data.polynomial.laurent ⟷ Mathlib.Data.Polynomial.Laurent

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

@@ -3,7 +3,7 @@ Copyright (c) 2022 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 -/
-import Data.Polynomial.AlgebraMap
+import Algebra.Polynomial.AlgebraMap
 import RingTheory.Localization.Basic
 
 #align_import data.polynomial.laurent from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"

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

@@ -384,7 +384,7 @@ theorem trunc_C_mul_T (n : ℤ) (r : R) : trunc (C r * T n) = ite (0 ≤ n) (mon
   by_cases n0 : 0 ≤ n
   · lift n to ℕ using n0
     erw [comap_domain_single, to_finsupp_iso_symm_apply]
-    simp only [Int.coe_nat_nonneg, Int.toNat_coe_nat, if_true, to_finsupp_iso_apply,
+    simp only [Int.natCast_nonneg, Int.toNat_natCast, if_true, to_finsupp_iso_apply,
       to_finsupp_monomial]
   · lift -n to ℕ using (neg_pos.mpr (not_le.mp n0)).le with m
     rw [to_finsupp_iso_apply, to_finsupp_inj, if_neg n0]
@@ -405,7 +405,7 @@ theorem leftInverse_trunc_toLaurent :
   · exact fun f g hf hg => by simp only [hf, hg, _root_.map_add]
   ·
     exact fun n r => by
-      simp only [Polynomial.toLaurent_C_mul_T, trunc_C_mul_T, Int.coe_nat_nonneg, Int.toNat_coe_nat,
+      simp only [Polynomial.toLaurent_C_mul_T, trunc_C_mul_T, Int.natCast_nonneg, Int.toNat_natCast,
         if_true]
 #align laurent_polynomial.left_inverse_trunc_to_laurent LaurentPolynomial.leftInverse_trunc_toLaurent
 -/

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

@@ -550,10 +550,10 @@ theorem degree_zero : degree (0 : R[T;T⁻¹]) = ⊥ :=
 theorem degree_eq_bot_iff {f : R[T;T⁻¹]} : f.degree = ⊥ ↔ f = 0 :=
   by
   refine' ⟨fun h => _, fun h => by rw [h, degree_zero]⟩
-  rw [degree, Finset.max_eq_sup_withBot] at h 
+  rw [degree, Finset.max_eq_sup_withBot] at h
   ext n
   refine' not_not.mp fun f0 => _
-  simp_rw [Finset.sup_eq_bot_iff, Finsupp.mem_support_iff, Ne.def, WithBot.coe_ne_bot] at h 
+  simp_rw [Finset.sup_eq_bot_iff, Finsupp.mem_support_iff, Ne.def, WithBot.coe_ne_bot] at h
   exact h n f0
 #align laurent_polynomial.degree_eq_bot_iff LaurentPolynomial.degree_eq_bot_iff
 -/

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 -/
-import Mathbin.Data.Polynomial.AlgebraMap
-import Mathbin.RingTheory.Localization.Basic
+import Data.Polynomial.AlgebraMap
+import RingTheory.Localization.Basic
 
 #align_import data.polynomial.laurent from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -287,8 +287,8 @@ theorem Polynomial.toLaurent_C_mul_X_pow (n : ℕ) (r : R) :
 instance invertibleT (n : ℤ) : Invertible (T n : R[T;T⁻¹])
     where
   invOf := T (-n)
-  invOf_mul_self := by rw [← T_add, add_left_neg, T_zero]
-  mul_invOf_self := by rw [← T_add, add_right_neg, T_zero]
+  invOf_hMul_self := by rw [← T_add, add_left_neg, T_zero]
+  hMul_invOf_self := by rw [← T_add, add_right_neg, T_zero]
 #align laurent_polynomial.invertible_T LaurentPolynomial.invertibleT
 -/
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
-
-! This file was ported from Lean 3 source module data.polynomial.laurent
-! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Polynomial.AlgebraMap
 import Mathbin.RingTheory.Localization.Basic
 
+#align_import data.polynomial.laurent from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"
+
 /-!  # Laurent polynomials
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

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

@@ -94,7 +94,6 @@ abbrev LaurentPolynomial (R : Type _) [Semiring R] :=
 #align laurent_polynomial LaurentPolynomial
 -/
 
--- mathport name: «expr [T;T⁻¹]»
 local notation:9000 R "[T;T⁻¹]" => LaurentPolynomial R
 
 #print Polynomial.toLaurent /-
@@ -105,12 +104,14 @@ def Polynomial.toLaurent [Semiring R] : R[X] →+* R[T;T⁻¹] :=
 #align polynomial.to_laurent Polynomial.toLaurent
 -/
 
+#print Polynomial.toLaurent_apply /-
 /-- This is not a simp lemma, as it is usually preferable to use the lemmas about `C` and `X`
 instead. -/
 theorem Polynomial.toLaurent_apply [Semiring R] (p : R[X]) :
     p.toLaurent = p.toFinsupp.mapDomain coe :=
   rfl
 #align polynomial.to_laurent_apply Polynomial.toLaurent_apply
+-/
 
 #print Polynomial.toLaurentAlg /-
 /-- The `R`-algebra map, taking a polynomial with coefficients in `R` to a Laurent polynomial
@@ -122,10 +123,12 @@ def Polynomial.toLaurentAlg [CommSemiring R] : R[X] →ₐ[R] R[T;T⁻¹] :=
 #align polynomial.to_laurent_alg Polynomial.toLaurentAlg
 -/
 
+#print Polynomial.toLaurentAlg_apply /-
 @[simp]
 theorem Polynomial.toLaurentAlg_apply [CommSemiring R] (f : R[X]) : f.toLaurentAlg = f.toLaurent :=
   rfl
 #align polynomial.to_laurent_alg_apply Polynomial.toLaurentAlg_apply
+-/
 
 namespace LaurentPolynomial
 
@@ -133,9 +136,11 @@ section Semiring
 
 variable [Semiring R]
 
+#print LaurentPolynomial.single_zero_one_eq_one /-
 theorem single_zero_one_eq_one : (single 0 1 : R[T;T⁻¹]) = (1 : R[T;T⁻¹]) :=
   rfl
 #align laurent_polynomial.single_zero_one_eq_one LaurentPolynomial.single_zero_one_eq_one
+-/
 
 /-!  ### The functions `C` and `T`. -/
 
@@ -148,11 +153,14 @@ def C : R →+* R[T;T⁻¹] :=
 #align laurent_polynomial.C LaurentPolynomial.C
 -/
 
+#print LaurentPolynomial.algebraMap_apply /-
 theorem algebraMap_apply {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A] (r : R) :
     algebraMap R (LaurentPolynomial A) r = C (algebraMap R A r) :=
   rfl
 #align laurent_polynomial.algebra_map_apply LaurentPolynomial.algebraMap_apply
+-/
 
+#print LaurentPolynomial.C_eq_algebraMap /-
 /-- When we have `[comm_semiring R]`, the function `C` is the same as `algebra_map R R[T;T⁻¹]`.
 (But note that `C` is defined when `R` is not necessarily commutative, in which case
 `algebra_map` is not available.)
@@ -160,10 +168,13 @@ theorem algebraMap_apply {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R
 theorem C_eq_algebraMap {R : Type _} [CommSemiring R] (r : R) : C r = algebraMap R R[T;T⁻¹] r :=
   rfl
 #align laurent_polynomial.C_eq_algebra_map LaurentPolynomial.C_eq_algebraMap
+-/
 
+#print LaurentPolynomial.single_eq_C /-
 theorem single_eq_C (r : R) : single 0 r = C r :=
   rfl
 #align laurent_polynomial.single_eq_C LaurentPolynomial.single_eq_C
+-/
 
 #print LaurentPolynomial.T /-
 /-- The function `n ↦ T ^ n`, implemented as a sequence `ℤ → R[T;T⁻¹]`.
@@ -194,10 +205,12 @@ theorem T_sub (m n : ℤ) : (T (m - n) : R[T;T⁻¹]) = T m * T (-n) := by rw [
 #align laurent_polynomial.T_sub LaurentPolynomial.T_sub
 -/
 
+#print LaurentPolynomial.T_pow /-
 @[simp]
 theorem T_pow (m : ℤ) (n : ℕ) : (T m ^ n : R[T;T⁻¹]) = T (n * m) := by
   rw [T, T, single_pow n, one_pow, nsmul_eq_mul]
 #align laurent_polynomial.T_pow LaurentPolynomial.T_pow
+-/
 
 #print LaurentPolynomial.mul_T_assoc /-
 /-- The `simp` version of `mul_assoc`, in the presence of `T`'s. -/
@@ -207,11 +220,14 @@ theorem mul_T_assoc (f : R[T;T⁻¹]) (m n : ℤ) : f * T m * T n = f * T (m + n
 #align laurent_polynomial.mul_T_assoc LaurentPolynomial.mul_T_assoc
 -/
 
+#print LaurentPolynomial.single_eq_C_mul_T /-
 @[simp]
 theorem single_eq_C_mul_T (r : R) (n : ℤ) : (single n r : R[T;T⁻¹]) = (C r * T n : R[T;T⁻¹]) := by
   convert single_mul_single.symm <;> simp
 #align laurent_polynomial.single_eq_C_mul_T LaurentPolynomial.single_eq_C_mul_T
+-/
 
+#print Polynomial.toLaurent_C_mul_T /-
 -- This lemma locks in the right changes and is what Lean proved directly.
 -- The actual `simp`-normal form of a Laurent monomial is `C a * T n`, whenever it can be reached.
 @[simp]
@@ -220,42 +236,55 @@ theorem Polynomial.toLaurent_C_mul_T (n : ℕ) (r : R) :
   show mapDomain coe (monomial n r).toFinsupp = (C r * T n : R[T;T⁻¹]) by
     rw [to_finsupp_monomial, map_domain_single, single_eq_C_mul_T]
 #align polynomial.to_laurent_C_mul_T Polynomial.toLaurent_C_mul_T
+-/
 
+#print Polynomial.toLaurent_C /-
 @[simp]
 theorem Polynomial.toLaurent_C (r : R) : (Polynomial.C r).toLaurent = C r :=
   by
   convert Polynomial.toLaurent_C_mul_T 0 r
   simp only [Int.ofNat_zero, T_zero, mul_one]
 #align polynomial.to_laurent_C Polynomial.toLaurent_C
+-/
 
+#print Polynomial.toLaurent_X /-
 @[simp]
 theorem Polynomial.toLaurent_X : (Polynomial.X.toLaurent : R[T;T⁻¹]) = T 1 :=
   by
   have : (Polynomial.X : R[X]) = monomial 1 1 := by simp [← C_mul_X_pow_eq_monomial]
   simp [this, Polynomial.toLaurent_C_mul_T]
 #align polynomial.to_laurent_X Polynomial.toLaurent_X
+-/
 
+#print Polynomial.toLaurent_one /-
 @[simp]
 theorem Polynomial.toLaurent_one : (Polynomial.toLaurent : R[X] → R[T;T⁻¹]) 1 = 1 :=
   map_one Polynomial.toLaurent
 #align polynomial.to_laurent_one Polynomial.toLaurent_one
+-/
 
+#print Polynomial.toLaurent_C_mul_eq /-
 @[simp]
 theorem Polynomial.toLaurent_C_mul_eq (r : R) (f : R[X]) :
     (Polynomial.C r * f).toLaurent = C r * f.toLaurent := by
   simp only [_root_.map_mul, Polynomial.toLaurent_C]
 #align polynomial.to_laurent_C_mul_eq Polynomial.toLaurent_C_mul_eq
+-/
 
+#print Polynomial.toLaurent_X_pow /-
 @[simp]
 theorem Polynomial.toLaurent_X_pow (n : ℕ) : (X ^ n : R[X]).toLaurent = T n := by
   simp only [map_pow, Polynomial.toLaurent_X, T_pow, mul_one]
 #align polynomial.to_laurent_X_pow Polynomial.toLaurent_X_pow
+-/
 
+#print Polynomial.toLaurent_C_mul_X_pow /-
 @[simp]
 theorem Polynomial.toLaurent_C_mul_X_pow (n : ℕ) (r : R) :
     (Polynomial.C r * X ^ n).toLaurent = C r * T n := by
   simp only [_root_.map_mul, Polynomial.toLaurent_C, Polynomial.toLaurent_X_pow]
 #align polynomial.to_laurent_C_mul_X_pow Polynomial.toLaurent_C_mul_X_pow
+-/
 
 #print LaurentPolynomial.invertibleT /-
 instance invertibleT (n : ℤ) : Invertible (T n : R[T;T⁻¹])
@@ -279,6 +308,7 @@ theorem isUnit_T (n : ℤ) : IsUnit (T n : R[T;T⁻¹]) :=
 #align laurent_polynomial.is_unit_T LaurentPolynomial.isUnit_T
 -/
 
+#print LaurentPolynomial.induction_on /-
 @[elab_as_elim]
 protected theorem induction_on {M : R[T;T⁻¹] → Prop} (p : R[T;T⁻¹]) (h_C : ∀ a, M (C a))
     (h_add : ∀ {p q}, M p → M q → M (p + q))
@@ -304,7 +334,9 @@ protected theorem induction_on {M : R[T;T⁻¹] → Prop} (p : R[T;T⁻¹]) (h_C
   · rfl
   · exact finsupp.not_mem_support_iff.mp h
 #align laurent_polynomial.induction_on LaurentPolynomial.induction_on
+-/
 
+#print LaurentPolynomial.induction_on' /-
 /-- To prove something about Laurent polynomials, it suffices to show that
 * the condition is closed under taking sums, and
 * it holds for monomials.
@@ -317,6 +349,7 @@ protected theorem induction_on' {M : R[T;T⁻¹] → Prop} (p : R[T;T⁻¹])
   convert h_C_mul_T 0 a
   exact (mul_one _).symm
 #align laurent_polynomial.induction_on' LaurentPolynomial.induction_on'
+-/
 
 #print LaurentPolynomial.commute_T /-
 theorem commute_T (n : ℤ) (f : R[T;T⁻¹]) : Commute (T n) f :=
@@ -344,6 +377,7 @@ def trunc : R[T;T⁻¹] →+ R[X] :=
 #align laurent_polynomial.trunc LaurentPolynomial.trunc
 -/
 
+#print LaurentPolynomial.trunc_C_mul_T /-
 @[simp]
 theorem trunc_C_mul_T (n : ℤ) (r : R) : trunc (C r * T n) = ite (0 ≤ n) (monomial n.toNat r) 0 :=
   by
@@ -363,7 +397,9 @@ theorem trunc_C_mul_T (n : ℤ) (r : R) : trunc (C r * T n) = ite (0 ≤ n) (mon
     simp only [coeff, comap_domain_apply, Int.ofNat_eq_coe, coeff_zero, single_apply_eq_zero, this,
       IsEmpty.forall_iff]
 #align laurent_polynomial.trunc_C_mul_T LaurentPolynomial.trunc_C_mul_T
+-/
 
+#print LaurentPolynomial.leftInverse_trunc_toLaurent /-
 @[simp]
 theorem leftInverse_trunc_toLaurent :
     Function.LeftInverse (trunc : R[T;T⁻¹] → R[X]) Polynomial.toLaurent :=
@@ -375,26 +411,36 @@ theorem leftInverse_trunc_toLaurent :
       simp only [Polynomial.toLaurent_C_mul_T, trunc_C_mul_T, Int.coe_nat_nonneg, Int.toNat_coe_nat,
         if_true]
 #align laurent_polynomial.left_inverse_trunc_to_laurent LaurentPolynomial.leftInverse_trunc_toLaurent
+-/
 
+#print Polynomial.trunc_toLaurent /-
 @[simp]
 theorem Polynomial.trunc_toLaurent (f : R[X]) : trunc f.toLaurent = f :=
   leftInverse_trunc_toLaurent _
 #align polynomial.trunc_to_laurent Polynomial.trunc_toLaurent
+-/
 
+#print Polynomial.toLaurent_injective /-
 theorem Polynomial.toLaurent_injective :
     Function.Injective (Polynomial.toLaurent : R[X] → R[T;T⁻¹]) :=
   leftInverse_trunc_toLaurent.Injective
 #align polynomial.to_laurent_injective Polynomial.toLaurent_injective
+-/
 
+#print Polynomial.toLaurent_inj /-
 @[simp]
 theorem Polynomial.toLaurent_inj (f g : R[X]) : f.toLaurent = g.toLaurent ↔ f = g :=
   ⟨fun h => Polynomial.toLaurent_injective h, congr_arg _⟩
 #align polynomial.to_laurent_inj Polynomial.toLaurent_inj
+-/
 
+#print Polynomial.toLaurent_ne_zero /-
 theorem Polynomial.toLaurent_ne_zero {f : R[X]} : f ≠ 0 ↔ f.toLaurent ≠ 0 :=
   (map_ne_zero_iff _ Polynomial.toLaurent_injective).symm
 #align polynomial.to_laurent_ne_zero Polynomial.toLaurent_ne_zero
+-/
 
+#print LaurentPolynomial.exists_T_pow /-
 theorem exists_T_pow (f : R[T;T⁻¹]) : ∃ (n : ℕ) (f' : R[X]), f'.toLaurent = f * T n :=
   by
   apply f.induction_on' _ fun n a => _ <;> clear f
@@ -408,7 +454,9 @@ theorem exists_T_pow (f : R[T;T⁻¹]) : ∃ (n : ℕ) (f' : R[X]), f'.toLaurent
       simp only [Int.negSucc_eq, Polynomial.toLaurent_C, Int.ofNat_succ, mul_T_assoc, add_left_neg,
         T_zero, mul_one]
 #align laurent_polynomial.exists_T_pow LaurentPolynomial.exists_T_pow
+-/
 
+#print LaurentPolynomial.induction_on_mul_T /-
 /-- This is a version of `exists_T_pow` stated as an induction principle. -/
 @[elab_as_elim]
 theorem induction_on_mul_T {Q : R[T;T⁻¹] → Prop} (f : R[T;T⁻¹])
@@ -419,7 +467,9 @@ theorem induction_on_mul_T {Q : R[T;T⁻¹] → Prop} (f : R[T;T⁻¹])
     mul_assoc, ← hf]
   exact Qf
 #align laurent_polynomial.induction_on_mul_T LaurentPolynomial.induction_on_mul_T
+-/
 
+#print LaurentPolynomial.reduce_to_polynomial_of_mul_T /-
 /-- Suppose that `Q` is a statement about Laurent polynomials such that
 * `Q` is true on *ordinary* polynomials;
 * `Q (f * T)` implies `Q f`;
@@ -433,19 +483,25 @@ theorem reduce_to_polynomial_of_mul_T (f : R[T;T⁻¹]) {Q : R[T;T⁻¹] → Pro
   · convert QT _ _
     simpa using hn
 #align laurent_polynomial.reduce_to_polynomial_of_mul_T LaurentPolynomial.reduce_to_polynomial_of_mul_T
+-/
 
 section Support
 
+#print LaurentPolynomial.support_C_mul_T /-
 theorem support_C_mul_T (a : R) (n : ℤ) : (C a * T n).support ⊆ {n} := by
   simpa only [← single_eq_C_mul_T] using support_single_subset
 #align laurent_polynomial.support_C_mul_T LaurentPolynomial.support_C_mul_T
+-/
 
+#print LaurentPolynomial.support_C_mul_T_of_ne_zero /-
 theorem support_C_mul_T_of_ne_zero {a : R} (a0 : a ≠ 0) (n : ℤ) : (C a * T n).support = {n} :=
   by
   rw [← single_eq_C_mul_T]
   exact support_single_ne_zero _ a0
 #align laurent_polynomial.support_C_mul_T_of_ne_zero LaurentPolynomial.support_C_mul_T_of_ne_zero
+-/
 
+#print LaurentPolynomial.toLaurent_support /-
 /-- The support of a polynomial `f` is a finset in `ℕ`.  The lemma `to_laurent_support f`
 shows that the support of `f.to_laurent` is the same finset, but viewed in `ℤ` under the natural
 inclusion `ℕ ↪ ℤ`. -/
@@ -470,6 +526,7 @@ theorem toLaurent_support (f : R[X]) : f.toLaurent.support = f.support.map Nat.c
     · rw [this]
       exact Disjoint.mono_left (support_C_mul_T _ _) (by simpa)
 #align laurent_polynomial.to_laurent_support LaurentPolynomial.toLaurent_support
+-/
 
 end Support
 
@@ -484,11 +541,14 @@ def degree (f : R[T;T⁻¹]) : WithBot ℤ :=
 #align laurent_polynomial.degree LaurentPolynomial.degree
 -/
 
+#print LaurentPolynomial.degree_zero /-
 @[simp]
 theorem degree_zero : degree (0 : R[T;T⁻¹]) = ⊥ :=
   rfl
 #align laurent_polynomial.degree_zero LaurentPolynomial.degree_zero
+-/
 
+#print LaurentPolynomial.degree_eq_bot_iff /-
 @[simp]
 theorem degree_eq_bot_iff {f : R[T;T⁻¹]} : f.degree = ⊥ ↔ f = 0 :=
   by
@@ -499,11 +559,13 @@ theorem degree_eq_bot_iff {f : R[T;T⁻¹]} : f.degree = ⊥ ↔ f = 0 :=
   simp_rw [Finset.sup_eq_bot_iff, Finsupp.mem_support_iff, Ne.def, WithBot.coe_ne_bot] at h 
   exact h n f0
 #align laurent_polynomial.degree_eq_bot_iff LaurentPolynomial.degree_eq_bot_iff
+-/
 
 section ExactDegrees
 
 open scoped Classical
 
+#print LaurentPolynomial.degree_C_mul_T /-
 @[simp]
 theorem degree_C_mul_T (n : ℤ) (a : R) (a0 : a ≠ 0) : (C a * T n).degree = n :=
   by
@@ -513,12 +575,15 @@ theorem degree_C_mul_T (n : ℤ) (a : R) (a0 : a ≠ 0) : (C a * T n).degree = n
   simp only [← single_eq_C_mul_T, single_eq_same, a0, Ne.def, not_false_iff, eq_self_iff_true,
     and_self_iff]
 #align laurent_polynomial.degree_C_mul_T LaurentPolynomial.degree_C_mul_T
+-/
 
