align polynomial.chebyshev.T_real_cos Polynomial.Chebyshev.T_real_cos
 
 /-- The `n`-th Chebyshev polynomial of the second kind evaluates on `cos θ` to the
 value `sin ((n + 1) * θ) / sin θ`. -/
 @[simp]
-theorem U_real_cos : (U ℝ n).eval (cos θ) * sin θ = sin ((n + 1) * θ) := by
-  exact_mod_cast U_complex_cos θ n
+theorem U_real_cos : (U ℝ n).eval (cos θ) * sin θ = sin ((n + 1) * θ) :=
+  mod_cast U_complex_cos θ n
 #align polynomial.chebyshev.U_real_cos Polynomial.Chebyshev.U_real_cos
 
 end Real

@@ -103,7 +103,8 @@ theorem U_complex_cos (n : ℕ) : (U ℂ n).eval (cos θ) * sin θ = sin ((n + 1
 
 end Complex
 
--- ### Real versions
+/-! ### Real versions -/
+
 section Real
 
 open Real

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

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

@@ -72,7 +72,7 @@ variable (θ : ℂ)
 value `cos (n * θ)`. -/
 @[simp]
 theorem T_complex_cos : ∀ n, (T ℂ n).eval (cos θ) = cos (n * θ)
-  | 0 => by simp only [T_zero, eval_one, Nat.cast_zero, MulZeroClass.zero_mul, cos_zero]
+  | 0 => by simp only [T_zero, eval_one, Nat.cast_zero, zero_mul, cos_zero]
   | 1 => by simp only [eval_X, one_mul, T_one, Nat.cast_one]
   | n + 2 => by
     -- Porting note: partially rewrote proof for lean4 numerals.

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

This has nice performance benefits.

@@ -23,7 +23,7 @@ namespace Polynomial.Chebyshev
 
 open Polynomial
 
-variable {R A : Type _} [CommRing R] [CommRing A] [Algebra R A]
+variable {R A : Type*} [CommRing R] [CommRing A] [Algebra R A]
 
 @[simp]
 theorem aeval_T (x : A) (n : ℕ) : aeval x (T R n) = (T A n).eval x := by

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.chebyshev
-! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Complex.Exponential
 import Mathlib.Data.Complex.Module
 import Mathlib.Data.Polynomial.AlgebraMap
 import Mathlib.RingTheory.Polynomial.Chebyshev
 
+#align_import analysis.special_functions.trigonometric.chebyshev from "leanprover-community/mathlib"@"2c1d8ca2812b64f88992a5294ea3dba144755cd1"
+
 /-!
 # Multiple angle formulas in terms of Chebyshev polynomials
 

@@ -52,15 +52,15 @@ theorem algebraMap_eval_U (x : R) (n : ℕ) :
 
 -- Porting note: added type ascriptions to the statement
 @[simp, norm_cast]
-theorem complex_of_real_eval_T : ∀ (x : ℝ) n, (((T ℝ n).eval x : ℝ) : ℂ) = (T ℂ n).eval (x : ℂ) :=
+theorem complex_ofReal_eval_T : ∀ (x : ℝ) n, (((T ℝ n).eval x : ℝ) : ℂ) = (T ℂ n).eval (x : ℂ) :=
   @algebraMap_eval_T ℝ ℂ _ _ _
-#align polynomial.chebyshev.complex_of_real_eval_T Polynomial.Chebyshev.complex_of_real_eval_T
+#align polynomial.chebyshev.complex_of_real_eval_T Polynomial.Chebyshev.complex_ofReal_eval_T
 
 -- Porting note: added type ascriptions to the statement
 @[simp, norm_cast]
-theorem complex_of_real_eval_U : ∀ (x : ℝ) n, (((U ℝ n).eval x : ℝ) : ℂ) = (U ℂ n).eval (x : ℂ) :=
+theorem complex_ofReal_eval_U : ∀ (x : ℝ) n, (((U ℝ n).eval x : ℝ) : ℂ) = (U ℂ n).eval (x : ℂ) :=
   @algebraMap_eval_U ℝ ℂ _ _ _
-#align polynomial.chebyshev.complex_of_real_eval_U Polynomial.Chebyshev.complex_of_real_eval_U
+#align polynomial.chebyshev.complex_of_real_eval_U Polynomial.Chebyshev.complex_ofReal_eval_U
 
 /-! ### Complex versions -/