+#print LaurentPolynomial.degree_C_mul_T_ite /-
 theorem degree_C_mul_T_ite (n : ℤ) (a : R) : (C a * T n).degree = ite (a = 0) ⊥ n := by
   split_ifs with h h <;>
     simp only [h, map_zero, MulZeroClass.zero_mul, degree_zero, degree_C_mul_T, Ne.def,
       not_false_iff]
 #align laurent_polynomial.degree_C_mul_T_ite LaurentPolynomial.degree_C_mul_T_ite
+-/
 
 #print LaurentPolynomial.degree_T /-
 @[simp]
@@ -529,26 +594,32 @@ theorem degree_T [Nontrivial R] (n : ℤ) : (T n : R[T;T⁻¹]).degree = n :=
 #align laurent_polynomial.degree_T LaurentPolynomial.degree_T
 -/
 
+#print LaurentPolynomial.degree_C /-
 theorem degree_C {a : R} (a0 : a ≠ 0) : (C a).degree = 0 :=
   by
   rw [← mul_one (C a), ← T_zero]
   exact degree_C_mul_T 0 a a0
 #align laurent_polynomial.degree_C LaurentPolynomial.degree_C
+-/
 
+#print LaurentPolynomial.degree_C_ite /-
 theorem degree_C_ite (a : R) : (C a).degree = ite (a = 0) ⊥ 0 := by
   split_ifs with h h <;> simp only [h, map_zero, degree_zero, degree_C, Ne.def, not_false_iff]
 #align laurent_polynomial.degree_C_ite LaurentPolynomial.degree_C_ite
+-/
 
 end ExactDegrees
 
 section DegreeBounds
 
+#print LaurentPolynomial.degree_C_mul_T_le /-
 theorem degree_C_mul_T_le (n : ℤ) (a : R) : (C a * T n).degree ≤ n :=
   by
   by_cases a0 : a = 0
   · simp only [a0, map_zero, MulZeroClass.zero_mul, degree_zero, bot_le]
   · exact (degree_C_mul_T n a a0).le
 #align laurent_polynomial.degree_C_mul_T_le LaurentPolynomial.degree_C_mul_T_le
+-/
 
 #print LaurentPolynomial.degree_T_le /-
 theorem degree_T_le (n : ℤ) : (T n : R[T;T⁻¹]).degree ≤ n :=
@@ -556,9 +627,11 @@ theorem degree_T_le (n : ℤ) : (T n : R[T;T⁻¹]).degree ≤ n :=
 #align laurent_polynomial.degree_T_le LaurentPolynomial.degree_T_le
 -/
 
+#print LaurentPolynomial.degree_C_le /-
 theorem degree_C_le (a : R) : (C a).degree ≤ 0 :=
   (le_of_eq (by rw [T_zero, mul_one])).trans (degree_C_mul_T_le 0 a)
 #align laurent_polynomial.degree_C_le LaurentPolynomial.degree_C_le
+-/
 
 end DegreeBounds
 
@@ -584,14 +657,18 @@ instance algebraPolynomial (R : Type _) [CommSemiring R] : Algebra R[X] R[T;T⁻
 #align laurent_polynomial.algebra_polynomial LaurentPolynomial.algebraPolynomial
 -/
 
+#print LaurentPolynomial.algebraMap_X_pow /-
 theorem algebraMap_X_pow (n : ℕ) : algebraMap R[X] R[T;T⁻¹] (X ^ n) = T n :=
   Polynomial.toLaurent_X_pow n
 #align laurent_polynomial.algebra_map_X_pow LaurentPolynomial.algebraMap_X_pow
+-/
 
+#print LaurentPolynomial.algebraMap_eq_toLaurent /-
 @[simp]
 theorem algebraMap_eq_toLaurent (f : R[X]) : algebraMap R[X] R[T;T⁻¹] f = f.toLaurent :=
   rfl
 #align laurent_polynomial.algebra_map_eq_to_laurent LaurentPolynomial.algebraMap_eq_toLaurent
+-/
 
 #print LaurentPolynomial.isLocalization /-
 theorem isLocalization : IsLocalization (Submonoid.closure ({X} : Set R[X])) R[T;T⁻¹] :=

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

@@ -395,7 +395,7 @@ theorem Polynomial.toLaurent_ne_zero {f : R[X]} : f ≠ 0 ↔ f.toLaurent ≠ 0
   (map_ne_zero_iff _ Polynomial.toLaurent_injective).symm
 #align polynomial.to_laurent_ne_zero Polynomial.toLaurent_ne_zero
 
-theorem exists_T_pow (f : R[T;T⁻¹]) : ∃ (n : ℕ)(f' : R[X]), f'.toLaurent = f * T n :=
+theorem exists_T_pow (f : R[T;T⁻¹]) : ∃ (n : ℕ) (f' : R[X]), f'.toLaurent = f * T n :=
   by
   apply f.induction_on' _ fun n a => _ <;> clear f
   · rintro f g ⟨m, fn, hf⟩ ⟨n, gn, hg⟩
@@ -493,10 +493,10 @@ theorem degree_zero : degree (0 : R[T;T⁻¹]) = ⊥ :=
 theorem degree_eq_bot_iff {f : R[T;T⁻¹]} : f.degree = ⊥ ↔ f = 0 :=
   by
   refine' ⟨fun h => _, fun h => by rw [h, degree_zero]⟩
-  rw [degree, Finset.max_eq_sup_withBot] at h
+  rw [degree, Finset.max_eq_sup_withBot] at h 
   ext n
   refine' not_not.mp fun f0 => _
-  simp_rw [Finset.sup_eq_bot_iff, Finsupp.mem_support_iff, Ne.def, WithBot.coe_ne_bot] at h
+  simp_rw [Finset.sup_eq_bot_iff, Finsupp.mem_support_iff, Ne.def, WithBot.coe_ne_bot] at h 
   exact h n f0
 #align laurent_polynomial.degree_eq_bot_iff LaurentPolynomial.degree_eq_bot_iff
 

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

@@ -122,12 +122,10 @@ def Polynomial.toLaurentAlg [CommSemiring R] : R[X] →ₐ[R] R[T;T⁻¹] :=
 #align polynomial.to_laurent_alg Polynomial.toLaurentAlg
 -/
 
-#print Polynomial.toLaurentAlg_apply /-
 @[simp]
 theorem Polynomial.toLaurentAlg_apply [CommSemiring R] (f : R[X]) : f.toLaurentAlg = f.toLaurent :=
   rfl
 #align polynomial.to_laurent_alg_apply Polynomial.toLaurentAlg_apply
--/
 
 namespace LaurentPolynomial
 
@@ -600,13 +598,13 @@ theorem isLocalization : IsLocalization (Submonoid.closure ({X} : Set R[X])) R[T
   { map_units := fun t => by
       cases' t with t ht
       rcases submonoid.mem_closure_singleton.mp ht with ⟨n, rfl⟩
-      simp only [is_unit_T n, [anonymous], algebra_map_eq_to_laurent, Polynomial.toLaurent_X_pow]
+      simp only [is_unit_T n, SetLike.coe_mk, algebra_map_eq_to_laurent, Polynomial.toLaurent_X_pow]
     surj := fun f =>
       by
       induction' f using LaurentPolynomial.induction_on_mul_T with f n
       have := (Submonoid.closure ({X} : Set R[X])).pow_mem Submonoid.mem_closure_singleton_self n
       refine' ⟨(f, ⟨_, this⟩), _⟩
-      simp only [[anonymous], algebra_map_eq_to_laurent, Polynomial.toLaurent_X_pow, mul_T_assoc,
+      simp only [SetLike.coe_mk, algebra_map_eq_to_laurent, Polynomial.toLaurent_X_pow, mul_T_assoc,
         add_left_neg, T_zero, mul_one]
     eq_iff_exists := fun f g =>
       by

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

@@ -77,7 +77,7 @@ Lots is missing!
 -/
 
 
-open Polynomial BigOperators
+open scoped Polynomial BigOperators
 
 open Polynomial AddMonoidAlgebra Finsupp
 
@@ -504,7 +504,7 @@ theorem degree_eq_bot_iff {f : R[T;T⁻¹]} : f.degree = ⊥ ↔ f = 0 :=
 
 section ExactDegrees
 
-open Classical
+open scoped Classical
 
 @[simp]
 theorem degree_C_mul_T (n : ℤ) (a : R) (a0 : a ≠ 0) : (C a * T n).degree = n :=
@@ -552,9 +552,11 @@ theorem degree_C_mul_T_le (n : ℤ) (a : R) : (C a * T n).degree ≤ n :=
   · exact (degree_C_mul_T n a a0).le
 #align laurent_polynomial.degree_C_mul_T_le LaurentPolynomial.degree_C_mul_T_le
 
+#print LaurentPolynomial.degree_T_le /-
 theorem degree_T_le (n : ℤ) : (T n : R[T;T⁻¹]).degree ≤ n :=
   (le_of_eq (by rw [map_one, one_mul])).trans (degree_C_mul_T_le n (1 : R))
 #align laurent_polynomial.degree_T_le LaurentPolynomial.degree_T_le
+-/
 
 theorem degree_C_le (a : R) : (C a).degree ≤ 0 :=
   (le_of_eq (by rw [T_zero, mul_one])).trans (degree_C_mul_T_le 0 a)

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

@@ -105,12 +105,6 @@ def Polynomial.toLaurent [Semiring R] : R[X] →+* R[T;T⁻¹] :=
 #align polynomial.to_laurent Polynomial.toLaurent
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_apply Polynomial.toLaurent_applyₓ'. -/
 /-- This is not a simp lemma, as it is usually preferable to use the lemmas about `C` and `X`
 instead. -/
 theorem Polynomial.toLaurent_apply [Semiring R] (p : R[X]) :
@@ -141,12 +135,6 @@ section Semiring
 
 variable [Semiring R]
 
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-Case conversion may be inaccurate. Consider using '#align laurent_polynomial.single_zero_one_eq_one LaurentPolynomial.single_zero_one_eq_oneₓ'. -/
 theorem single_zero_one_eq_one : (single 0 1 : R[T;T⁻¹]) = (1 : R[T;T⁻¹]) :=
   rfl
 #align laurent_polynomial.single_zero_one_eq_one LaurentPolynomial.single_zero_one_eq_one
@@ -162,17 +150,11 @@ def C : R →+* R[T;T⁻¹] :=
 #align laurent_polynomial.C LaurentPolynomial.C
 -/
 
-/- warning: laurent_polynomial.algebra_map_apply -> LaurentPolynomial.algebraMap_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align laurent_polynomial.algebra_map_apply LaurentPolynomial.algebraMap_applyₓ'. -/
 theorem algebraMap_apply {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A] (r : R) :
     algebraMap R (LaurentPolynomial A) r = C (algebraMap R A r) :=
   rfl
 #align laurent_polynomial.algebra_map_apply LaurentPolynomial.algebraMap_apply
 
-/- warning: laurent_polynomial.C_eq_algebra_map -> LaurentPolynomial.C_eq_algebraMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align laurent_polynomial.C_eq_algebra_map LaurentPolynomial.C_eq_algebraMapₓ'. -/
 /-- When we have `[comm_semiring R]`, the function `C` is the same as `algebra_map R R[T;T⁻¹]`.
 (But note that `C` is defined when `R` is not necessarily commutative, in which case
 `algebra_map` is not available.)
@@ -181,12 +163,6 @@ theorem C_eq_algebraMap {R : Type _} [CommSemiring R] (r : R) : C r = algebraMap
   rfl
 #align laurent_polynomial.C_eq_algebra_map LaurentPolynomial.C_eq_algebraMap
 
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 theorem single_eq_C (r : R) : single 0 r = C r :=
   rfl
 #align laurent_polynomial.single_eq_C LaurentPolynomial.single_eq_C
@@ -220,12 +196,6 @@ theorem T_sub (m n : ℤ) : (T (m - n) : R[T;T⁻¹]) = T m * T (-n) := by rw [
 #align laurent_polynomial.T_sub LaurentPolynomial.T_sub
 -/
 
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 @[simp]
 theorem T_pow (m : ℤ) (n : ℕ) : (T m ^ n : R[T;T⁻¹]) = T (n * m) := by
   rw [T, T, single_pow n, one_pow, nsmul_eq_mul]
@@ -239,20 +209,11 @@ theorem mul_T_assoc (f : R[T;T⁻¹]) (m n : ℤ) : f * T m * T n = f * T (m + n
 #align laurent_polynomial.mul_T_assoc LaurentPolynomial.mul_T_assoc
 -/
 
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 @[simp]
 theorem single_eq_C_mul_T (r : R) (n : ℤ) : (single n r : R[T;T⁻¹]) = (C r * T n : R[T;T⁻¹]) := by
   convert single_mul_single.symm <;> simp
 #align laurent_polynomial.single_eq_C_mul_T LaurentPolynomial.single_eq_C_mul_T
 
-/- warning: polynomial.to_laurent_C_mul_T -> Polynomial.toLaurent_C_mul_T is a dubious translation:
-<too large>
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 -- This lemma locks in the right changes and is what Lean proved directly.
 -- The actual `simp`-normal form of a Laurent monomial is `C a * T n`, whenever it can be reached.
 @[simp]
@@ -262,9 +223,6 @@ theorem Polynomial.toLaurent_C_mul_T (n : ℕ) (r : R) :
     rw [to_finsupp_monomial, map_domain_single, single_eq_C_mul_T]
 #align polynomial.to_laurent_C_mul_T Polynomial.toLaurent_C_mul_T
 
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 @[simp]
 theorem Polynomial.toLaurent_C (r : R) : (Polynomial.C r).toLaurent = C r :=
   by
@@ -272,12 +230,6 @@ theorem Polynomial.toLaurent_C (r : R) : (Polynomial.C r).toLaurent = C r :=
   simp only [Int.ofNat_zero, T_zero, mul_one]
 #align polynomial.to_laurent_C Polynomial.toLaurent_C
 
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 @[simp]
 theorem Polynomial.toLaurent_X : (Polynomial.X.toLaurent : R[T;T⁻¹]) = T 1 :=
   by
@@ -285,40 +237,22 @@ theorem Polynomial.toLaurent_X : (Polynomial.X.toLaurent : R[T;T⁻¹]) = T 1 :=
   simp [this, Polynomial.toLaurent_C_mul_T]
 #align polynomial.to_laurent_X Polynomial.toLaurent_X
 
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 @[simp]
 theorem Polynomial.toLaurent_one : (Polynomial.toLaurent : R[X] → R[T;T⁻¹]) 1 = 1 :=
   map_one Polynomial.toLaurent
 #align polynomial.to_laurent_one Polynomial.toLaurent_one
 
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 @[simp]
 theorem Polynomial.toLaurent_C_mul_eq (r : R) (f : R[X]) :
     (Polynomial.C r * f).toLaurent = C r * f.toLaurent := by
   simp only [_root_.map_mul, Polynomial.toLaurent_C]
 #align polynomial.to_laurent_C_mul_eq Polynomial.toLaurent_C_mul_eq
 
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 @[simp]
 theorem Polynomial.toLaurent_X_pow (n : ℕ) : (X ^ n : R[X]).toLaurent = T n := by
   simp only [map_pow, Polynomial.toLaurent_X, T_pow, mul_one]
 #align polynomial.to_laurent_X_pow Polynomial.toLaurent_X_pow
 
-/- warning: polynomial.to_laurent_C_mul_X_pow -> Polynomial.toLaurent_C_mul_X_pow is a dubious translation:
-<too large>
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 @[simp]
 theorem Polynomial.toLaurent_C_mul_X_pow (n : ℕ) (r : R) :
     (Polynomial.C r * X ^ n).toLaurent = C r * T n := by
@@ -347,9 +281,6 @@ theorem isUnit_T (n : ℤ) : IsUnit (T n : R[T;T⁻¹]) :=
 #align laurent_polynomial.is_unit_T LaurentPolynomial.isUnit_T
 -/
 
-/- warning: laurent_polynomial.induction_on -> LaurentPolynomial.induction_on is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align laurent_polynomial.induction_on LaurentPolynomial.induction_onₓ'. -/
 @[elab_as_elim]
 protected theorem induction_on {M : R[T;T⁻¹] → Prop} (p : R[T;T⁻¹]) (h_C : ∀ a, M (C a))
     (h_add : ∀ {p q}, M p → M q → M (p + q))
@@ -376,12 +307,6 @@ protected theorem induction_on {M : R[T;T⁻¹] → Prop} (p : R[T;T⁻¹]) (h_C
   · exact finsupp.not_mem_support_iff.mp h
 #align laurent_polynomial.induction_on LaurentPolynomial.induction_on
 
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 /-- To prove something about Laurent polynomials, it suffices to show that
 * the condition is closed under taking sums, and
 * it holds for monomials.
@@ -421,9 +346,6 @@ def trunc : R[T;T⁻¹] →+ R[X] :=
 #align laurent_polynomial.trunc LaurentPolynomial.trunc
 -/
 
-/- warning: laurent_polynomial.trunc_C_mul_T -> LaurentPolynomial.trunc_C_mul_T is a dubious translation:
-<too large>
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 @[simp]
 theorem trunc_C_mul_T (n : ℤ) (r : R) : trunc (C r * T n) = ite (0 ≤ n) (monomial n.toNat r) 0 :=
   by
@@ -444,9 +366,6 @@ theorem trunc_C_mul_T (n : ℤ) (r : R) : trunc (C r * T n) = ite (0 ≤ n) (mon
       IsEmpty.forall_iff]
 #align laurent_polynomial.trunc_C_mul_T LaurentPolynomial.trunc_C_mul_T
 
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-<too large>
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 @[simp]
 theorem leftInverse_trunc_toLaurent :
     Function.LeftInverse (trunc : R[T;T⁻¹] → R[X]) Polynomial.toLaurent :=
@@ -459,52 +378,25 @@ theorem leftInverse_trunc_toLaurent :
         if_true]
 #align laurent_polynomial.left_inverse_trunc_to_laurent LaurentPolynomial.leftInverse_trunc_toLaurent
 
-/- warning: polynomial.trunc_to_laurent -> Polynomial.trunc_toLaurent is a dubious translation:
-<too large>
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 @[simp]
 theorem Polynomial.trunc_toLaurent (f : R[X]) : trunc f.toLaurent = f :=
   leftInverse_trunc_toLaurent _
 #align polynomial.trunc_to_laurent Polynomial.trunc_toLaurent
 
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 theorem Polynomial.toLaurent_injective :
     Function.Injective (Polynomial.toLaurent : R[X] → R[T;T⁻¹]) :=
   leftInverse_trunc_toLaurent.Injective
 #align polynomial.to_laurent_injective Polynomial.toLaurent_injective
 
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 @[simp]
 theorem Polynomial.toLaurent_inj (f g : R[X]) : f.toLaurent = g.toLaurent ↔ f = g :=
   ⟨fun h => Polynomial.toLaurent_injective h, congr_arg _⟩
 #align polynomial.to_laurent_inj Polynomial.toLaurent_inj
 
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 theorem Polynomial.toLaurent_ne_zero {f : R[X]} : f ≠ 0 ↔ f.toLaurent ≠ 0 :=
   (map_ne_zero_iff _ Polynomial.toLaurent_injective).symm
 #align polynomial.to_laurent_ne_zero Polynomial.toLaurent_ne_zero
 
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-Case conversion may be inaccurate. Consider using '#align laurent_polynomial.exists_T_pow LaurentPolynomial.exists_T_powₓ'. -/
 theorem exists_T_pow (f : R[T;T⁻¹]) : ∃ (n : ℕ)(f' : R[X]), f'.toLaurent = f * T n :=
   by
   apply f.induction_on' _ fun n a => _ <;> clear f
@@ -519,12 +411,6 @@ theorem exists_T_pow (f : R[T;T⁻¹]) : ∃ (n : ℕ)(f' : R[X]), f'.toLaurent
         T_zero, mul_one]
 #align laurent_polynomial.exists_T_pow LaurentPolynomial.exists_T_pow
 
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-Case conversion may be inaccurate. Consider using '#align laurent_polynomial.induction_on_mul_T LaurentPolynomial.induction_on_mul_Tₓ'. -/
 /-- This is a version of `exists_T_pow` stated as an induction principle. -/
 @[elab_as_elim]
 theorem induction_on_mul_T {Q : R[T;T⁻¹] → Prop} (f : R[T;T⁻¹])
@@ -536,12 +422,6 @@ theorem induction_on_mul_T {Q : R[T;T⁻¹] → Prop} (f : R[T;T⁻¹])
   exact Qf
 #align laurent_polynomial.induction_on_mul_T LaurentPolynomial.induction_on_mul_T
 
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-Case conversion may be inaccurate. Consider using '#align laurent_polynomial.reduce_to_polynomial_of_mul_T LaurentPolynomial.reduce_to_polynomial_of_mul_Tₓ'. -/
 /-- Suppose that `Q` is a statement about Laurent polynomials such that
 * `Q` is true on *ordinary* polynomials;
 * `Q (f * T)` implies `Q f`;
@@ -558,34 +438,16 @@ theorem reduce_to_polynomial_of_mul_T (f : R[T;T⁻¹]) {Q : R[T;T⁻¹] → Pro
 
 section Support
 
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 theorem support_C_mul_T (a : R) (n : ℤ) : (C a * T n).support ⊆ {n} := by
   simpa only [← single_eq_C_mul_T] using support_single_subset
 #align laurent_polynomial.support_C_mul_T LaurentPolynomial.support_C_mul_T
 
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 theorem support_C_mul_T_of_ne_zero {a : R} (a0 : a ≠ 0) (n : ℤ) : (C a * T n).support = {n} :=
   by
   rw [← single_eq_C_mul_T]
   exact support_single_ne_zero _ a0
 #align laurent_polynomial.support_C_mul_T_of_ne_zero LaurentPolynomial.support_C_mul_T_of_ne_zero
 
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 /-- The support of a polynomial `f` is a finset in `ℕ`.  The lemma `to_laurent_support f`
 shows that the support of `f.to_laurent` is the same finset, but viewed in `ℤ` under the natural
 inclusion `ℕ ↪ ℤ`. -/
@@ -624,23 +486,11 @@ def degree (f : R[T;T⁻¹]) : WithBot ℤ :=
 #align laurent_polynomial.degree LaurentPolynomial.degree
 -/
 
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 @[simp]
 theorem degree_zero : degree (0 : R[T;T⁻¹]) = ⊥ :=
   rfl
 #align laurent_polynomial.degree_zero LaurentPolynomial.degree_zero
 
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 @[simp]
 theorem degree_eq_bot_iff {f : R[T;T⁻¹]} : f.degree = ⊥ ↔ f = 0 :=
   by
@@ -656,12 +506,6 @@ section ExactDegrees
 
 open Classical
 
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 @[simp]
 theorem degree_C_mul_T (n : ℤ) (a : R) (a0 : a ≠ 0) : (C a * T n).degree = n :=
   by
@@ -672,12 +516,6 @@ theorem degree_C_mul_T (n : ℤ) (a : R) (a0 : a ≠ 0) : (C a * T n).degree = n
     and_self_iff]
 #align laurent_polynomial.degree_C_mul_T LaurentPolynomial.degree_C_mul_T
 
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 theorem degree_C_mul_T_ite (n : ℤ) (a : R) : (C a * T n).degree = ite (a = 0) ⊥ n := by
   split_ifs with h h <;>
     simp only [h, map_zero, MulZeroClass.zero_mul, degree_zero, degree_C_mul_T, Ne.def,
@@ -693,24 +531,12 @@ theorem degree_T [Nontrivial R] (n : ℤ) : (T n : R[T;T⁻¹]).degree = n :=
 #align laurent_polynomial.degree_T LaurentPolynomial.degree_T
 -/
 
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 theorem degree_C {a : R} (a0 : a ≠ 0) : (C a).degree = 0 :=
   by
   rw [← mul_one (C a), ← T_zero]
   exact degree_C_mul_T 0 a a0
 #align laurent_polynomial.degree_C LaurentPolynomial.degree_C
 
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 theorem degree_C_ite (a : R) : (C a).degree = ite (a = 0) ⊥ 0 := by
   split_ifs with h h <;> simp only [h, map_zero, degree_zero, degree_C, Ne.def, not_false_iff]
 #align laurent_polynomial.degree_C_ite LaurentPolynomial.degree_C_ite
@@ -719,12 +545,6 @@ end ExactDegrees
 
 section DegreeBounds
 
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 theorem degree_C_mul_T_le (n : ℤ) (a : R) : (C a * T n).degree ≤ n :=
   by
   by_cases a0 : a = 0
@@ -732,22 +552,10 @@ theorem degree_C_mul_T_le (n : ℤ) (a : R) : (C a * T n).degree ≤ n :=
   · exact (degree_C_mul_T n a a0).le
 #align laurent_polynomial.degree_C_mul_T_le LaurentPolynomial.degree_C_mul_T_le
 
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 theorem degree_T_le (n : ℤ) : (T n : R[T;T⁻¹]).degree ≤ n :=
   (le_of_eq (by rw [map_one, one_mul])).trans (degree_C_mul_T_le n (1 : R))
 #align laurent_polynomial.degree_T_le LaurentPolynomial.degree_T_le
 
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 theorem degree_C_le (a : R) : (C a).degree ≤ 0 :=
   (le_of_eq (by rw [T_zero, mul_one])).trans (degree_C_mul_T_le 0 a)
 #align laurent_polynomial.degree_C_le LaurentPolynomial.degree_C_le
@@ -776,16 +584,10 @@ instance algebraPolynomial (R : Type _) [CommSemiring R] : Algebra R[X] R[T;T⁻
 #align laurent_polynomial.algebra_polynomial LaurentPolynomial.algebraPolynomial
 -/
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align laurent_polynomial.algebra_map_X_pow LaurentPolynomial.algebraMap_X_powₓ'. -/
 theorem algebraMap_X_pow (n : ℕ) : algebraMap R[X] R[T;T⁻¹] (X ^ n) = T n :=
   Polynomial.toLaurent_X_pow n
 #align laurent_polynomial.algebra_map_X_pow LaurentPolynomial.algebraMap_X_pow
 
-/- warning: laurent_polynomial.algebra_map_eq_to_laurent -> LaurentPolynomial.algebraMap_eq_toLaurent is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align laurent_polynomial.algebra_map_eq_to_laurent LaurentPolynomial.algebraMap_eq_toLaurentₓ'. -/
 @[simp]
 theorem algebraMap_eq_toLaurent (f : R[X]) : algebraMap R[X] R[T;T⁻¹] f = f.toLaurent :=
   rfl

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

@@ -210,9 +210,7 @@ theorem T_zero : (T 0 : R[T;T⁻¹]) = 1 :=
 -/
 
 #print LaurentPolynomial.T_add /-
-theorem T_add (m n : ℤ) : (T (m + n) : R[T;T⁻¹]) = T m * T n :=
-  by
-  convert single_mul_single.symm
+theorem T_add (m n : ℤ) : (T (m + n) : R[T;T⁻¹]) = T m * T n := by convert single_mul_single.symm;
   simp [T]
 #align laurent_polynomial.T_add LaurentPolynomial.T_add
 -/
@@ -368,11 +366,8 @@ protected theorem induction_on {M : R[T;T⁻¹] → Prop} (p : R[T;T⁻¹]) (h_C
   have B : ∀ s : Finset ℤ, M (s.Sum fun n : ℤ => C (p.to_fun n) * T n) :=
     by
     apply Finset.induction
-    · convert h_C 0
-      simp only [Finset.sum_empty, _root_.map_zero]
-    · intro n s ns ih
-      rw [Finset.sum_insert ns]
-      exact h_add A ih
+    · convert h_C 0; simp only [Finset.sum_empty, _root_.map_zero]
+    · intro n s ns ih; rw [Finset.sum_insert ns]; exact h_add A ih
   convert B p.support
   ext a
   simp_rw [← single_eq_C_mul_T, Finset.sum_apply', single_apply, Finset.sum_ite_eq']

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

@@ -163,10 +163,7 @@ def C : R →+* R[T;T⁻¹] :=
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.algebra_map_apply LaurentPolynomial.algebraMap_applyₓ'. -/
 theorem algebraMap_apply {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A] (r : R) :
     algebraMap R (LaurentPolynomial A) r = C (algebraMap R A r) :=
@@ -174,10 +171,7 @@ theorem algebraMap_apply {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R
 #align laurent_polynomial.algebra_map_apply LaurentPolynomial.algebraMap_apply
 
 /- warning: laurent_polynomial.C_eq_algebra_map -> LaurentPolynomial.C_eq_algebraMap is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.C_eq_algebra_map LaurentPolynomial.C_eq_algebraMapₓ'. -/
 /-- When we have `[comm_semiring R]`, the function `C` is the same as `algebra_map R R[T;T⁻¹]`.
 (But note that `C` is defined when `R` is not necessarily commutative, in which case
@@ -259,10 +253,7 @@ theorem single_eq_C_mul_T (r : R) (n : ℤ) : (single n r : R[T;T⁻¹]) = (C r
 #align laurent_polynomial.single_eq_C_mul_T LaurentPolynomial.single_eq_C_mul_T
 
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 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_C_mul_T Polynomial.toLaurent_C_mul_Tₓ'. -/
 -- This lemma locks in the right changes and is what Lean proved directly.
 -- The actual `simp`-normal form of a Laurent monomial is `C a * T n`, whenever it can be reached.
@@ -274,10 +265,7 @@ theorem Polynomial.toLaurent_C_mul_T (n : ℕ) (r : R) :
 #align polynomial.to_laurent_C_mul_T Polynomial.toLaurent_C_mul_T
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_C Polynomial.toLaurent_Cₓ'. -/
 @[simp]
 theorem Polynomial.toLaurent_C (r : R) : (Polynomial.C r).toLaurent = C r :=
@@ -311,10 +299,7 @@ theorem Polynomial.toLaurent_one : (Polynomial.toLaurent : R[X] → R[T;T⁻¹])
 #align polynomial.to_laurent_one Polynomial.toLaurent_one
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_C_mul_eq Polynomial.toLaurent_C_mul_eqₓ'. -/
 @[simp]
 theorem Polynomial.toLaurent_C_mul_eq (r : R) (f : R[X]) :
@@ -334,10 +319,7 @@ theorem Polynomial.toLaurent_X_pow (n : ℕ) : (X ^ n : R[X]).toLaurent = T n :=
 #align polynomial.to_laurent_X_pow Polynomial.toLaurent_X_pow
 
 /- warning: polynomial.to_laurent_C_mul_X_pow -> Polynomial.toLaurent_C_mul_X_pow is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_C_mul_X_pow Polynomial.toLaurent_C_mul_X_powₓ'. -/
 @[simp]
 theorem Polynomial.toLaurent_C_mul_X_pow (n : ℕ) (r : R) :
@@ -368,10 +350,7 @@ theorem isUnit_T (n : ℤ) : IsUnit (T n : R[T;T⁻¹]) :=
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.induction_on LaurentPolynomial.induction_onₓ'. -/
 @[elab_as_elim]
 protected theorem induction_on {M : R[T;T⁻¹] → Prop} (p : R[T;T⁻¹]) (h_C : ∀ a, M (C a))
@@ -448,10 +427,7 @@ def trunc : R[T;T⁻¹] →+ R[X] :=
 -/
 
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 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.trunc_C_mul_T LaurentPolynomial.trunc_C_mul_Tₓ'. -/
 @[simp]
 theorem trunc_C_mul_T (n : ℤ) (r : R) : trunc (C r * T n) = ite (0 ≤ n) (monomial n.toNat r) 0 :=
@@ -474,10 +450,7 @@ theorem trunc_C_mul_T (n : ℤ) (r : R) : trunc (C r * T n) = ite (0 ≤ n) (mon
 #align laurent_polynomial.trunc_C_mul_T LaurentPolynomial.trunc_C_mul_T
 
 /- warning: laurent_polynomial.left_inverse_trunc_to_laurent -> LaurentPolynomial.leftInverse_trunc_toLaurent is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.left_inverse_trunc_to_laurent LaurentPolynomial.leftInverse_trunc_toLaurentₓ'. -/
 @[simp]
 theorem leftInverse_trunc_toLaurent :
@@ -492,10 +465,7 @@ theorem leftInverse_trunc_toLaurent :
 #align laurent_polynomial.left_inverse_trunc_to_laurent LaurentPolynomial.leftInverse_trunc_toLaurent
 
 /- warning: polynomial.trunc_to_laurent -> Polynomial.trunc_toLaurent is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.trunc_to_laurent Polynomial.trunc_toLaurentₓ'. -/
 @[simp]
 theorem Polynomial.trunc_toLaurent (f : R[X]) : trunc f.toLaurent = f :=
@@ -812,20 +782,14 @@ instance algebraPolynomial (R : Type _) [CommSemiring R] : Algebra R[X] R[T;T⁻
 -/
 
 /- warning: laurent_polynomial.algebra_map_X_pow -> LaurentPolynomial.algebraMap_X_pow is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.algebra_map_X_pow LaurentPolynomial.algebraMap_X_powₓ'. -/
 theorem algebraMap_X_pow (n : ℕ) : algebraMap R[X] R[T;T⁻¹] (X ^ n) = T n :=
   Polynomial.toLaurent_X_pow n
 #align laurent_polynomial.algebra_map_X_pow LaurentPolynomial.algebraMap_X_pow
 
 /- warning: laurent_polynomial.algebra_map_eq_to_laurent -> LaurentPolynomial.algebraMap_eq_toLaurent is a dubious translation:
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(CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt)))))) (algebraMap.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt) (LaurentPolynomial.algebraPolynomial.{u1} R _inst_1)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.algebra_map_eq_to_laurent LaurentPolynomial.algebraMap_eq_toLaurentₓ'. -/
 @[simp]
 theorem algebraMap_eq_toLaurent (f : R[X]) : algebraMap R[X] R[T;T⁻¹] f = f.toLaurent :=

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

@@ -262,7 +262,7 @@ theorem single_eq_C_mul_T (r : R) (n : ℤ) : (single n r : R[T;T⁻¹]) = (C r
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (r : R), Eq.{succ u1} (LaurentPolynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (LaurentPolynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 (Nat.cast.{0} Int instNatCastInt n)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (LaurentPolynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 (Nat.cast.{0} Int instNatCastInt n)))
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_C_mul_T Polynomial.toLaurent_C_mul_Tₓ'. -/
 -- This lemma locks in the right changes and is what Lean proved directly.
 -- The actual `simp`-normal form of a Laurent monomial is `C a * T n`, whenever it can be reached.
@@ -451,7 +451,7 @@ def trunc : R[T;T⁻¹] →+ R[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (fun (_x : AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) => (LaurentPolynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (AddMonoidHom.hasCoeToFun.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.trunc.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 n))) (ite.{succ u1} (Polynomial.{u1} R _inst_1) (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) n) (Int.decLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) n) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (Int.toNat n)) r) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : LaurentPolynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R 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R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r) 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(LaurentPolynomial.T.{u1} R _inst_1 n))) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (fun (_x : LaurentPolynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : LaurentPolynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (AddHomClass.toFunLike.{u1, u1, u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddZeroClass.toAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))))))) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))))) (LaurentPolynomial.trunc.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 n))) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) r) (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) n) (Int.decLe (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) n) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (Int.toNat n)) r) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) r) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.zero.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.trunc_C_mul_T LaurentPolynomial.trunc_C_mul_Tₓ'. -/
 @[simp]
 theorem trunc_C_mul_T (n : ℤ) (r : R) : trunc (C r * T n) = ite (0 ≤ n) (monomial n.toNat r) 0 :=
@@ -464,7 +464,7 @@ theorem trunc_C_mul_T (n : ℤ) (r : R) : trunc (C r * T n) = ite (0 ≤ n) (mon
     erw [comap_domain_single, to_finsupp_iso_symm_apply]
     simp only [Int.coe_nat_nonneg, Int.toNat_coe_nat, if_true, to_finsupp_iso_apply,
       to_finsupp_monomial]
-  · lift -n to ℕ using (neg_pos.mpr (not_le.mp n0)).le
+  · lift -n to ℕ using (neg_pos.mpr (not_le.mp n0)).le with m
     rw [to_finsupp_iso_apply, to_finsupp_inj, if_neg n0]
     erw [to_finsupp_iso_symm_apply]
     ext a

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -464,7 +464,7 @@ theorem trunc_C_mul_T (n : ℤ) (r : R) : trunc (C r * T n) = ite (0 ≤ n) (mon
     erw [comap_domain_single, to_finsupp_iso_symm_apply]
     simp only [Int.coe_nat_nonneg, Int.toNat_coe_nat, if_true, to_finsupp_iso_apply,
       to_finsupp_monomial]
-  · lift -n to ℕ using (neg_pos.mpr (not_le.mp n0)).le with m
+  · lift -n to ℕ using (neg_pos.mpr (not_le.mp n0)).le
     rw [to_finsupp_iso_apply, to_finsupp_inj, if_neg n0]
     erw [to_finsupp_iso_symm_apply]
     ext a

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

@@ -109,7 +109,7 @@ def Polynomial.toLaurent [Semiring R] : R[X] →+* R[T;T⁻¹] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1), Eq.{succ u1} (LaurentPolynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) p) (Finsupp.mapDomain.{0, 0, u1} Nat Int R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe)))) (Polynomial.toFinsupp.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) p) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) p) (AddMonoidAlgebra.mapDomain.{u1, 0, 0} R Nat _inst_1 Int (Nat.cast.{0} Int instNatCastInt) (Polynomial.toFinsupp.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) p) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) p) (AddMonoidAlgebra.mapDomain.{u1, 0, 0} R Nat _inst_1 Int (Nat.cast.{0} Int instNatCastInt) (Polynomial.toFinsupp.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_apply Polynomial.toLaurent_applyₓ'. -/
 /-- This is not a simp lemma, as it is usually preferable to use the lemmas about `C` and `X`
 instead. -/
@@ -166,7 +166,7 @@ def C : R →+* R[T;T⁻¹] :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_2 : CommSemiring.{u1} R] [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_2 _inst_3] (r : R), Eq.{succ u2} (LaurentPolynomial.{u2} A _inst_3) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R (LaurentPolynomial.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u2} (LaurentPolynomial.{u2} A _inst_3) (AddMonoidAlgebra.semiring.{u2, 0} A Int _inst_3 Int.addMonoid))) (fun (_x : RingHom.{u1, u2} R (LaurentPolynomial.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u2} (LaurentPolynomial.{u2} A _inst_3) (AddMonoidAlgebra.semiring.{u2, 0} A Int _inst_3 Int.addMonoid))) => R -> (LaurentPolynomial.{u2} A _inst_3)) (RingHom.hasCoeToFun.{u1, u2} R (LaurentPolynomial.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u2} (LaurentPolynomial.{u2} A _inst_3) (AddMonoidAlgebra.semiring.{u2, 0} A Int _inst_3 Int.addMonoid))) (algebraMap.{u1, u2} R (LaurentPolynomial.{u2} A _inst_3) _inst_2 (AddMonoidAlgebra.semiring.{u2, 0} A Int _inst_3 Int.addMonoid) (AddMonoidAlgebra.algebra.{u2, 0, u1} A Int R _inst_2 _inst_3 _inst_4 Int.addMonoid)) r) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} A (LaurentPolynomial.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u2, 0} A Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u2, u2} A (LaurentPolynomial.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u2, 0} A Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => A -> (LaurentPolynomial.{u2} A _inst_3)) (RingHom.hasCoeToFun.{u2, u2} A (LaurentPolynomial.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u2, 0} A Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u2} A _inst_3) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} R A _inst_2 _inst_3 _inst_4) r))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_2 : CommSemiring.{u2} R] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_2 _inst_3] (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} A _inst_3) r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} A _inst_3) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} A _inst_3) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} A _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} A _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u2, u1} R (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt)))))) (algebraMap.{u2, u1} R (LaurentPolynomial.{u1} A _inst_3) _inst_2 (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt) (AddMonoidAlgebra.algebra.{u1, 0, u2} A Int R _inst_2 _inst_3 _inst_4 Int.instAddMonoidInt)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) => LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} A _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} A _inst_3))))) (algebraMap.{u2, u1} R A _inst_2 _inst_3 _inst_4) r))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_2 : CommSemiring.{u2} R] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_2 _inst_3] (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} A _inst_3) r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} A _inst_3) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} A _inst_3) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} A _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} A _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u2, u1} R (LaurentPolynomial.{u1} A _inst_3) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} A _inst_3) (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt)))))) (algebraMap.{u2, u1} R (LaurentPolynomial.{u1} A _inst_3) _inst_2 (AddMonoidAlgebra.semiring.{u1, 0} A Int _inst_3 Int.instAddMonoidInt) (AddMonoidAlgebra.algebra.{u1, 0, u2} A Int R _inst_2 _inst_3 _inst_4 Int.instAddMonoidInt)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) => LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (LaurentPolynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) Int _inst_3 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} A _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} A _inst_3))))) (algebraMap.{u2, u1} R A _inst_2 _inst_3 _inst_4) r))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.algebra_map_apply LaurentPolynomial.algebraMap_applyₓ'. -/
 theorem algebraMap_apply {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A] (r : R) :
     algebraMap R (LaurentPolynomial A) r = C (algebraMap R A r) :=
@@ -177,7 +177,7 @@ theorem algebraMap_apply {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_2 : CommSemiring.{u1} R] (r : R), Eq.{succ u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2))) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2))) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.addMonoid))) (algebraMap.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) _inst_2 (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.addMonoid) (AddMonoidAlgebra.algebra.{u1, 0, u1} R Int R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_2) (Algebra.id.{u1} R _inst_2) Int.addMonoid)) r)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_2 : CommSemiring.{u1} R] (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt)))))) (algebraMap.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) _inst_2 (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt) (AddMonoidAlgebra.algebra.{u1, 0, u1} R Int R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_2) (Algebra.id.{u1} R _inst_2) Int.instAddMonoidInt)) r)
+  forall {R : Type.{u1}} [_inst_2 : CommSemiring.{u1} R] (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt)))))) (algebraMap.{u1, u1} R (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) _inst_2 (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_2) Int.instAddMonoidInt) (AddMonoidAlgebra.algebra.{u1, 0, u1} R Int R _inst_2 (CommSemiring.toSemiring.{u1} R _inst_2) (Algebra.id.{u1} R _inst_2) Int.instAddMonoidInt)) r)
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.C_eq_algebra_map LaurentPolynomial.C_eq_algebraMapₓ'. -/
 /-- When we have `[comm_semiring R]`, the function `C` is the same as `algebra_map R R[T;T⁻¹]`.
 (But note that `C` is defined when `R` is not necessarily commutative, in which case
@@ -191,7 +191,7 @@ theorem C_eq_algebraMap {R : Type _} [CommSemiring R] (r : R) : C r = algebraMap
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} (Finsupp.{0, u1} Int R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Finsupp.single.{0, u1} Int R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) r)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} (Finsupp.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Finsupp.single.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} (Finsupp.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Finsupp.single.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r)
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.single_eq_C LaurentPolynomial.single_eq_Cₓ'. -/
 theorem single_eq_C (r : R) : single 0 r = C r :=
   rfl
@@ -251,7 +251,7 @@ theorem mul_T_assoc (f : R[T;T⁻¹]) (m n : ℤ) : f * T m * T n = f * T (m + n
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (n : Int), Eq.{succ u1} (Finsupp.{0, u1} Int R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Finsupp.single.{0, u1} Int R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) n r) (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (n : Int), Eq.{succ u1} (Finsupp.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Finsupp.single.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) n r) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) r) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) r) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 n))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (n : Int), Eq.{succ u1} (Finsupp.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Finsupp.single.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) n r) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 n))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.single_eq_C_mul_T LaurentPolynomial.single_eq_C_mul_Tₓ'. -/
 @[simp]
 theorem single_eq_C_mul_T (r : R) (n : ℤ) : (single n r : R[T;T⁻¹]) = (C r * T n : R[T;T⁻¹]) := by
@@ -262,7 +262,7 @@ theorem single_eq_C_mul_T (r : R) (n : ℤ) : (single n r : R[T;T⁻¹]) = (C r
 lean 3 declaration is
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 but is expected to have type
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Polynomial.{u1} R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (LaurentPolynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 (Nat.cast.{0} Int instNatCastInt n)))
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_C_mul_T Polynomial.toLaurent_C_mul_Tₓ'. -/
 -- This lemma locks in the right changes and is what Lean proved directly.
 -- The actual `simp`-normal form of a Laurent monomial is `C a * T n`, whenever it can be reached.
@@ -277,7 +277,7 @@ theorem Polynomial.toLaurent_C_mul_T (n : ℕ) (r : R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} (LaurentPolynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) r)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r)
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_C Polynomial.toLaurent_Cₓ'. -/
 @[simp]
 theorem Polynomial.toLaurent_C (r : R) : (Polynomial.C r).toLaurent = C r :=
@@ -290,7 +290,7 @@ theorem Polynomial.toLaurent_C (r : R) : (Polynomial.C r).toLaurent = C r :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (LaurentPolynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) (LaurentPolynomial.T.{u1} R _inst_1 (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) (LaurentPolynomial.T.{u1} R _inst_1 (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) (LaurentPolynomial.T.{u1} R _inst_1 (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_X Polynomial.toLaurent_Xₓ'. -/
 @[simp]
 theorem Polynomial.toLaurent_X : (Polynomial.X.toLaurent : R[T;T⁻¹]) = T 1 :=
@@ -303,7 +303,7 @@ theorem Polynomial.toLaurent_X : (Polynomial.X.toLaurent : R[T;T⁻¹]) = T 1 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (LaurentPolynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 1 (One.one.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.hasOne.{u1} R _inst_1))))) (OfNat.ofNat.{u1} (LaurentPolynomial.{u1} R _inst_1) 1 (OfNat.mk.{u1} (LaurentPolynomial.{u1} R _inst_1) 1 (One.one.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.one.{u1, 0} R Int _inst_1 Int.hasZero))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (AddMonoidAlgebra.one.{u1, 0} R Int _inst_1 (CommMonoidWithZero.toZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (AddMonoidAlgebra.one.{u1, 0} R Int _inst_1 (CommMonoidWithZero.toZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_one Polynomial.toLaurent_oneₓ'. -/
 @[simp]
 theorem Polynomial.toLaurent_one : (Polynomial.toLaurent : R[X] → R[T;T⁻¹]) 1 = 1 :=
@@ -314,7 +314,7 @@ theorem Polynomial.toLaurent_one : (Polynomial.toLaurent : R[X] → R[T;T⁻¹])
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (LaurentPolynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r) f)) (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) f))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) 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_inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) 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_inst_1) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) r) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) 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(Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) f)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f))
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_C_mul_eq Polynomial.toLaurent_C_mul_eqₓ'. -/
 @[simp]
 theorem Polynomial.toLaurent_C_mul_eq (r : R) (f : R[X]) :
@@ -326,7 +326,7 @@ theorem Polynomial.toLaurent_C_mul_eq (r : R) (f : R[X]) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat), Eq.{succ u1} (LaurentPolynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)) (LaurentPolynomial.T.{u1} R _inst_1 ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)) (LaurentPolynomial.T.{u1} R _inst_1 (Nat.cast.{0} Int instNatCastInt n))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)) (LaurentPolynomial.T.{u1} R _inst_1 (Nat.cast.{0} Int instNatCastInt n))
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_X_pow Polynomial.toLaurent_X_powₓ'. -/
 @[simp]
 theorem Polynomial.toLaurent_X_pow (n : ℕ) : (X ^ n : R[X]).toLaurent = T n := by
@@ -337,7 +337,7 @@ theorem Polynomial.toLaurent_X_pow (n : ℕ) : (X ^ n : R[X]).toLaurent = T n :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (r : R), Eq.{succ u1} (LaurentPolynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n))) (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n)))
 but is expected to have type
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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) 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(AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun 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_inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) r) (LaurentPolynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) 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+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (LaurentPolynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 (Nat.cast.{0} Int instNatCastInt n)))
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_C_mul_X_pow Polynomial.toLaurent_C_mul_X_powₓ'. -/
 @[simp]
 theorem Polynomial.toLaurent_C_mul_X_pow (n : ℕ) (r : R) :
@@ -371,7 +371,7 @@ theorem isUnit_T (n : ℤ) : IsUnit (T n : R[T;T⁻¹]) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : (LaurentPolynomial.{u1} R _inst_1) -> Prop} (p : LaurentPolynomial.{u1} R _inst_1), (forall (a : R), M (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a)) -> (forall {p : LaurentPolynomial.{u1} R _inst_1} {q : LaurentPolynomial.{u1} R _inst_1}, (M p) -> (M q) -> (M (HAdd.hAdd.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (Distrib.toHasAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonUnitalNonAssocSemiring.{u1, 0} R Int _inst_1 Int.hasAdd)))) p q))) -> (forall (n : Nat) (a : R), (M (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n)))) -> (M (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))))))) -> (forall (n : Nat) (a : R), (M (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 (Neg.neg.{0} Int Int.hasNeg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n))))) -> (M (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) (Neg.neg.{0} Int Int.hasNeg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n)) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))))))) -> (M p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : (LaurentPolynomial.{u1} R _inst_1) -> Prop} (p : LaurentPolynomial.{u1} R _inst_1), (forall (a : R), M (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a)) -> (forall {p : LaurentPolynomial.{u1} R _inst_1} {q : LaurentPolynomial.{u1} R _inst_1}, (M p) -> (M q) -> (M (HAdd.hAdd.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (Distrib.toAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonUnitalNonAssocSemiring.{u1, 0} R Int _inst_1 Int.instAddInt)))) p q))) -> (forall (n : Nat) (a : R), (M (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 (Nat.cast.{0} Int instNatCastInt n)))) -> (M (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (Nat.cast.{0} Int instNatCastInt n) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))))) -> (forall (n : Nat) (a : R), (M (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 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(OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))))) -> (forall (n : Nat) (a : R), (M (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 (Neg.neg.{0} Int Int.instNegInt (Nat.cast.{0} Int instNatCastInt n))))) -> (M (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (Neg.neg.{0} Int Int.instNegInt (Nat.cast.{0} Int instNatCastInt n)) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))))) -> (M p)
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.induction_on LaurentPolynomial.induction_onₓ'. -/
 @[elab_as_elim]
 protected theorem induction_on {M : R[T;T⁻¹] → Prop} (p : R[T;T⁻¹]) (h_C : ∀ a, M (C a))
@@ -406,7 +406,7 @@ protected theorem induction_on {M : R[T;T⁻¹] → Prop} (p : R[T;T⁻¹]) (h_C
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : (LaurentPolynomial.{u1} R _inst_1) -> Prop} (p : LaurentPolynomial.{u1} R _inst_1), (forall (p : LaurentPolynomial.{u1} R _inst_1) (q : LaurentPolynomial.{u1} R _inst_1), (M p) -> (M q) -> (M (HAdd.hAdd.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (Distrib.toHasAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonUnitalNonAssocSemiring.{u1, 0} R Int _inst_1 Int.hasAdd)))) p q))) -> (forall (n : Int) (a : R), M (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) -> (M p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : (LaurentPolynomial.{u1} R _inst_1) -> Prop} (p : LaurentPolynomial.{u1} R _inst_1), (forall (p : LaurentPolynomial.{u1} R _inst_1) (q : LaurentPolynomial.{u1} R _inst_1), (M p) -> (M q) -> (M (HAdd.hAdd.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (Distrib.toAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonUnitalNonAssocSemiring.{u1, 0} R Int _inst_1 Int.instAddInt)))) p q))) -> (forall (n : Int) (a : R), M (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) -> (M p)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : (LaurentPolynomial.{u1} R _inst_1) -> Prop} (p : LaurentPolynomial.{u1} R _inst_1), (forall (p : LaurentPolynomial.{u1} R _inst_1) (q : LaurentPolynomial.{u1} R _inst_1), (M p) -> (M q) -> (M (HAdd.hAdd.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (Distrib.toAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonUnitalNonAssocSemiring.{u1, 0} R Int _inst_1 Int.instAddInt)))) p q))) -> (forall (n : Int) (a : R), M (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) -> (M p)
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.induction_on' LaurentPolynomial.induction_on'ₓ'. -/
 /-- To prove something about Laurent polynomials, it suffices to show that
 * the condition is closed under taking sums, and
@@ -451,7 +451,7 @@ def trunc : R[T;T⁻¹] →+ R[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (fun (_x : AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) => (LaurentPolynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (AddMonoidHom.hasCoeToFun.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.trunc.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) 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 but is expected to have type
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(Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) 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+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : LaurentPolynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R 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R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 n))) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (fun (_x : LaurentPolynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : LaurentPolynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (AddHomClass.toFunLike.{u1, u1, u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddZeroClass.toAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))))))) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))))) (LaurentPolynomial.trunc.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) r) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) 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(Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (Int.toNat n)) r) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) r) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.zero.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.trunc_C_mul_T LaurentPolynomial.trunc_C_mul_Tₓ'. -/
 @[simp]
 theorem trunc_C_mul_T (n : ℤ) (r : R) : trunc (C r * T n) = ite (0 ≤ n) (monomial n.toNat r) 0 :=
@@ -477,7 +477,7 @@ theorem trunc_C_mul_T (n : ℤ) (r : R) : trunc (C r * T n) = ite (0 ≤ n) (mon
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Function.LeftInverse.{succ u1, succ u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (fun (_x : AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) => (LaurentPolynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (AddMonoidHom.hasCoeToFun.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.trunc.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Function.LeftInverse.{succ u1, succ u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (fun (_x : LaurentPolynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : LaurentPolynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (AddHomClass.toFunLike.{u1, u1, u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddZeroClass.toAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))))))) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))))) (LaurentPolynomial.trunc.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Function.LeftInverse.{succ u1, succ u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (fun (_x : LaurentPolynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : LaurentPolynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (AddHomClass.toFunLike.{u1, u1, u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddZeroClass.toAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))))))) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))))) (LaurentPolynomial.trunc.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.left_inverse_trunc_to_laurent LaurentPolynomial.leftInverse_trunc_toLaurentₓ'. -/
 @[simp]
 theorem leftInverse_trunc_toLaurent :
@@ -495,7 +495,7 @@ theorem leftInverse_trunc_toLaurent :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (fun (_x : AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) => (LaurentPolynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (AddMonoidHom.hasCoeToFun.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.trunc.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) f)) f
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : LaurentPolynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (a : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (fun (_x : LaurentPolynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : LaurentPolynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (AddHomClass.toFunLike.{u1, u1, u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddZeroClass.toAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))))))) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R 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(NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))))) (LaurentPolynomial.trunc.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) 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(AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f)) f
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : LaurentPolynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (a : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) 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Int Int.instAddMonoidInt))))))) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))))) (LaurentPolynomial.trunc.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f)) f
 Case conversion may be inaccurate. Consider using '#align polynomial.trunc_to_laurent Polynomial.trunc_toLaurentₓ'. -/
 @[simp]
 theorem Polynomial.trunc_toLaurent (f : R[X]) : trunc f.toLaurent = f :=
@@ -506,7 +506,7 @@ theorem Polynomial.trunc_toLaurent (f : R[X]) : trunc f.toLaurent = f :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Function.Injective.{succ u1, succ u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Function.Injective.{succ u1, succ u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Function.Injective.{succ u1, succ u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1))
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_injective Polynomial.toLaurent_injectiveₓ'. -/
 theorem Polynomial.toLaurent_injective :
     Function.Injective (Polynomial.toLaurent : R[X] → R[T;T⁻¹]) :=
@@ -517,7 +517,7 @@ theorem Polynomial.toLaurent_injective :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), Iff (Eq.{succ u1} (LaurentPolynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) f) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) g)) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) f g)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) g)) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) f g)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) g)) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) f g)
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_inj Polynomial.toLaurent_injₓ'. -/
 @[simp]
 theorem Polynomial.toLaurent_inj (f g : R[X]) : f.toLaurent = g.toLaurent ↔ f = g :=
@@ -528,7 +528,7 @@ theorem Polynomial.toLaurent_inj (f g : R[X]) : f.toLaurent = g.toLaurent ↔ f
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Ne.{succ u1} (Polynomial.{u1} R _inst_1) f (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) (Ne.{succ u1} (LaurentPolynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) f) (OfNat.ofNat.{u1} (LaurentPolynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (LaurentPolynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (LaurentPolynomial.{u1} R _inst_1) (MulZeroClass.toHasZero.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonUnitalNonAssocSemiring.{u1, 0} R Int _inst_1 Int.hasAdd)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Ne.{succ u1} (Polynomial.{u1} R _inst_1) f (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (AddMonoidAlgebra.semiring.{u1, 0} R Int _inst_1 Int.instAddMonoidInt))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Ne.{succ u1} (Polynomial.{u1} R _inst_1) f (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (AddMonoidAlgebra.semiring.{u1, 0} R Int _inst_1 Int.instAddMonoidInt))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_ne_zero Polynomial.toLaurent_ne_zeroₓ'. -/
 theorem Polynomial.toLaurent_ne_zero {f : R[X]} : f ≠ 0 ↔ f.toLaurent ≠ 0 :=
   (map_ne_zero_iff _ Polynomial.toLaurent_injective).symm
@@ -538,7 +538,7 @@ theorem Polynomial.toLaurent_ne_zero {f : R[X]} : f ≠ 0 ↔ f.toLaurent ≠ 0
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : LaurentPolynomial.{u1} R _inst_1), Exists.{1} Nat (fun (n : Nat) => Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (f' : Polynomial.{u1} R _inst_1) => Eq.{succ u1} (LaurentPolynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) f') (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) f (LaurentPolynomial.T.{u1} R _inst_1 ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : LaurentPolynomial.{u1} R _inst_1), Exists.{1} Nat (fun (n : Nat) => Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (f' : Polynomial.{u1} R _inst_1) => Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f') (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f') (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f') (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) f (LaurentPolynomial.T.{u1} R _inst_1 (Nat.cast.{0} Int instNatCastInt n)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : LaurentPolynomial.{u1} R _inst_1), Exists.{1} Nat (fun (n : Nat) => Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (f' : Polynomial.{u1} R _inst_1) => Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f') (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f') (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f') (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) f (LaurentPolynomial.T.{u1} R _inst_1 (Nat.cast.{0} Int instNatCastInt n)))))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.exists_T_pow LaurentPolynomial.exists_T_powₓ'. -/
 theorem exists_T_pow (f : R[T;T⁻¹]) : ∃ (n : ℕ)(f' : R[X]), f'.toLaurent = f * T n :=
   by
@@ -558,7 +558,7 @@ theorem exists_T_pow (f : R[T;T⁻¹]) : ∃ (n : ℕ)(f' : R[X]), f'.toLaurent
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {Q : (LaurentPolynomial.{u1} R _inst_1) -> Prop} (f : LaurentPolynomial.{u1} R _inst_1), (forall {f : Polynomial.{u1} R _inst_1} {n : Nat}, Q (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) f) (LaurentPolynomial.T.{u1} R _inst_1 (Neg.neg.{0} Int Int.hasNeg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n))))) -> (Q f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {Q : (LaurentPolynomial.{u1} R _inst_1) -> Prop} (f : LaurentPolynomial.{u1} R _inst_1), (forall {f : Polynomial.{u1} R _inst_1} {n : Nat}, Q (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f) (LaurentPolynomial.T.{u1} R _inst_1 (Neg.neg.{0} Int Int.instNegInt (Nat.cast.{0} Int instNatCastInt n))))) -> (Q f)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {Q : (LaurentPolynomial.{u1} R _inst_1) -> Prop} (f : LaurentPolynomial.{u1} R _inst_1), (forall {f : Polynomial.{u1} R _inst_1} {n : Nat}, Q (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f) (LaurentPolynomial.T.{u1} R _inst_1 (Neg.neg.{0} Int Int.instNegInt (Nat.cast.{0} Int instNatCastInt n))))) -> (Q f)
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.induction_on_mul_T LaurentPolynomial.induction_on_mul_Tₓ'. -/
 /-- This is a version of `exists_T_pow` stated as an induction principle. -/
 @[elab_as_elim]
@@ -575,7 +575,7 @@ theorem induction_on_mul_T {Q : R[T;T⁻¹] → Prop} (f : R[T;T⁻¹])
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : LaurentPolynomial.{u1} R _inst_1) {Q : (LaurentPolynomial.{u1} R _inst_1) -> Prop}, (forall (f : Polynomial.{u1} R _inst_1), Q (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) f)) -> (forall (f : LaurentPolynomial.{u1} R _inst_1), (Q (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) f (LaurentPolynomial.T.{u1} R _inst_1 (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))))) -> (Q f)) -> (Q f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : LaurentPolynomial.{u1} R _inst_1) {Q : (LaurentPolynomial.{u1} R _inst_1) -> Prop}, (forall (f : Polynomial.{u1} R _inst_1), Q (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f)) -> (forall (f : LaurentPolynomial.{u1} R _inst_1), (Q (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) f (LaurentPolynomial.T.{u1} R _inst_1 (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))) -> (Q f)) -> (Q f)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : LaurentPolynomial.{u1} R _inst_1) {Q : (LaurentPolynomial.{u1} R _inst_1) -> Prop}, (forall (f : Polynomial.{u1} R _inst_1), Q (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f)) -> (forall (f : LaurentPolynomial.{u1} R _inst_1), (Q (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) f (LaurentPolynomial.T.{u1} R _inst_1 (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))) -> (Q f)) -> (Q f)
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.reduce_to_polynomial_of_mul_T LaurentPolynomial.reduce_to_polynomial_of_mul_Tₓ'. -/
 /-- Suppose that `Q` is a statement about Laurent polynomials such that
 * `Q` is true on *ordinary* polynomials;
@@ -597,7 +597,7 @@ section Support
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R) (n : Int), HasSubset.Subset.{0} (Finset.{0} Int) (Finset.hasSubset.{0} Int) (Finsupp.support.{0, u1} Int R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) (Singleton.singleton.{0, 0} Int (Finset.{0} Int) (Finset.hasSingleton.{0} Int) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R) (n : Int), HasSubset.Subset.{0} (Finset.{0} Int) (Finset.instHasSubsetFinset.{0} Int) (Finsupp.support.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (Finsupp.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) (Singleton.singleton.{0, 0} Int (Finset.{0} Int) (Finset.instSingletonFinset.{0} Int) n)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R) (n : Int), HasSubset.Subset.{0} (Finset.{0} Int) (Finset.instHasSubsetFinset.{0} Int) (Finsupp.support.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (Finsupp.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) (Singleton.singleton.{0, 0} Int (Finset.{0} Int) (Finset.instSingletonFinset.{0} Int) n)
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.support_C_mul_T LaurentPolynomial.support_C_mul_Tₓ'. -/
 theorem support_C_mul_T (a : R) (n : ℤ) : (C a * T n).support ⊆ {n} := by
   simpa only [← single_eq_C_mul_T] using support_single_subset
@@ -607,7 +607,7 @@ theorem support_C_mul_T (a : R) (n : ℤ) : (C a * T n).support ⊆ {n} := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (forall (n : Int), Eq.{1} (Finset.{0} Int) (Finsupp.support.{0, u1} Int R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) (Singleton.singleton.{0, 0} Int (Finset.{0} Int) (Finset.hasSingleton.{0} Int) n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (forall (n : Int), Eq.{1} (Finset.{0} Int) (Finsupp.support.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (Finsupp.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) (Singleton.singleton.{0, 0} Int (Finset.{0} Int) (Finset.instSingletonFinset.{0} Int) n))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (forall (n : Int), Eq.{1} (Finset.{0} Int) (Finsupp.support.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (Finsupp.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) (Singleton.singleton.{0, 0} Int (Finset.{0} Int) (Finset.instSingletonFinset.{0} Int) n))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.support_C_mul_T_of_ne_zero LaurentPolynomial.support_C_mul_T_of_ne_zeroₓ'. -/
 theorem support_C_mul_T_of_ne_zero {a : R} (a0 : a ≠ 0) (n : ℤ) : (C a * T n).support = {n} :=
   by
@@ -619,7 +619,7 @@ theorem support_C_mul_T_of_ne_zero {a : R} (a0 : a ≠ 0) (n : ℤ) : (C a * T n
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{1} (Finset.{0} Int) (Finsupp.support.{0, u1} Int R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) f)) (Finset.map.{0, 0} Nat Int (Nat.castEmbedding.{0} Int (AddGroupWithOne.toAddMonoidWithOne.{0} Int (AddCommGroupWithOne.toAddGroupWithOne.{0} Int (Ring.toAddCommGroupWithOne.{0} Int Int.ring))) (StrictOrderedSemiring.to_charZero.{0} Int (StrictOrderedRing.toStrictOrderedSemiring.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))) (Polynomial.support.{u1} R _inst_1 f))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{1} (Finset.{0} Int) (Finsupp.support.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f)) (Finset.map.{0, 0} Nat Int (Nat.castEmbedding.{0} Int (AddGroupWithOne.toAddMonoidWithOne.{0} Int (Ring.toAddGroupWithOne.{0} Int Int.instRingInt)) (StrictOrderedSemiring.to_charZero.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.support.{u1} R _inst_1 f))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{1} (Finset.{0} Int) (Finsupp.support.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f)) (Finset.map.{0, 0} Nat Int (Nat.castEmbedding.{0} Int (AddGroupWithOne.toAddMonoidWithOne.{0} Int (Ring.toAddGroupWithOne.{0} Int Int.instRingInt)) (StrictOrderedSemiring.to_charZero.{0} Int (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Int (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Int (LinearOrderedCommRing.toLinearOrderedCommSemiring.{0} Int Int.linearOrderedCommRing))))) (Polynomial.support.{u1} R _inst_1 f))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.to_laurent_support LaurentPolynomial.toLaurent_supportₓ'. -/
 /-- The support of a polynomial `f` is a finset in `ℕ`.  The lemma `to_laurent_support f`
 shows that the support of `f.to_laurent` is the same finset, but viewed in `ℤ` under the natural
@@ -695,7 +695,7 @@ open Classical
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (a : R), (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} (WithBot.{0} Int) (LaurentPolynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (WithBot.{0} Int) (HasLiftT.mk.{1, 1} Int (WithBot.{0} Int) (CoeTCₓ.coe.{1, 1} Int (WithBot.{0} Int) (WithBot.hasCoeT.{0} Int))) n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (a : R), (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} (WithBot.{0} Int) (LaurentPolynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) (WithBot.some.{0} Int n))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (a : R), (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} (WithBot.{0} Int) (LaurentPolynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) (WithBot.some.{0} Int n))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_C_mul_T LaurentPolynomial.degree_C_mul_Tₓ'. -/
 @[simp]
 theorem degree_C_mul_T (n : ℤ) (a : R) (a0 : a ≠ 0) : (C a * T n).degree = n :=
@@ -711,7 +711,7 @@ theorem degree_C_mul_T (n : ℤ) (a : R) (a0 : a ≠ 0) : (C a * T n).degree = n
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (a : R), Eq.{1} (WithBot.{0} Int) (LaurentPolynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) (ite.{1} (WithBot.{0} Int) (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (Classical.propDecidable (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) (Bot.bot.{0} (WithBot.{0} Int) (WithBot.hasBot.{0} Int)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (WithBot.{0} Int) (HasLiftT.mk.{1, 1} Int (WithBot.{0} Int) (CoeTCₓ.coe.{1, 1} Int (WithBot.{0} Int) (WithBot.hasCoeT.{0} Int))) n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (a : R), Eq.{1} (WithBot.{0} Int) (LaurentPolynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) (ite.{1} (WithBot.{0} Int) (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (Classical.propDecidable (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (Bot.bot.{0} (WithBot.{0} Int) (WithBot.bot.{0} Int)) (WithBot.some.{0} Int n))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (a : R), Eq.{1} (WithBot.{0} Int) (LaurentPolynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) (ite.{1} (WithBot.{0} Int) (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (Classical.propDecidable (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (Bot.bot.{0} (WithBot.{0} Int) (WithBot.bot.{0} Int)) (WithBot.some.{0} Int n))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_C_mul_T_ite LaurentPolynomial.degree_C_mul_T_iteₓ'. -/
 theorem degree_C_mul_T_ite (n : ℤ) (a : R) : (C a * T n).degree = ite (a = 0) ⊥ n := by
   split_ifs with h h <;>
@@ -732,7 +732,7 @@ theorem degree_T [Nontrivial R] (n : ℤ) : (T n : R[T;T⁻¹]).degree = n :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} (WithBot.{0} Int) (LaurentPolynomial.degree.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a)) (OfNat.ofNat.{0} (WithBot.{0} Int) 0 (OfNat.mk.{0} (WithBot.{0} Int) 0 (Zero.zero.{0} (WithBot.{0} Int) (WithBot.hasZero.{0} Int Int.hasZero)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} (WithBot.{0} Int) (LaurentPolynomial.degree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a)) (OfNat.ofNat.{0} (WithBot.{0} Int) 0 (Zero.toOfNat0.{0} (WithBot.{0} Int) (WithBot.zero.{0} Int (CommMonoidWithZero.toZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {a : R}, (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} (WithBot.{0} Int) (LaurentPolynomial.degree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a)) (OfNat.ofNat.{0} (WithBot.{0} Int) 0 (Zero.toOfNat0.{0} (WithBot.{0} Int) (WithBot.zero.{0} Int (CommMonoidWithZero.toZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_C LaurentPolynomial.degree_Cₓ'. -/
 theorem degree_C {a : R} (a0 : a ≠ 0) : (C a).degree = 0 :=
   by
@@ -744,7 +744,7 @@ theorem degree_C {a : R} (a0 : a ≠ 0) : (C a).degree = 0 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), Eq.{1} (WithBot.{0} Int) (LaurentPolynomial.degree.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a)) (ite.{1} (WithBot.{0} Int) (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (Classical.propDecidable (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) (Bot.bot.{0} (WithBot.{0} Int) (WithBot.hasBot.{0} Int)) (OfNat.ofNat.{0} (WithBot.{0} Int) 0 (OfNat.mk.{0} (WithBot.{0} Int) 0 (Zero.zero.{0} (WithBot.{0} Int) (WithBot.hasZero.{0} Int Int.hasZero)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), Eq.{1} (WithBot.{0} Int) (LaurentPolynomial.degree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a)) (ite.{1} (WithBot.{0} Int) (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (Classical.propDecidable (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (Bot.bot.{0} (WithBot.{0} Int) (WithBot.bot.{0} Int)) (OfNat.ofNat.{0} (WithBot.{0} Int) 0 (Zero.toOfNat0.{0} (WithBot.{0} Int) (WithBot.zero.{0} Int (CommMonoidWithZero.toZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), Eq.{1} (WithBot.{0} Int) (LaurentPolynomial.degree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a)) (ite.{1} (WithBot.{0} Int) (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (Classical.propDecidable (Eq.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (Bot.bot.{0} (WithBot.{0} Int) (WithBot.bot.{0} Int)) (OfNat.ofNat.{0} (WithBot.{0} Int) 0 (Zero.toOfNat0.{0} (WithBot.{0} Int) (WithBot.zero.{0} Int (CommMonoidWithZero.toZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_C_ite LaurentPolynomial.degree_C_iteₓ'. -/
 theorem degree_C_ite (a : R) : (C a).degree = ite (a = 0) ⊥ 0 := by
   split_ifs with h h <;> simp only [h, map_zero, degree_zero, degree_C, Ne.def, not_false_iff]
@@ -758,7 +758,7 @@ section DegreeBounds
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (a : R), LE.le.{0} (WithBot.{0} Int) (Preorder.toHasLe.{0} (WithBot.{0} Int) (WithBot.preorder.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (LaurentPolynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (WithBot.{0} Int) (HasLiftT.mk.{1, 1} Int (WithBot.{0} Int) (CoeTCₓ.coe.{1, 1} Int (WithBot.{0} Int) (WithBot.hasCoeT.{0} Int))) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (a : R), LE.le.{0} (WithBot.{0} Int) (Preorder.toLE.{0} (WithBot.{0} Int) (WithBot.preorder.{0} Int (PartialOrder.toPreorder.{0} Int (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (LaurentPolynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) (WithBot.some.{0} Int n)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (a : R), LE.le.{0} (WithBot.{0} Int) (Preorder.toLE.{0} (WithBot.{0} Int) (WithBot.preorder.{0} Int (PartialOrder.toPreorder.{0} Int (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (LaurentPolynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) (WithBot.some.{0} Int n)
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_C_mul_T_le LaurentPolynomial.degree_C_mul_T_leₓ'. -/
 theorem degree_C_mul_T_le (n : ℤ) (a : R) : (C a * T n).degree ≤ n :=
   by
@@ -781,7 +781,7 @@ theorem degree_T_le (n : ℤ) : (T n : R[T;T⁻¹]).degree ≤ n :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), LE.le.{0} (WithBot.{0} Int) (Preorder.toHasLe.{0} (WithBot.{0} Int) (WithBot.preorder.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (LaurentPolynomial.degree.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a)) (OfNat.ofNat.{0} (WithBot.{0} Int) 0 (OfNat.mk.{0} (WithBot.{0} Int) 0 (Zero.zero.{0} (WithBot.{0} Int) (WithBot.hasZero.{0} Int Int.hasZero))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), LE.le.{0} (WithBot.{0} Int) (Preorder.toLE.{0} (WithBot.{0} Int) (WithBot.preorder.{0} Int (PartialOrder.toPreorder.{0} Int (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (LaurentPolynomial.degree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a)) (OfNat.ofNat.{0} (WithBot.{0} Int) 0 (Zero.toOfNat0.{0} (WithBot.{0} Int) (WithBot.zero.{0} Int (CommMonoidWithZero.toZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), LE.le.{0} (WithBot.{0} Int) (Preorder.toLE.{0} (WithBot.{0} Int) (WithBot.preorder.{0} Int (PartialOrder.toPreorder.{0} Int (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (LaurentPolynomial.degree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a)) (OfNat.ofNat.{0} (WithBot.{0} Int) 0 (Zero.toOfNat0.{0} (WithBot.{0} Int) (WithBot.zero.{0} Int (CommMonoidWithZero.toZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_C_le LaurentPolynomial.degree_C_leₓ'. -/
 theorem degree_C_le (a : R) : (C a).degree ≤ 0 :=
   (le_of_eq (by rw [T_zero, mul_one])).trans (degree_C_mul_T_le 0 a)
@@ -815,7 +815,7 @@ instance algebraPolynomial (R : Type _) [CommSemiring R] : Algebra R[X] R[T;T⁻
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Nat), Eq.{succ u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.addMonoid))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.addMonoid))) (algebraMap.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.addMonoid) (LaurentPolynomial.algebraPolynomial.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (LaurentPolynomial.T.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt)))))) (algebraMap.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt) (LaurentPolynomial.algebraPolynomial.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (LaurentPolynomial.T.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Nat.cast.{0} Int instNatCastInt n))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (n : Nat), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt)))))) (algebraMap.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt) (LaurentPolynomial.algebraPolynomial.{u1} R _inst_1)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)) (LaurentPolynomial.T.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Nat.cast.{0} Int instNatCastInt n))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.algebra_map_X_pow LaurentPolynomial.algebraMap_X_powₓ'. -/
 theorem algebraMap_X_pow (n : ℕ) : algebraMap R[X] R[T;T⁻¹] (X ^ n) = T n :=
   Polynomial.toLaurent_X_pow n
@@ -825,7 +825,7 @@ theorem algebraMap_X_pow (n : ℕ) : algebraMap R[X] R[T;T⁻¹] (X ^ n) = T n :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.addMonoid))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.addMonoid))) (algebraMap.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.addMonoid) (LaurentPolynomial.algebraPolynomial.{u1} R _inst_1)) f) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt)))))) (algebraMap.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt) (LaurentPolynomial.algebraPolynomial.{u1} R _inst_1)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt)))))) (algebraMap.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt) (LaurentPolynomial.algebraPolynomial.{u1} R _inst_1)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f)
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.algebra_map_eq_to_laurent LaurentPolynomial.algebraMap_eq_toLaurentₓ'. -/
 @[simp]
 theorem algebraMap_eq_toLaurent (f : R[X]) : algebraMap R[X] R[T;T⁻¹] f = f.toLaurent :=

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 
 ! This file was ported from Lean 3 source module data.polynomial.laurent
-! leanprover-community/mathlib commit 831c494092374cfe9f50591ed0ac81a25efc5b86
+! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.RingTheory.Localization.Basic
 
 /-!  # Laurent polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We introduce Laurent polynomials over a semiring `R`.  Mathematically, they are expressions of the
 form
 $$
@@ -259,7 +262,7 @@ theorem single_eq_C_mul_T (r : R) (n : ℤ) : (single n r : R[T;T⁻¹]) = (C r
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (r : R), Eq.{succ u1} (LaurentPolynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Nat) (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} 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LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int 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(AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) r) (LaurentPolynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) r) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 (Nat.cast.{0} Int instNatCastInt n)))
 Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_C_mul_T Polynomial.toLaurent_C_mul_Tₓ'. -/
 -- This lemma locks in the right changes and is what Lean proved directly.
 -- The actual `simp`-normal form of a Laurent monomial is `C a * T n`, whenever it can be reached.
@@ -448,7 +451,7 @@ def trunc : R[T;T⁻¹] →+ R[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (fun (_x : AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) => (LaurentPolynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (AddMonoidHom.hasCoeToFun.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.trunc.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 n))) (ite.{succ u1} (Polynomial.{u1} R _inst_1) (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) n) (Int.decLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) n) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (Int.toNat n)) r) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : LaurentPolynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) r) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) r) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r) 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(Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddZeroClass.toAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))))))) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))))) (LaurentPolynomial.trunc.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) r) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) r) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) r) (LaurentPolynomial.T.{u1} R _inst_1 n))) (ite.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) r) (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) n) (Int.decLe (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) n) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (Int.toNat n)) r) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) r) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.zero.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.trunc_C_mul_T LaurentPolynomial.trunc_C_mul_Tₓ'. -/
 @[simp]
 theorem trunc_C_mul_T (n : ℤ) (r : R) : trunc (C r * T n) = ite (0 ≤ n) (monomial n.toNat r) 0 :=

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

@@ -753,7 +753,7 @@ section DegreeBounds
 
 /- warning: laurent_polynomial.degree_C_mul_T_le -> LaurentPolynomial.degree_C_mul_T_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (a : R), LE.le.{0} (WithBot.{0} Int) (Preorder.toLE.{0} (WithBot.{0} Int) (WithBot.preorder.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (LaurentPolynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (WithBot.{0} Int) (HasLiftT.mk.{1, 1} Int (WithBot.{0} Int) (CoeTCₓ.coe.{1, 1} Int (WithBot.{0} Int) (WithBot.hasCoeT.{0} Int))) n)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (a : R), LE.le.{0} (WithBot.{0} Int) (Preorder.toHasLe.{0} (WithBot.{0} Int) (WithBot.preorder.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (LaurentPolynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (WithBot.{0} Int) (HasLiftT.mk.{1, 1} Int (WithBot.{0} Int) (CoeTCₓ.coe.{1, 1} Int (WithBot.{0} Int) (WithBot.hasCoeT.{0} Int))) n)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int) (a : R), LE.le.{0} (WithBot.{0} Int) (Preorder.toLE.{0} (WithBot.{0} Int) (WithBot.preorder.{0} Int (PartialOrder.toPreorder.{0} Int (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (LaurentPolynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 n))) (WithBot.some.{0} Int n)
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_C_mul_T_le LaurentPolynomial.degree_C_mul_T_leₓ'. -/
@@ -764,15 +764,19 @@ theorem degree_C_mul_T_le (n : ℤ) (a : R) : (C a * T n).degree ≤ n :=
   · exact (degree_C_mul_T n a a0).le
 #align laurent_polynomial.degree_C_mul_T_le LaurentPolynomial.degree_C_mul_T_le
 
-#print LaurentPolynomial.degree_T_le /-
+/- warning: laurent_polynomial.degree_T_le -> LaurentPolynomial.degree_T_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int), LE.le.{0} (WithBot.{0} Int) (Preorder.toHasLe.{0} (WithBot.{0} Int) (WithBot.preorder.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (LaurentPolynomial.degree.{u1} R _inst_1 (LaurentPolynomial.T.{u1} R _inst_1 n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (WithBot.{0} Int) (HasLiftT.mk.{1, 1} Int (WithBot.{0} Int) (CoeTCₓ.coe.{1, 1} Int (WithBot.{0} Int) (WithBot.hasCoeT.{0} Int))) n)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (n : Int), LE.le.{0} (WithBot.{0} Int) (Preorder.toLE.{0} (WithBot.{0} Int) (WithBot.preorder.{0} Int (PartialOrder.toPreorder.{0} Int (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (LaurentPolynomial.degree.{u1} R _inst_1 (LaurentPolynomial.T.{u1} R _inst_1 n)) (WithBot.some.{0} Int n)
+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_T_le LaurentPolynomial.degree_T_leₓ'. -/
 theorem degree_T_le (n : ℤ) : (T n : R[T;T⁻¹]).degree ≤ n :=
   (le_of_eq (by rw [map_one, one_mul])).trans (degree_C_mul_T_le n (1 : R))
 #align laurent_polynomial.degree_T_le LaurentPolynomial.degree_T_le
--/
 
 /- warning: laurent_polynomial.degree_C_le -> LaurentPolynomial.degree_C_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), LE.le.{0} (WithBot.{0} Int) (Preorder.toLE.{0} (WithBot.{0} Int) (WithBot.preorder.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (LaurentPolynomial.degree.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a)) (OfNat.ofNat.{0} (WithBot.{0} Int) 0 (OfNat.mk.{0} (WithBot.{0} Int) 0 (Zero.zero.{0} (WithBot.{0} Int) (WithBot.hasZero.{0} Int Int.hasZero))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), LE.le.{0} (WithBot.{0} Int) (Preorder.toHasLe.{0} (WithBot.{0} Int) (WithBot.preorder.{0} Int (PartialOrder.toPreorder.{0} Int (OrderedAddCommGroup.toPartialOrder.{0} Int (StrictOrderedRing.toOrderedAddCommGroup.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (LaurentPolynomial.degree.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => R -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (LaurentPolynomial.C.{u1} R _inst_1) a)) (OfNat.ofNat.{0} (WithBot.{0} Int) 0 (OfNat.mk.{0} (WithBot.{0} Int) 0 (Zero.zero.{0} (WithBot.{0} Int) (WithBot.hasZero.{0} Int Int.hasZero))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (a : R), LE.le.{0} (WithBot.{0} Int) (Preorder.toLE.{0} (WithBot.{0} Int) (WithBot.preorder.{0} Int (PartialOrder.toPreorder.{0} Int (StrictOrderedRing.toPartialOrder.{0} Int (LinearOrderedRing.toStrictOrderedRing.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (LaurentPolynomial.degree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a)) (OfNat.ofNat.{0} (WithBot.{0} Int) 0 (Zero.toOfNat0.{0} (WithBot.{0} Int) (WithBot.zero.{0} Int (CommMonoidWithZero.toZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))))
 Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_C_le LaurentPolynomial.degree_C_leₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ad820c4997738e2f542f8a20f32911f52020e26

@@ -82,22 +82,32 @@ noncomputable section
 
 variable {R : Type _}
 
+#print LaurentPolynomial /-
 /-- The semiring of Laurent polynomials with coefficients in the semiring `R`.
 We denote it by `R[T;T⁻¹]`.
 The ring homomorphism `C : R →+* R[T;T⁻¹]` includes `R` as the constant polynomials. -/
 abbrev LaurentPolynomial (R : Type _) [Semiring R] :=
   AddMonoidAlgebra R ℤ
 #align laurent_polynomial LaurentPolynomial
+-/
 
 -- mathport name: «expr [T;T⁻¹]»
 local notation:9000 R "[T;T⁻¹]" => LaurentPolynomial R
 
+#print Polynomial.toLaurent /-
 /-- The ring homomorphism, taking a polynomial with coefficients in `R` to a Laurent polynomial
 with coefficients in `R`. -/
 def Polynomial.toLaurent [Semiring R] : R[X] →+* R[T;T⁻¹] :=
   (mapDomainRingHom R Int.ofNatHom).comp (toFinsuppIso R)
 #align polynomial.to_laurent Polynomial.toLaurent
+-/
 
+/- warning: polynomial.to_laurent_apply -> Polynomial.toLaurent_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1), Eq.{succ u1} (LaurentPolynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) p) (Finsupp.mapDomain.{0, 0, u1} Nat Int R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe)))) (Polynomial.toFinsupp.{u1} R _inst_1 p))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) p) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) p) (AddMonoidAlgebra.mapDomain.{u1, 0, 0} R Nat _inst_1 Int (Nat.cast.{0} Int instNatCastInt) (Polynomial.toFinsupp.{u1} R _inst_1 p))
+Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_apply Polynomial.toLaurent_applyₓ'. -/
 /-- This is not a simp lemma, as it is usually preferable to use the lemmas about `C` and `X`
 instead. -/
 theorem Polynomial.toLaurent_apply [Semiring R] (p : R[X]) :
@@ -105,6 +115,7 @@ theorem Polynomial.toLaurent_apply [Semiring R] (p : R[X]) :
   rfl
 #align polynomial.to_laurent_apply Polynomial.toLaurent_apply
 
+#print Polynomial.toLaurentAlg /-
 /-- The `R`-algebra map, taking a polynomial with coefficients in `R` to a Laurent polynomial
 with coefficients in `R`. -/
 def Polynomial.toLaurentAlg [CommSemiring R] : R[X] →ₐ[R] R[T;T⁻¹] :=
@@ -112,11 +123,14 @@ def Polynomial.toLaurentAlg [CommSemiring R] : R[X] →ₐ[R] R[T;T⁻¹] :=
   refine' AlgHom.comp _ (to_finsupp_iso_alg R).toAlgHom
   exact map_domain_alg_hom R R Int.ofNatHom
 #align polynomial.to_laurent_alg Polynomial.toLaurentAlg
+-/
 
+#print Polynomial.toLaurentAlg_apply /-
 @[simp]
 theorem Polynomial.toLaurentAlg_apply [CommSemiring R] (f : R[X]) : f.toLaurentAlg = f.toLaurent :=
   rfl
 #align polynomial.to_laurent_alg_apply Polynomial.toLaurentAlg_apply
+-/
 
 namespace LaurentPolynomial
 
@@ -124,6 +138,12 @@ section Semiring
 
 variable [Semiring R]
 
+/- warning: laurent_polynomial.single_zero_one_eq_one -> LaurentPolynomial.single_zero_one_eq_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (Finsupp.{0, u1} Int R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Finsupp.single.{0, u1} Int R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} (LaurentPolynomial.{u1} R _inst_1) 1 (OfNat.mk.{u1} (LaurentPolynomial.{u1} R _inst_1) 1 (One.one.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.one.{u1, 0} R Int _inst_1 Int.hasZero))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (Finsupp.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Finsupp.single.{0, u1} Int R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (OfNat.ofNat.{u1} (LaurentPolynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.one.{u1, 0} R Int _inst_1 (CommMonoidWithZero.toZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))))
+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.single_zero_one_eq_one LaurentPolynomial.single_zero_one_eq_oneₓ'. -/
 theorem single_zero_one_eq_one : (single 0 1 : R[T;T⁻¹]) = (1 : R[T;T⁻¹]) :=
   rfl
 #align laurent_polynomial.single_zero_one_eq_one LaurentPolynomial.single_zero_one_eq_one
@@ -131,134 +151,230 @@ theorem single_zero_one_eq_one : (single 0 1 : R[T;T⁻¹]) = (1 : R[T;T⁻¹])
 /-!  ### The functions `C` and `T`. -/
 
 
+#print LaurentPolynomial.C /-
 /-- The ring homomorphism `C`, including `R` into the ring of Laurent polynomials over `R` as
 the constant Laurent polynomials. -/
-def c : R →+* R[T;T⁻¹] :=
+def C : R →+* R[T;T⁻¹] :=
   singleZeroRingHom
-#align laurent_polynomial.C LaurentPolynomial.c
+#align laurent_polynomial.C LaurentPolynomial.C
+-/
 
+/- warning: laurent_polynomial.algebra_map_apply -> LaurentPolynomial.algebraMap_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.algebra_map_apply LaurentPolynomial.algebraMap_applyₓ'. -/
 theorem algebraMap_apply {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A] (r : R) :
-    algebraMap R (LaurentPolynomial A) r = c (algebraMap R A r) :=
+    algebraMap R (LaurentPolynomial A) r = C (algebraMap R A r) :=
   rfl
 #align laurent_polynomial.algebra_map_apply LaurentPolynomial.algebraMap_apply
 
+/- warning: laurent_polynomial.C_eq_algebra_map -> LaurentPolynomial.C_eq_algebraMap is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.C_eq_algebra_map LaurentPolynomial.C_eq_algebraMapₓ'. -/
 /-- When we have `[comm_semiring R]`, the function `C` is the same as `algebra_map R R[T;T⁻¹]`.
 (But note that `C` is defined when `R` is not necessarily commutative, in which case
 `algebra_map` is not available.)
 -/
-theorem c_eq_algebraMap {R : Type _} [CommSemiring R] (r : R) : c r = algebraMap R R[T;T⁻¹] r :=
+theorem C_eq_algebraMap {R : Type _} [CommSemiring R] (r : R) : C r = algebraMap R R[T;T⁻¹] r :=
   rfl
-#align laurent_polynomial.C_eq_algebra_map LaurentPolynomial.c_eq_algebraMap
-
-theorem single_eq_c (r : R) : single 0 r = c r :=
+#align laurent_polynomial.C_eq_algebra_map LaurentPolynomial.C_eq_algebraMap
+
+/- warning: laurent_polynomial.single_eq_C -> LaurentPolynomial.single_eq_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.single_eq_C LaurentPolynomial.single_eq_Cₓ'. -/
+theorem single_eq_C (r : R) : single 0 r = C r :=
   rfl
-#align laurent_polynomial.single_eq_C LaurentPolynomial.single_eq_c
+#align laurent_polynomial.single_eq_C LaurentPolynomial.single_eq_C
 
+#print LaurentPolynomial.T /-
 /-- The function `n ↦ T ^ n`, implemented as a sequence `ℤ → R[T;T⁻¹]`.
 
 Using directly `T ^ n` does not work, since we want the exponents to be of Type `ℤ` and there
 is no `ℤ`-power defined on `R[T;T⁻¹]`.  Using that `T` is a unit introduces extra coercions.
 For these reasons, the definition of `T` is as a sequence. -/
-def t (n : ℤ) : R[T;T⁻¹] :=
+def T (n : ℤ) : R[T;T⁻¹] :=
   single n 1
-#align laurent_polynomial.T LaurentPolynomial.t
+#align laurent_polynomial.T LaurentPolynomial.T
+-/
 
+#print LaurentPolynomial.T_zero /-
 @[simp]
-theorem t_zero : (t 0 : R[T;T⁻¹]) = 1 :=
+theorem T_zero : (T 0 : R[T;T⁻¹]) = 1 :=
   rfl
-#align laurent_polynomial.T_zero LaurentPolynomial.t_zero
+#align laurent_polynomial.T_zero LaurentPolynomial.T_zero
+-/
 
-theorem t_add (m n : ℤ) : (t (m + n) : R[T;T⁻¹]) = t m * t n :=
+#print LaurentPolynomial.T_add /-
+theorem T_add (m n : ℤ) : (T (m + n) : R[T;T⁻¹]) = T m * T n :=
   by
   convert single_mul_single.symm
   simp [T]
-#align laurent_polynomial.T_add LaurentPolynomial.t_add
+#align laurent_polynomial.T_add LaurentPolynomial.T_add
+-/
 
-theorem t_sub (m n : ℤ) : (t (m - n) : R[T;T⁻¹]) = t m * t (-n) := by rw [← T_add, sub_eq_add_neg]
-#align laurent_polynomial.T_sub LaurentPolynomial.t_sub
+#print LaurentPolynomial.T_sub /-
+theorem T_sub (m n : ℤ) : (T (m - n) : R[T;T⁻¹]) = T m * T (-n) := by rw [← T_add, sub_eq_add_neg]
+#align laurent_polynomial.T_sub LaurentPolynomial.T_sub
+-/
 
+/- warning: laurent_polynomial.T_pow -> LaurentPolynomial.T_pow is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.T_pow LaurentPolynomial.T_powₓ'. -/
 @[simp]
-theorem t_pow (m : ℤ) (n : ℕ) : (t m ^ n : R[T;T⁻¹]) = t (n * m) := by
+theorem T_pow (m : ℤ) (n : ℕ) : (T m ^ n : R[T;T⁻¹]) = T (n * m) := by
   rw [T, T, single_pow n, one_pow, nsmul_eq_mul]
-#align laurent_polynomial.T_pow LaurentPolynomial.t_pow
+#align laurent_polynomial.T_pow LaurentPolynomial.T_pow
 
+#print LaurentPolynomial.mul_T_assoc /-
 /-- The `simp` version of `mul_assoc`, in the presence of `T`'s. -/
 @[simp]
-theorem mul_t_assoc (f : R[T;T⁻¹]) (m n : ℤ) : f * t m * t n = f * t (m + n) := by
+theorem mul_T_assoc (f : R[T;T⁻¹]) (m n : ℤ) : f * T m * T n = f * T (m + n) := by
   simp [← T_add, mul_assoc]
-#align laurent_polynomial.mul_T_assoc LaurentPolynomial.mul_t_assoc
+#align laurent_polynomial.mul_T_assoc LaurentPolynomial.mul_T_assoc
+-/
 
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.single_eq_C_mul_T LaurentPolynomial.single_eq_C_mul_Tₓ'. -/
 @[simp]
-theorem single_eq_c_mul_t (r : R) (n : ℤ) : (single n r : R[T;T⁻¹]) = (c r * t n : R[T;T⁻¹]) := by
+theorem single_eq_C_mul_T (r : R) (n : ℤ) : (single n r : R[T;T⁻¹]) = (C r * T n : R[T;T⁻¹]) := by
   convert single_mul_single.symm <;> simp
-#align laurent_polynomial.single_eq_C_mul_T LaurentPolynomial.single_eq_c_mul_t
-
+#align laurent_polynomial.single_eq_C_mul_T LaurentPolynomial.single_eq_C_mul_T
+
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+Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_C_mul_T Polynomial.toLaurent_C_mul_Tₓ'. -/
 -- This lemma locks in the right changes and is what Lean proved directly.
 -- The actual `simp`-normal form of a Laurent monomial is `C a * T n`, whenever it can be reached.
 @[simp]
-theorem Polynomial.toLaurent_c_mul_t (n : ℕ) (r : R) :
-    ((Polynomial.monomial n r).toLaurent : R[T;T⁻¹]) = c r * t n :=
-  show mapDomain coe (monomial n r).toFinsupp = (c r * t n : R[T;T⁻¹]) by
+theorem Polynomial.toLaurent_C_mul_T (n : ℕ) (r : R) :
+    ((Polynomial.monomial n r).toLaurent : R[T;T⁻¹]) = C r * T n :=
+  show mapDomain coe (monomial n r).toFinsupp = (C r * T n : R[T;T⁻¹]) by
     rw [to_finsupp_monomial, map_domain_single, single_eq_C_mul_T]
-#align polynomial.to_laurent_C_mul_T Polynomial.toLaurent_c_mul_t
-
+#align polynomial.to_laurent_C_mul_T Polynomial.toLaurent_C_mul_T
+
+/- warning: polynomial.to_laurent_C -> Polynomial.toLaurent_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_C Polynomial.toLaurent_Cₓ'. -/
 @[simp]
-theorem Polynomial.toLaurent_c (r : R) : (Polynomial.C r).toLaurent = c r :=
+theorem Polynomial.toLaurent_C (r : R) : (Polynomial.C r).toLaurent = C r :=
   by
-  convert Polynomial.toLaurent_c_mul_t 0 r
+  convert Polynomial.toLaurent_C_mul_T 0 r
   simp only [Int.ofNat_zero, T_zero, mul_one]
-#align polynomial.to_laurent_C Polynomial.toLaurent_c
-
+#align polynomial.to_laurent_C Polynomial.toLaurent_C
+
+/- warning: polynomial.to_laurent_X -> Polynomial.toLaurent_X is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_X Polynomial.toLaurent_Xₓ'. -/
 @[simp]
-theorem Polynomial.toLaurent_x : (Polynomial.X.toLaurent : R[T;T⁻¹]) = t 1 :=
+theorem Polynomial.toLaurent_X : (Polynomial.X.toLaurent : R[T;T⁻¹]) = T 1 :=
   by
   have : (Polynomial.X : R[X]) = monomial 1 1 := by simp [← C_mul_X_pow_eq_monomial]
-  simp [this, Polynomial.toLaurent_c_mul_t]
-#align polynomial.to_laurent_X Polynomial.toLaurent_x
-
+  simp [this, Polynomial.toLaurent_C_mul_T]
+#align polynomial.to_laurent_X Polynomial.toLaurent_X
+
+/- warning: polynomial.to_laurent_one -> Polynomial.toLaurent_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_one Polynomial.toLaurent_oneₓ'. -/
 @[simp]
 theorem Polynomial.toLaurent_one : (Polynomial.toLaurent : R[X] → R[T;T⁻¹]) 1 = 1 :=
   map_one Polynomial.toLaurent
 #align polynomial.to_laurent_one Polynomial.toLaurent_one
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_C_mul_eq Polynomial.toLaurent_C_mul_eqₓ'. -/
 @[simp]
-theorem Polynomial.toLaurent_c_mul_eq (r : R) (f : R[X]) :
-    (Polynomial.C r * f).toLaurent = c r * f.toLaurent := by
-  simp only [_root_.map_mul, Polynomial.toLaurent_c]
-#align polynomial.to_laurent_C_mul_eq Polynomial.toLaurent_c_mul_eq
-
+theorem Polynomial.toLaurent_C_mul_eq (r : R) (f : R[X]) :
+    (Polynomial.C r * f).toLaurent = C r * f.toLaurent := by
+  simp only [_root_.map_mul, Polynomial.toLaurent_C]
+#align polynomial.to_laurent_C_mul_eq Polynomial.toLaurent_C_mul_eq
+
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+Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_X_pow Polynomial.toLaurent_X_powₓ'. -/
 @[simp]
-theorem Polynomial.toLaurent_x_pow (n : ℕ) : (X ^ n : R[X]).toLaurent = t n := by
-  simp only [map_pow, Polynomial.toLaurent_x, T_pow, mul_one]
-#align polynomial.to_laurent_X_pow Polynomial.toLaurent_x_pow
-
+theorem Polynomial.toLaurent_X_pow (n : ℕ) : (X ^ n : R[X]).toLaurent = T n := by
+  simp only [map_pow, Polynomial.toLaurent_X, T_pow, mul_one]
+#align polynomial.to_laurent_X_pow Polynomial.toLaurent_X_pow
+
+/- warning: polynomial.to_laurent_C_mul_X_pow -> Polynomial.toLaurent_C_mul_X_pow is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_C_mul_X_pow Polynomial.toLaurent_C_mul_X_powₓ'. -/
 @[simp]
-theorem Polynomial.toLaurent_c_mul_x_pow (n : ℕ) (r : R) :
-    (Polynomial.C r * X ^ n).toLaurent = c r * t n := by
-  simp only [_root_.map_mul, Polynomial.toLaurent_c, Polynomial.toLaurent_x_pow]
-#align polynomial.to_laurent_C_mul_X_pow Polynomial.toLaurent_c_mul_x_pow
+theorem Polynomial.toLaurent_C_mul_X_pow (n : ℕ) (r : R) :
+    (Polynomial.C r * X ^ n).toLaurent = C r * T n := by
+  simp only [_root_.map_mul, Polynomial.toLaurent_C, Polynomial.toLaurent_X_pow]
+#align polynomial.to_laurent_C_mul_X_pow Polynomial.toLaurent_C_mul_X_pow
 
-instance invertibleT (n : ℤ) : Invertible (t n : R[T;T⁻¹])
+#print LaurentPolynomial.invertibleT /-
+instance invertibleT (n : ℤ) : Invertible (T n : R[T;T⁻¹])
     where
-  invOf := t (-n)
+  invOf := T (-n)
   invOf_mul_self := by rw [← T_add, add_left_neg, T_zero]
   mul_invOf_self := by rw [← T_add, add_right_neg, T_zero]
 #align laurent_polynomial.invertible_T LaurentPolynomial.invertibleT
+-/
 
+#print LaurentPolynomial.invOf_T /-
 @[simp]
-theorem invOf_t (n : ℤ) : ⅟ (t n : R[T;T⁻¹]) = t (-n) :=
+theorem invOf_T (n : ℤ) : ⅟ (T n : R[T;T⁻¹]) = T (-n) :=
   rfl
-#align laurent_polynomial.inv_of_T LaurentPolynomial.invOf_t
+#align laurent_polynomial.inv_of_T LaurentPolynomial.invOf_T
+-/
 
-theorem isUnit_t (n : ℤ) : IsUnit (t n : R[T;T⁻¹]) :=
+#print LaurentPolynomial.isUnit_T /-
+theorem isUnit_T (n : ℤ) : IsUnit (T n : R[T;T⁻¹]) :=
   isUnit_of_invertible _
-#align laurent_polynomial.is_unit_T LaurentPolynomial.isUnit_t
+#align laurent_polynomial.is_unit_T LaurentPolynomial.isUnit_T
+-/
 
+/- warning: laurent_polynomial.induction_on -> LaurentPolynomial.induction_on is a dubious translation:
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((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) a) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} R (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (LaurentPolynomial.C.{u1} R _inst_1) a) (LaurentPolynomial.T.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (Neg.neg.{0} Int Int.instNegInt (Nat.cast.{0} Int instNatCastInt n)) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))))) -> (M p)
+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.induction_on LaurentPolynomial.induction_onₓ'. -/
 @[elab_as_elim]
-protected theorem induction_on {M : R[T;T⁻¹] → Prop} (p : R[T;T⁻¹]) (h_C : ∀ a, M (c a))
+protected theorem induction_on {M : R[T;T⁻¹] → Prop} (p : R[T;T⁻¹]) (h_C : ∀ a, M (C a))
     (h_add : ∀ {p q}, M p → M q → M (p + q))
-    (h_C_mul_T : ∀ (n : ℕ) (a : R), M (c a * t n) → M (c a * t (n + 1)))
-    (h_C_mul_T_Z : ∀ (n : ℕ) (a : R), M (c a * t (-n)) → M (c a * t (-n - 1))) : M p :=
+    (h_C_mul_T : ∀ (n : ℕ) (a : R), M (C a * T n) → M (C a * T (n + 1)))
+    (h_C_mul_T_Z : ∀ (n : ℕ) (a : R), M (C a * T (-n)) → M (C a * T (-n - 1))) : M p :=
   by
   have A : ∀ {n : ℤ} {a : R}, M (C a * T n) :=
     by
@@ -283,41 +399,59 @@ protected theorem induction_on {M : R[T;T⁻¹] → Prop} (p : R[T;T⁻¹]) (h_C
   · exact finsupp.not_mem_support_iff.mp h
 #align laurent_polynomial.induction_on LaurentPolynomial.induction_on
 
+/- warning: laurent_polynomial.induction_on' -> LaurentPolynomial.induction_on' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.induction_on' LaurentPolynomial.induction_on'ₓ'. -/
 /-- To prove something about Laurent polynomials, it suffices to show that
 * the condition is closed under taking sums, and
 * it holds for monomials.
 -/
 @[elab_as_elim]
 protected theorem induction_on' {M : R[T;T⁻¹] → Prop} (p : R[T;T⁻¹])
-    (h_add : ∀ p q, M p → M q → M (p + q)) (h_C_mul_T : ∀ (n : ℤ) (a : R), M (c a * t n)) : M p :=
+    (h_add : ∀ p q, M p → M q → M (p + q)) (h_C_mul_T : ∀ (n : ℤ) (a : R), M (C a * T n)) : M p :=
   by
   refine' p.induction_on (fun a => _) h_add _ _ <;> try exact fun n f _ => h_C_mul_T _ f
   convert h_C_mul_T 0 a
   exact (mul_one _).symm
 #align laurent_polynomial.induction_on' LaurentPolynomial.induction_on'
 
-theorem commute_t (n : ℤ) (f : R[T;T⁻¹]) : Commute (t n) f :=
+#print LaurentPolynomial.commute_T /-
+theorem commute_T (n : ℤ) (f : R[T;T⁻¹]) : Commute (T n) f :=
   f.inductionOn' (fun p q Tp Tq => Commute.add_right Tp Tq) fun m a =>
-    show t n * _ = _
+    show T n * _ = _
       by
       rw [T, T, ← single_eq_C, single_mul_single, single_mul_single, single_mul_single]
       simp [add_comm]
-#align laurent_polynomial.commute_T LaurentPolynomial.commute_t
+#align laurent_polynomial.commute_T LaurentPolynomial.commute_T
+-/
 
+#print LaurentPolynomial.T_mul /-
 @[simp]
-theorem t_mul (n : ℤ) (f : R[T;T⁻¹]) : t n * f = f * t n :=
-  (commute_t n f).Eq
-#align laurent_polynomial.T_mul LaurentPolynomial.t_mul
+theorem T_mul (n : ℤ) (f : R[T;T⁻¹]) : T n * f = f * T n :=
+  (commute_T n f).Eq
+#align laurent_polynomial.T_mul LaurentPolynomial.T_mul
+-/
 
+#print LaurentPolynomial.trunc /-
 /-- `trunc : R[T;T⁻¹] →+ R[X]` maps a Laurent polynomial `f` to the polynomial whose terms of
 nonnegative degree coincide with the ones of `f`.  The terms of negative degree of `f` "vanish".
 `trunc` is a left-inverse to `polynomial.to_laurent`. -/
 def trunc : R[T;T⁻¹] →+ R[X] :=
   (toFinsuppIso R).symm.toAddMonoidHom.comp <| comapDomain.addMonoidHom fun a b => Int.ofNat.inj
 #align laurent_polynomial.trunc LaurentPolynomial.trunc
+-/
 
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.trunc_C_mul_T LaurentPolynomial.trunc_C_mul_Tₓ'. -/
 @[simp]
-theorem trunc_c_mul_t (n : ℤ) (r : R) : trunc (c r * t n) = ite (0 ≤ n) (monomial n.toNat r) 0 :=
+theorem trunc_C_mul_T (n : ℤ) (r : R) : trunc (C r * T n) = ite (0 ≤ n) (monomial n.toNat r) 0 :=
   by
   apply (to_finsupp_iso R).Injective
   rw [← single_eq_C_mul_T, Trunc, AddMonoidHom.coe_comp, Function.comp_apply,
@@ -334,8 +468,14 @@ theorem trunc_c_mul_t (n : ℤ) (r : R) : trunc (c r * t n) = ite (0 ≤ n) (mon
     have := ((not_le.mp n0).trans_le (Int.ofNat_zero_le a)).ne'
     simp only [coeff, comap_domain_apply, Int.ofNat_eq_coe, coeff_zero, single_apply_eq_zero, this,
       IsEmpty.forall_iff]
-#align laurent_polynomial.trunc_C_mul_T LaurentPolynomial.trunc_c_mul_t
-
+#align laurent_polynomial.trunc_C_mul_T LaurentPolynomial.trunc_C_mul_T
+
+/- warning: laurent_polynomial.left_inverse_trunc_to_laurent -> LaurentPolynomial.leftInverse_trunc_toLaurent is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Function.LeftInverse.{succ u1, succ u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (fun (_x : LaurentPolynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : LaurentPolynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (AddHomClass.toFunLike.{u1, u1, u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddZeroClass.toAdd.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))))))) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))))) (LaurentPolynomial.trunc.{u1} R _inst_1)) (FunLike.coe.{succ 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1))
+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.left_inverse_trunc_to_laurent LaurentPolynomial.leftInverse_trunc_toLaurentₓ'. -/
 @[simp]
 theorem leftInverse_trunc_toLaurent :
     Function.LeftInverse (trunc : R[T;T⁻¹] → R[X]) Polynomial.toLaurent :=
@@ -344,80 +484,140 @@ theorem leftInverse_trunc_toLaurent :
   · exact fun f g hf hg => by simp only [hf, hg, _root_.map_add]
   ·
     exact fun n r => by
-      simp only [Polynomial.toLaurent_c_mul_t, trunc_C_mul_T, Int.coe_nat_nonneg, Int.toNat_coe_nat,
+      simp only [Polynomial.toLaurent_C_mul_T, trunc_C_mul_T, Int.coe_nat_nonneg, Int.toNat_coe_nat,
         if_true]
 #align laurent_polynomial.left_inverse_trunc_to_laurent LaurentPolynomial.leftInverse_trunc_toLaurent
 
+/- warning: polynomial.trunc_to_laurent -> Polynomial.trunc_toLaurent is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (fun (_x : AddMonoidHom.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) => (LaurentPolynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (AddMonoidHom.hasCoeToFun.{u1, u1} (LaurentPolynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid)))))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (LaurentPolynomial.trunc.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) f)) f
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.trunc_to_laurent Polynomial.trunc_toLaurentₓ'. -/
 @[simp]
 theorem Polynomial.trunc_toLaurent (f : R[X]) : trunc f.toLaurent = f :=
   leftInverse_trunc_toLaurent _
 #align polynomial.trunc_to_laurent Polynomial.trunc_toLaurent
 
+/- warning: polynomial.to_laurent_injective -> Polynomial.toLaurent_injective is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_injective Polynomial.toLaurent_injectiveₓ'. -/
 theorem Polynomial.toLaurent_injective :
     Function.Injective (Polynomial.toLaurent : R[X] → R[T;T⁻¹]) :=
   leftInverse_trunc_toLaurent.Injective
 #align polynomial.to_laurent_injective Polynomial.toLaurent_injective
 
+/- warning: polynomial.to_laurent_inj -> Polynomial.toLaurent_inj is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_inj Polynomial.toLaurent_injₓ'. -/
 @[simp]
 theorem Polynomial.toLaurent_inj (f g : R[X]) : f.toLaurent = g.toLaurent ↔ f = g :=
   ⟨fun h => Polynomial.toLaurent_injective h, congr_arg _⟩
 #align polynomial.to_laurent_inj Polynomial.toLaurent_inj
 
+/- warning: polynomial.to_laurent_ne_zero -> Polynomial.toLaurent_ne_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.to_laurent_ne_zero Polynomial.toLaurent_ne_zeroₓ'. -/
 theorem Polynomial.toLaurent_ne_zero {f : R[X]} : f ≠ 0 ↔ f.toLaurent ≠ 0 :=
   (map_ne_zero_iff _ Polynomial.toLaurent_injective).symm
 #align polynomial.to_laurent_ne_zero Polynomial.toLaurent_ne_zero
 
-theorem exists_t_pow (f : R[T;T⁻¹]) : ∃ (n : ℕ)(f' : R[X]), f'.toLaurent = f * t n :=
+/- warning: laurent_polynomial.exists_T_pow -> LaurentPolynomial.exists_T_pow is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.exists_T_pow LaurentPolynomial.exists_T_powₓ'. -/
+theorem exists_T_pow (f : R[T;T⁻¹]) : ∃ (n : ℕ)(f' : R[X]), f'.toLaurent = f * T n :=
   by
   apply f.induction_on' _ fun n a => _ <;> clear f
   · rintro f g ⟨m, fn, hf⟩ ⟨n, gn, hg⟩
     refine' ⟨m + n, fn * X ^ n + gn * X ^ m, _⟩
-    simp only [hf, hg, add_mul, add_comm (n : ℤ), map_add, map_mul, Polynomial.toLaurent_x_pow,
+    simp only [hf, hg, add_mul, add_comm (n : ℤ), map_add, map_mul, Polynomial.toLaurent_X_pow,
       mul_T_assoc, Int.ofNat_add]
   · cases' n with n n
     · exact ⟨0, Polynomial.C a * X ^ n, by simp⟩
     · refine' ⟨n + 1, Polynomial.C a, _⟩
-      simp only [Int.negSucc_eq, Polynomial.toLaurent_c, Int.ofNat_succ, mul_T_assoc, add_left_neg,
+      simp only [Int.negSucc_eq, Polynomial.toLaurent_C, Int.ofNat_succ, mul_T_assoc, add_left_neg,
         T_zero, mul_one]
-#align laurent_polynomial.exists_T_pow LaurentPolynomial.exists_t_pow
-
+#align laurent_polynomial.exists_T_pow LaurentPolynomial.exists_T_pow
+
+/- warning: laurent_polynomial.induction_on_mul_T -> LaurentPolynomial.induction_on_mul_T is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {Q : (LaurentPolynomial.{u1} R _inst_1) -> Prop} (f : LaurentPolynomial.{u1} R _inst_1), (forall {f : Polynomial.{u1} R _inst_1} {n : Nat}, Q (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) f) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.instAddInt)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R _inst_1) => LaurentPolynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R _inst_1) f) (LaurentPolynomial.T.{u1} R _inst_1 (Neg.neg.{0} Int Int.instNegInt (Nat.cast.{0} Int instNatCastInt n))))) -> (Q f)
+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.induction_on_mul_T LaurentPolynomial.induction_on_mul_Tₓ'. -/
 /-- This is a version of `exists_T_pow` stated as an induction principle. -/
 @[elab_as_elim]
-theorem induction_on_mul_t {Q : R[T;T⁻¹] → Prop} (f : R[T;T⁻¹])
-    (Qf : ∀ {f : R[X]} {n : ℕ}, Q (f.toLaurent * t (-n))) : Q f :=
+theorem induction_on_mul_T {Q : R[T;T⁻¹] → Prop} (f : R[T;T⁻¹])
+    (Qf : ∀ {f : R[X]} {n : ℕ}, Q (f.toLaurent * T (-n))) : Q f :=
   by
   rcases f.exists_T_pow with ⟨n, f', hf⟩
   rw [← mul_one f, ← T_zero, ← Nat.cast_zero, ← Nat.sub_self n, Nat.cast_sub rfl.le, T_sub, ←
     mul_assoc, ← hf]
   exact Qf
-#align laurent_polynomial.induction_on_mul_T LaurentPolynomial.induction_on_mul_t
-
+#align laurent_polynomial.induction_on_mul_T LaurentPolynomial.induction_on_mul_T
+
+/- warning: laurent_polynomial.reduce_to_polynomial_of_mul_T -> LaurentPolynomial.reduce_to_polynomial_of_mul_T is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : LaurentPolynomial.{u1} R _inst_1) {Q : (LaurentPolynomial.{u1} R _inst_1) -> Prop}, (forall (f : Polynomial.{u1} R _inst_1), Q (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R _inst_1) -> (LaurentPolynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int _inst_1 (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R _inst_1) f)) -> (forall (f : LaurentPolynomial.{u1} R _inst_1), (Q (HMul.hMul.{u1, u1, u1} (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (LaurentPolynomial.{u1} R _inst_1) (instHMul.{u1} (LaurentPolynomial.{u1} R _inst_1) (AddMonoidAlgebra.hasMul.{u1, 0} R Int _inst_1 Int.hasAdd)) f (LaurentPolynomial.T.{u1} R _inst_1 (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))))) -> (Q f)) -> (Q f)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.reduce_to_polynomial_of_mul_T LaurentPolynomial.reduce_to_polynomial_of_mul_Tₓ'. -/
 /-- Suppose that `Q` is a statement about Laurent polynomials such that
 * `Q` is true on *ordinary* polynomials;
 * `Q (f * T)` implies `Q f`;
 it follow that `Q` is true on all Laurent polynomials. -/
-theorem reduce_to_polynomial_of_mul_t (f : R[T;T⁻¹]) {Q : R[T;T⁻¹] → Prop}
-    (Qf : ∀ f : R[X], Q f.toLaurent) (QT : ∀ f, Q (f * t 1) → Q f) : Q f :=
+theorem reduce_to_polynomial_of_mul_T (f : R[T;T⁻¹]) {Q : R[T;T⁻¹] → Prop}
+    (Qf : ∀ f : R[X], Q f.toLaurent) (QT : ∀ f, Q (f * T 1) → Q f) : Q f :=
   by
-  induction' f using LaurentPolynomial.induction_on_mul_t with f n
+  induction' f using LaurentPolynomial.induction_on_mul_T with f n
   induction' n with n hn
   · simpa only [Int.ofNat_zero, neg_zero, T_zero, mul_one] using Qf _
   · convert QT _ _
     simpa using hn
-#align laurent_polynomial.reduce_to_polynomial_of_mul_T LaurentPolynomial.reduce_to_polynomial_of_mul_t
+#align laurent_polynomial.reduce_to_polynomial_of_mul_T LaurentPolynomial.reduce_to_polynomial_of_mul_T
 
 section Support
 
-theorem support_c_mul_t (a : R) (n : ℤ) : (c a * t n).support ⊆ {n} := by
+/- warning: laurent_polynomial.support_C_mul_T -> LaurentPolynomial.support_C_mul_T is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.support_C_mul_T LaurentPolynomial.support_C_mul_Tₓ'. -/
+theorem support_C_mul_T (a : R) (n : ℤ) : (C a * T n).support ⊆ {n} := by
   simpa only [← single_eq_C_mul_T] using support_single_subset
-#align laurent_polynomial.support_C_mul_T LaurentPolynomial.support_c_mul_t
-
-theorem support_c_mul_t_of_ne_zero {a : R} (a0 : a ≠ 0) (n : ℤ) : (c a * t n).support = {n} :=
+#align laurent_polynomial.support_C_mul_T LaurentPolynomial.support_C_mul_T
+
+/- warning: laurent_polynomial.support_C_mul_T_of_ne_zero -> LaurentPolynomial.support_C_mul_T_of_ne_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.support_C_mul_T_of_ne_zero LaurentPolynomial.support_C_mul_T_of_ne_zeroₓ'. -/
+theorem support_C_mul_T_of_ne_zero {a : R} (a0 : a ≠ 0) (n : ℤ) : (C a * T n).support = {n} :=
   by
   rw [← single_eq_C_mul_T]
   exact support_single_ne_zero _ a0
-#align laurent_polynomial.support_C_mul_T_of_ne_zero LaurentPolynomial.support_c_mul_t_of_ne_zero
-
+#align laurent_polynomial.support_C_mul_T_of_ne_zero LaurentPolynomial.support_C_mul_T_of_ne_zero
+
+/- warning: laurent_polynomial.to_laurent_support -> LaurentPolynomial.toLaurent_support is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.to_laurent_support LaurentPolynomial.toLaurent_supportₓ'. -/
 /-- The support of a polynomial `f` is a finset in `ℕ`.  The lemma `to_laurent_support f`
 shows that the support of `f.to_laurent` is the same finset, but viewed in `ℤ` under the natural
 inclusion `ℕ ↪ ℤ`. -/
@@ -435,7 +635,7 @@ theorem toLaurent_support (f : R[X]) : f.toLaurent.support = f.support.map Nat.c
         (by
           simp only [fs, Finset.erase_eq_of_not_mem as, Polynomial.support_erase,
             Finset.erase_insert_eq_erase])
-    rw [← monomial_add_erase f a, Finset.map_insert, ← this, map_add, Polynomial.toLaurent_c_mul_t,
+    rw [← monomial_add_erase f a, Finset.map_insert, ← this, map_add, Polynomial.toLaurent_C_mul_T,
       support_add_eq, Finset.insert_eq]
     · congr
       exact support_C_mul_T_of_ne_zero (polynomial.mem_support_iff.mp (by simp [fs])) _
@@ -447,18 +647,32 @@ end Support
 
 section Degrees
 
+#print LaurentPolynomial.degree /-
 /-- The degree of a Laurent polynomial takes values in `with_bot ℤ`.
 If `f : R[T;T⁻¹]` is a Laurent polynomial, then `f.degree` is the maximum of its support of `f`,
 or `⊥`, if `f = 0`. -/
 def degree (f : R[T;T⁻¹]) : WithBot ℤ :=
   f.support.max
 #align laurent_polynomial.degree LaurentPolynomial.degree
+-/
 
+/- warning: laurent_polynomial.degree_zero -> LaurentPolynomial.degree_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_zero LaurentPolynomial.degree_zeroₓ'. -/
 @[simp]
 theorem degree_zero : degree (0 : R[T;T⁻¹]) = ⊥ :=
   rfl
 #align laurent_polynomial.degree_zero LaurentPolynomial.degree_zero
 
+/- warning: laurent_polynomial.degree_eq_bot_iff -> LaurentPolynomial.degree_eq_bot_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_eq_bot_iff LaurentPolynomial.degree_eq_bot_iffₓ'. -/
 @[simp]
 theorem degree_eq_bot_iff {f : R[T;T⁻¹]} : f.degree = ⊥ ↔ f = 0 :=
   by
@@ -474,57 +688,97 @@ section ExactDegrees
 
 open Classical
 
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_C_mul_T LaurentPolynomial.degree_C_mul_Tₓ'. -/
 @[simp]
-theorem degree_c_mul_t (n : ℤ) (a : R) (a0 : a ≠ 0) : (c a * t n).degree = n :=
+theorem degree_C_mul_T (n : ℤ) (a : R) (a0 : a ≠ 0) : (C a * T n).degree = n :=
   by
   rw [degree]
   convert Finset.max_singleton
   refine' support_eq_singleton.mpr _
   simp only [← single_eq_C_mul_T, single_eq_same, a0, Ne.def, not_false_iff, eq_self_iff_true,
     and_self_iff]
-#align laurent_polynomial.degree_C_mul_T LaurentPolynomial.degree_c_mul_t
-
-theorem degree_c_mul_t_ite (n : ℤ) (a : R) : (c a * t n).degree = ite (a = 0) ⊥ n := by
+#align laurent_polynomial.degree_C_mul_T LaurentPolynomial.degree_C_mul_T
+
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_C_mul_T_ite LaurentPolynomial.degree_C_mul_T_iteₓ'. -/
+theorem degree_C_mul_T_ite (n : ℤ) (a : R) : (C a * T n).degree = ite (a = 0) ⊥ n := by
   split_ifs with h h <;>
     simp only [h, map_zero, MulZeroClass.zero_mul, degree_zero, degree_C_mul_T, Ne.def,
       not_false_iff]
-#align laurent_polynomial.degree_C_mul_T_ite LaurentPolynomial.degree_c_mul_t_ite
+#align laurent_polynomial.degree_C_mul_T_ite LaurentPolynomial.degree_C_mul_T_ite
 
+#print LaurentPolynomial.degree_T /-
 @[simp]
-theorem degree_t [Nontrivial R] (n : ℤ) : (t n : R[T;T⁻¹]).degree = n :=
+theorem degree_T [Nontrivial R] (n : ℤ) : (T n : R[T;T⁻¹]).degree = n :=
   by
   rw [← one_mul (T n), ← map_one C]
   exact degree_C_mul_T n 1 (one_ne_zero : (1 : R) ≠ 0)
-#align laurent_polynomial.degree_T LaurentPolynomial.degree_t
+#align laurent_polynomial.degree_T LaurentPolynomial.degree_T
+-/
 
-theorem degree_c {a : R} (a0 : a ≠ 0) : (c a).degree = 0 :=
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_C LaurentPolynomial.degree_Cₓ'. -/
+theorem degree_C {a : R} (a0 : a ≠ 0) : (C a).degree = 0 :=
   by
   rw [← mul_one (C a), ← T_zero]
   exact degree_C_mul_T 0 a a0
-#align laurent_polynomial.degree_C LaurentPolynomial.degree_c
-
-theorem degree_c_ite (a : R) : (c a).degree = ite (a = 0) ⊥ 0 := by
+#align laurent_polynomial.degree_C LaurentPolynomial.degree_C
+
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_C_ite LaurentPolynomial.degree_C_iteₓ'. -/
+theorem degree_C_ite (a : R) : (C a).degree = ite (a = 0) ⊥ 0 := by
   split_ifs with h h <;> simp only [h, map_zero, degree_zero, degree_C, Ne.def, not_false_iff]
-#align laurent_polynomial.degree_C_ite LaurentPolynomial.degree_c_ite
+#align laurent_polynomial.degree_C_ite LaurentPolynomial.degree_C_ite
 
 end ExactDegrees
 
 section DegreeBounds
 
-theorem degree_c_mul_t_le (n : ℤ) (a : R) : (c a * t n).degree ≤ n :=
+/- warning: laurent_polynomial.degree_C_mul_T_le -> LaurentPolynomial.degree_C_mul_T_le is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_C_mul_T_le LaurentPolynomial.degree_C_mul_T_leₓ'. -/
+theorem degree_C_mul_T_le (n : ℤ) (a : R) : (C a * T n).degree ≤ n :=
   by
   by_cases a0 : a = 0
   · simp only [a0, map_zero, MulZeroClass.zero_mul, degree_zero, bot_le]
   · exact (degree_C_mul_T n a a0).le
-#align laurent_polynomial.degree_C_mul_T_le LaurentPolynomial.degree_c_mul_t_le
+#align laurent_polynomial.degree_C_mul_T_le LaurentPolynomial.degree_C_mul_T_le
 
-theorem degree_t_le (n : ℤ) : (t n : R[T;T⁻¹]).degree ≤ n :=
-  (le_of_eq (by rw [map_one, one_mul])).trans (degree_c_mul_t_le n (1 : R))
-#align laurent_polynomial.degree_T_le LaurentPolynomial.degree_t_le
+#print LaurentPolynomial.degree_T_le /-
+theorem degree_T_le (n : ℤ) : (T n : R[T;T⁻¹]).degree ≤ n :=
+  (le_of_eq (by rw [map_one, one_mul])).trans (degree_C_mul_T_le n (1 : R))
+#align laurent_polynomial.degree_T_le LaurentPolynomial.degree_T_le
+-/
 
-theorem degree_c_le (a : R) : (c a).degree ≤ 0 :=
-  (le_of_eq (by rw [T_zero, mul_one])).trans (degree_c_mul_t_le 0 a)
-#align laurent_polynomial.degree_C_le LaurentPolynomial.degree_c_le
+/- warning: laurent_polynomial.degree_C_le -> LaurentPolynomial.degree_C_le is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.degree_C_le LaurentPolynomial.degree_C_leₓ'. -/
+theorem degree_C_le (a : R) : (C a).degree ≤ 0 :=
+  (le_of_eq (by rw [T_zero, mul_one])).trans (degree_C_mul_T_le 0 a)
+#align laurent_polynomial.degree_C_le LaurentPolynomial.degree_C_le
 
 end DegreeBounds
 
@@ -542,32 +796,47 @@ section CommSemiring
 
 variable [CommSemiring R]
 
+#print LaurentPolynomial.algebraPolynomial /-
 instance algebraPolynomial (R : Type _) [CommSemiring R] : Algebra R[X] R[T;T⁻¹] :=
   { Polynomial.toLaurent with
     commutes' := fun f l => by simp [mul_comm]
     smul_def' := fun f l => rfl }
 #align laurent_polynomial.algebra_polynomial LaurentPolynomial.algebraPolynomial
+-/
 
-theorem algebraMap_x_pow (n : ℕ) : algebraMap R[X] R[T;T⁻¹] (X ^ n) = t n :=
-  Polynomial.toLaurent_x_pow n
-#align laurent_polynomial.algebra_map_X_pow LaurentPolynomial.algebraMap_x_pow
-
+/- warning: laurent_polynomial.algebra_map_X_pow -> LaurentPolynomial.algebraMap_X_pow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.algebra_map_X_pow LaurentPolynomial.algebraMap_X_powₓ'. -/
+theorem algebraMap_X_pow (n : ℕ) : algebraMap R[X] R[T;T⁻¹] (X ^ n) = T n :=
+  Polynomial.toLaurent_X_pow n
+#align laurent_polynomial.algebra_map_X_pow LaurentPolynomial.algebraMap_X_pow
+
+/- warning: laurent_polynomial.algebra_map_eq_to_laurent -> LaurentPolynomial.algebraMap_eq_toLaurent is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.addMonoid))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.addMonoid))) (algebraMap.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.addMonoid) (LaurentPolynomial.algebraPolynomial.{u1} R _inst_1)) f) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.addMonoid))) (Polynomial.toLaurent.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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(Polynomial.commSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.semiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) 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(Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LaurentPolynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoidAlgebra.nonAssocSemiring.{u1, 0} R Int (CommSemiring.toSemiring.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{0} Int Int.instAddMonoidInt)))))) (Polynomial.toLaurent.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f)
+Case conversion may be inaccurate. Consider using '#align laurent_polynomial.algebra_map_eq_to_laurent LaurentPolynomial.algebraMap_eq_toLaurentₓ'. -/
 @[simp]
 theorem algebraMap_eq_toLaurent (f : R[X]) : algebraMap R[X] R[T;T⁻¹] f = f.toLaurent :=
   rfl
 #align laurent_polynomial.algebra_map_eq_to_laurent LaurentPolynomial.algebraMap_eq_toLaurent
 
+#print LaurentPolynomial.isLocalization /-
 theorem isLocalization : IsLocalization (Submonoid.closure ({X} : Set R[X])) R[T;T⁻¹] :=
   { map_units := fun t => by
       cases' t with t ht
       rcases submonoid.mem_closure_singleton.mp ht with ⟨n, rfl⟩
-      simp only [is_unit_T n, [anonymous], algebra_map_eq_to_laurent, Polynomial.toLaurent_x_pow]
+      simp only [is_unit_T n, [anonymous], algebra_map_eq_to_laurent, Polynomial.toLaurent_X_pow]
     surj := fun f =>
       by
-      induction' f using LaurentPolynomial.induction_on_mul_t with f n
+      induction' f using LaurentPolynomial.induction_on_mul_T with f n
       have := (Submonoid.closure ({X} : Set R[X])).pow_mem Submonoid.mem_closure_singleton_self n
       refine' ⟨(f, ⟨_, this⟩), _⟩
-      simp only [[anonymous], algebra_map_eq_to_laurent, Polynomial.toLaurent_x_pow, mul_T_assoc,
+      simp only [[anonymous], algebra_map_eq_to_laurent, Polynomial.toLaurent_X_pow, mul_T_assoc,
         add_left_neg, T_zero, mul_one]
     eq_iff_exists := fun f g =>
       by
@@ -579,6 +848,7 @@ theorem isLocalization : IsLocalization (Submonoid.closure ({X} : Set R[X])) R[T
         rcases submonoid.mem_closure_singleton.mp hX with ⟨n, rfl⟩
         exact mul_X_pow_injective n h }
 #align laurent_polynomial.is_localization LaurentPolynomial.isLocalization
+-/
 
 end CommSemiring
 

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

@@ -486,7 +486,8 @@ theorem degree_c_mul_t (n : ℤ) (a : R) (a0 : a ≠ 0) : (c a * t n).degree = n
 
 theorem degree_c_mul_t_ite (n : ℤ) (a : R) : (c a * t n).degree = ite (a = 0) ⊥ n := by
   split_ifs with h h <;>
-    simp only [h, map_zero, zero_mul, degree_zero, degree_C_mul_T, Ne.def, not_false_iff]
+    simp only [h, map_zero, MulZeroClass.zero_mul, degree_zero, degree_C_mul_T, Ne.def,
+      not_false_iff]
 #align laurent_polynomial.degree_C_mul_T_ite LaurentPolynomial.degree_c_mul_t_ite
 
 @[simp]
@@ -513,7 +514,7 @@ section DegreeBounds
 theorem degree_c_mul_t_le (n : ℤ) (a : R) : (c a * t n).degree ≤ n :=
   by
   by_cases a0 : a = 0
-  · simp only [a0, map_zero, zero_mul, degree_zero, bot_le]
+  · simp only [a0, map_zero, MulZeroClass.zero_mul, degree_zero, bot_le]
   · exact (degree_C_mul_T n a a0).le
 #align laurent_polynomial.degree_C_mul_T_le LaurentPolynomial.degree_c_mul_t_le
 

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

@@ -203,16 +203,16 @@ theorem Polynomial.toLaurent_c_mul_t (n : ℕ) (r : R) :
 #align polynomial.to_laurent_C_mul_T Polynomial.toLaurent_c_mul_t
 
 @[simp]
-theorem Polynomial.toLaurent_c (r : R) : (Polynomial.c r).toLaurent = c r :=
+theorem Polynomial.toLaurent_c (r : R) : (Polynomial.C r).toLaurent = c r :=
   by
   convert Polynomial.toLaurent_c_mul_t 0 r
   simp only [Int.ofNat_zero, T_zero, mul_one]
 #align polynomial.to_laurent_C Polynomial.toLaurent_c
 
 @[simp]
-theorem Polynomial.toLaurent_x : (Polynomial.x.toLaurent : R[T;T⁻¹]) = t 1 :=
+theorem Polynomial.toLaurent_x : (Polynomial.X.toLaurent : R[T;T⁻¹]) = t 1 :=
   by
-  have : (Polynomial.x : R[X]) = monomial 1 1 := by simp [← C_mul_X_pow_eq_monomial]
+  have : (Polynomial.X : R[X]) = monomial 1 1 := by simp [← C_mul_X_pow_eq_monomial]
   simp [this, Polynomial.toLaurent_c_mul_t]
 #align polynomial.to_laurent_X Polynomial.toLaurent_x
 
@@ -223,18 +223,18 @@ theorem Polynomial.toLaurent_one : (Polynomial.toLaurent : R[X] → R[T;T⁻¹])
 
 @[simp]
 theorem Polynomial.toLaurent_c_mul_eq (r : R) (f : R[X]) :
-    (Polynomial.c r * f).toLaurent = c r * f.toLaurent := by
+    (Polynomial.C r * f).toLaurent = c r * f.toLaurent := by
   simp only [_root_.map_mul, Polynomial.toLaurent_c]
 #align polynomial.to_laurent_C_mul_eq Polynomial.toLaurent_c_mul_eq
 
 @[simp]
-theorem Polynomial.toLaurent_x_pow (n : ℕ) : (x ^ n : R[X]).toLaurent = t n := by
+theorem Polynomial.toLaurent_x_pow (n : ℕ) : (X ^ n : R[X]).toLaurent = t n := by
   simp only [map_pow, Polynomial.toLaurent_x, T_pow, mul_one]
 #align polynomial.to_laurent_X_pow Polynomial.toLaurent_x_pow
 
 @[simp]
 theorem Polynomial.toLaurent_c_mul_x_pow (n : ℕ) (r : R) :
-    (Polynomial.c r * x ^ n).toLaurent = c r * t n := by
+    (Polynomial.C r * X ^ n).toLaurent = c r * t n := by
   simp only [_root_.map_mul, Polynomial.toLaurent_c, Polynomial.toLaurent_x_pow]
 #align polynomial.to_laurent_C_mul_X_pow Polynomial.toLaurent_c_mul_x_pow
 
@@ -375,8 +375,8 @@ theorem exists_t_pow (f : R[T;T⁻¹]) : ∃ (n : ℕ)(f' : R[X]), f'.toLaurent
     simp only [hf, hg, add_mul, add_comm (n : ℤ), map_add, map_mul, Polynomial.toLaurent_x_pow,
       mul_T_assoc, Int.ofNat_add]
   · cases' n with n n
-    · exact ⟨0, Polynomial.c a * X ^ n, by simp⟩
-    · refine' ⟨n + 1, Polynomial.c a, _⟩
+    · exact ⟨0, Polynomial.C a * X ^ n, by simp⟩
+    · refine' ⟨n + 1, Polynomial.C a, _⟩
       simp only [Int.negSucc_eq, Polynomial.toLaurent_c, Int.ofNat_succ, mul_T_assoc, add_left_neg,
         T_zero, mul_one]
 #align laurent_polynomial.exists_T_pow LaurentPolynomial.exists_t_pow
@@ -547,7 +547,7 @@ instance algebraPolynomial (R : Type _) [CommSemiring R] : Algebra R[X] R[T;T⁻
     smul_def' := fun f l => rfl }
 #align laurent_polynomial.algebra_polynomial LaurentPolynomial.algebraPolynomial
 
-theorem algebraMap_x_pow (n : ℕ) : algebraMap R[X] R[T;T⁻¹] (x ^ n) = t n :=
+theorem algebraMap_x_pow (n : ℕ) : algebraMap R[X] R[T;T⁻¹] (X ^ n) = t n :=
   Polynomial.toLaurent_x_pow n
 #align laurent_polynomial.algebra_map_X_pow LaurentPolynomial.algebraMap_x_pow
 
@@ -556,7 +556,7 @@ theorem algebraMap_eq_toLaurent (f : R[X]) : algebraMap R[X] R[T;T⁻¹] f = f.t
   rfl
 #align laurent_polynomial.algebra_map_eq_to_laurent LaurentPolynomial.algebraMap_eq_toLaurent
 
-theorem isLocalization : IsLocalization (Submonoid.closure ({x} : Set R[X])) R[T;T⁻¹] :=
+theorem isLocalization : IsLocalization (Submonoid.closure ({X} : Set R[X])) R[T;T⁻¹] :=
   { map_units := fun t => by
       cases' t with t ht
       rcases submonoid.mem_closure_singleton.mp ht with ⟨n, rfl⟩

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

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

@@ -3,9 +3,9 @@ Copyright (c) 2022 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 -/
-import Mathlib.Data.Polynomial.AlgebraMap
-import Mathlib.Data.Polynomial.Reverse
-import Mathlib.Data.Polynomial.Inductions
+import Mathlib.Algebra.Polynomial.AlgebraMap
+import Mathlib.Algebra.Polynomial.Reverse
+import Mathlib.Algebra.Polynomial.Inductions
 import Mathlib.RingTheory.Localization.Basic
 
 #align_import data.polynomial.laurent from "leanprover-community/mathlib"@"831c494092374cfe9f50591ed0ac81a25efc5b86"

Reduce the diff of #11499

Renames

All in the Int namespace:

• ofNat_eq_cast → ofNat_eq_natCast
• cast_eq_cast_iff_Nat → natCast_inj
• natCast_eq_ofNat → ofNat_eq_natCast
• coe_nat_sub → natCast_sub
• coe_nat_nonneg → natCast_nonneg
• sign_coe_add_one → sign_natCast_add_one
• nat_succ_eq_int_succ → natCast_succ
• succ_neg_nat_succ → succ_neg_natCast_succ
• coe_pred_of_pos → natCast_pred_of_pos
• coe_nat_div → natCast_div
• coe_nat_ediv → natCast_ediv
• sign_coe_nat_of_nonzero → sign_natCast_of_ne_zero
• toNat_coe_nat → toNat_natCast
• toNat_coe_nat_add_one → toNat_natCast_add_one
• coe_nat_dvd → natCast_dvd_natCast
• coe_nat_dvd_left → natCast_dvd
• coe_nat_dvd_right → dvd_natCast
• le_coe_nat_sub → le_natCast_sub
• succ_coe_nat_pos → succ_natCast_pos
• coe_nat_modEq_iff → natCast_modEq_iff
• coe_natAbs → natCast_natAbs
• coe_nat_eq_zero → natCast_eq_zero
• coe_nat_ne_zero → natCast_ne_zero
• coe_nat_ne_zero_iff_pos → natCast_ne_zero_iff_pos
• abs_coe_nat → abs_natCast
• coe_nat_nonpos_iff → natCast_nonpos_iff

Also rename Nat.coe_nat_dvd to Nat.cast_dvd_cast

@@ -379,7 +379,7 @@ theorem leftInverse_trunc_toLaurent :
   · intro f g hf hg
     simp only [hf, hg, _root_.map_add]
   · intro n r
-    simp only [Polynomial.toLaurent_C_mul_T, trunc_C_mul_T, Int.coe_nat_nonneg, Int.toNat_coe_nat,
+    simp only [Polynomial.toLaurent_C_mul_T, trunc_C_mul_T, Int.natCast_nonneg, Int.toNat_natCast,
       if_true]
 #align laurent_polynomial.left_inverse_trunc_to_laurent LaurentPolynomial.leftInverse_trunc_toLaurent
 

@@ -503,7 +503,7 @@ theorem degree_eq_bot_iff {f : R[T;T⁻¹]} : f.degree = ⊥ ↔ f = 0 := by
   rw [degree, Finset.max_eq_sup_withBot] at h
   ext n
   refine' not_not.mp fun f0 => _
-  simp_rw [Finset.sup_eq_bot_iff, Finsupp.mem_support_iff, Ne.def, WithBot.coe_ne_bot] at h
+  simp_rw [Finset.sup_eq_bot_iff, Finsupp.mem_support_iff, Ne, WithBot.coe_ne_bot] at h
   exact h n f0
 #align laurent_polynomial.degree_eq_bot_iff LaurentPolynomial.degree_eq_bot_iff
 
@@ -516,7 +516,7 @@ theorem degree_C_mul_T (n : ℤ) (a : R) (a0 : a ≠ 0) : degree (C a * T n) = n
   have : Finsupp.support (C a * T n) = {n} := by
     refine' support_eq_singleton.mpr _
     rw [← single_eq_C_mul_T]
-    simp only [single_eq_same, a0, Ne.def, not_false_iff, eq_self_iff_true, and_self_iff]
+    simp only [single_eq_same, a0, Ne, not_false_iff, eq_self_iff_true, and_self_iff]
   rw [this]
   exact Finset.max_singleton
 set_option linter.uppercaseLean3 false in
@@ -525,7 +525,7 @@ set_option linter.uppercaseLean3 false in
 theorem degree_C_mul_T_ite [DecidableEq R] (n : ℤ) (a : R) :
     degree (C a * T n) = if a = 0 then ⊥ else ↑n := by
   split_ifs with h <;>
-    simp only [h, map_zero, zero_mul, degree_zero, degree_C_mul_T, Ne.def,
+    simp only [h, map_zero, zero_mul, degree_zero, degree_C_mul_T, Ne,
       not_false_iff]
 set_option linter.uppercaseLean3 false in
 #align laurent_polynomial.degree_C_mul_T_ite LaurentPolynomial.degree_C_mul_T_ite
@@ -544,7 +544,7 @@ set_option linter.uppercaseLean3 false in
 #align laurent_polynomial.degree_C LaurentPolynomial.degree_C
 
 theorem degree_C_ite [DecidableEq R] (a : R) : (C a).degree = if a = 0 then ⊥ else 0 := by
-  split_ifs with h <;> simp only [h, map_zero, degree_zero, degree_C, Ne.def, not_false_iff]
+  split_ifs with h <;> simp only [h, map_zero, degree_zero, degree_C, Ne, not_false_iff]
 set_option linter.uppercaseLean3 false in
 #align laurent_polynomial.degree_C_ite LaurentPolynomial.degree_C_ite
 

Co-authored-by: damiano <adomani@gmail.com>

@@ -56,12 +56,11 @@ Lots is missing!
 -- A "better" definition of `trunc` would be as an `R`-linear map.  This works:
 --  ```
 --  def trunc : R[T;T⁻¹] →[R] R[X] :=
---  begin
---    refine (_ : R[ℕ] →[R] R[X]).comp _,
---    { exact ⟨(toFinsuppIso R).symm, by simp⟩ },
---    { refine ⟨λ r, comapDomain _ r (Set.injOn_of_injective (λ a b ab, Int.ofNat.inj ab) _), _⟩,
---      exact λ r f, comapDomain_smul _ _ _ }
---  end
+--    refine (?_ : R[ℕ] →[R] R[X]).comp ?_
+--    · exact ⟨(toFinsuppIso R).symm, by simp⟩
+--    · refine ⟨fun r ↦ comapDomain _ r
+--        (Set.injOn_of_injective (fun _ _ ↦ Int.ofNat.inj) _), ?_⟩
+--      exact fun r f ↦ comapDomain_smul ..
 --  ```
 --  but it would make sense to bundle the maps better, for a smoother user experience.
 --  I (DT) did not have the strength to embark on this (possibly short!) journey, after getting to

Classifies by adding issue number (#10691) to porting notes claiming was rw.

@@ -356,7 +356,7 @@ theorem trunc_C_mul_T (n : ℤ) (r : R) : trunc (C r * T n) = ite (0 ≤ n) (mon
   have : Function.Injective Int.ofNat := fun x y h => Int.ofNat_inj.mp h
   apply (toFinsuppIso R).injective
   rw [← single_eq_C_mul_T, trunc, AddMonoidHom.coe_comp, Function.comp_apply]
-  -- Porting note: was `rw`
+  -- Porting note (#10691): was `rw`
   erw [comapDomain.addMonoidHom_apply this]
   rw [toFinsuppIso_apply]
   -- Porting note: rewrote proof below relative to mathlib3.

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

@@ -243,25 +243,25 @@ theorem _root_.Polynomial.toLaurent_X : (toLaurent Polynomial.X : R[T;T⁻¹]) =
 set_option linter.uppercaseLean3 false in
 #align polynomial.to_laurent_X Polynomial.toLaurent_X
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem _root_.Polynomial.toLaurent_one : (Polynomial.toLaurent : R[X] → R[T;T⁻¹]) 1 = 1 :=
   map_one Polynomial.toLaurent
 #align polynomial.to_laurent_one Polynomial.toLaurent_one
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem _root_.Polynomial.toLaurent_C_mul_eq (r : R) (f : R[X]) :
     toLaurent (Polynomial.C r * f) = C r * toLaurent f := by
   simp only [_root_.map_mul, Polynomial.toLaurent_C]
 set_option linter.uppercaseLean3 false in
 #align polynomial.to_laurent_C_mul_eq Polynomial.toLaurent_C_mul_eq
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem _root_.Polynomial.toLaurent_X_pow (n : ℕ) : toLaurent (X ^ n : R[X]) = T n := by
   simp only [map_pow, Polynomial.toLaurent_X, T_pow, mul_one]
 set_option linter.uppercaseLean3 false in
 #align polynomial.to_laurent_X_pow Polynomial.toLaurent_X_pow
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem _root_.Polynomial.toLaurent_C_mul_X_pow (n : ℕ) (r : R) :
     toLaurent (Polynomial.C r * X ^ n) = C r * T n := by
   simp only [_root_.map_mul, Polynomial.toLaurent_C, Polynomial.toLaurent_X_pow]

The other direction is a consequence of IsLocalization.map_units.

Also do the same for LocalizationMap and IsLocalizedModule.

This means we have one less fact to prove when constructing an IsLocalization (etc.) instance (thus many proofs are golfed), but once we construct it we still have access to the eq_iff_exists lemmas (without the prime) so the API doesn't get less powerful.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -613,14 +613,10 @@ theorem isLocalization : IsLocalization (Submonoid.closure ({X} : Set R[X])) R[T
       refine' ⟨(f, ⟨_, this⟩), _⟩
       simp only [algebraMap_eq_toLaurent, Polynomial.toLaurent_X_pow, mul_T_assoc,
         add_left_neg, T_zero, mul_one]
-    eq_iff_exists' := fun {f g} => by
+    exists_of_eq := fun {f g} => by
       rw [algebraMap_eq_toLaurent, algebraMap_eq_toLaurent, Polynomial.toLaurent_inj]
-      refine' ⟨_, _⟩
-      · rintro rfl
-        exact ⟨1, rfl⟩
-      · rintro ⟨⟨h, hX⟩, h⟩
-        rcases Submonoid.mem_closure_singleton.mp hX with ⟨n, rfl⟩
-        exact (isRegular_X_pow n).left h }
+      rintro rfl
+      exact ⟨1, rfl⟩ }
 #align laurent_polynomial.is_localization LaurentPolynomial.isLocalization
 
 end CommSemiring

This doesn't change any polynomial operations, but:

• Makes some Decidable values computable (otherwise, they're pointless!)
• Add a few missing arguments to lemmas here and there to make them more general

This is exhaustive, within the directories it touches.

Once again, the use of letI := Classical.decEq R instead of classical here is because of the weird style of proofs in these files, where if is preferred to by_cases.

@@ -510,8 +510,6 @@ theorem degree_eq_bot_iff {f : R[T;T⁻¹]} : f.degree = ⊥ ↔ f = 0 := by
 
 section ExactDegrees
 
-open Classical
-
 @[simp]
 theorem degree_C_mul_T (n : ℤ) (a : R) (a0 : a ≠ 0) : degree (C a * T n) = n := by
   rw [degree]
@@ -525,7 +523,8 @@ theorem degree_C_mul_T (n : ℤ) (a : R) (a0 : a ≠ 0) : degree (C a * T n) = n
 set_option linter.uppercaseLean3 false in
 #align laurent_polynomial.degree_C_mul_T LaurentPolynomial.degree_C_mul_T
 
-theorem degree_C_mul_T_ite (n : ℤ) (a : R) : degree (C a * T n) = ite (a = 0) ⊥ ↑n := by
+theorem degree_C_mul_T_ite [DecidableEq R] (n : ℤ) (a : R) :
+    degree (C a * T n) = if a = 0 then ⊥ else ↑n := by
   split_ifs with h <;>
     simp only [h, map_zero, zero_mul, degree_zero, degree_C_mul_T, Ne.def,
       not_false_iff]
@@ -545,7 +544,7 @@ theorem degree_C {a : R} (a0 : a ≠ 0) : (C a).degree = 0 := by
 set_option linter.uppercaseLean3 false in
 #align laurent_polynomial.degree_C LaurentPolynomial.degree_C
 
-theorem degree_C_ite (a : R) : (C a).degree = ite (a = 0) ⊥ 0 := by
+theorem degree_C_ite [DecidableEq R] (a : R) : (C a).degree = if a = 0 then ⊥ else 0 := by
   split_ifs with h <;> simp only [h, map_zero, degree_zero, degree_C, Ne.def, not_false_iff]
 set_option linter.uppercaseLean3 false in
 #align laurent_polynomial.degree_C_ite LaurentPolynomial.degree_C_ite

Introduce the notation R[A] for AddMonoidAlgebra R A. This is to align Mathlibs notation with the standard notation for group ring.

The notation is scoped in AddMonoidAlgebra and there is no analogous notation for MonoidAlgebra.

I only used the notation for single-character R and As and only in the range [a-zA-Z].

The extra lines are all in Mathlib/Algebra/MonoidAlgebra/Basic.lean. They are accounted for by extra text in the doc-module and the actual notation.

Affected files:

Counterexamples/ZeroDivisorsInAddMonoidAlgebras
Algebra/AlgebraicCard
Algebra/MonoidAlgebra/Basic
Algebra/MonoidAlgebra/Degree
Algebra/MonoidAlgebra/Division
Algebra/MonoidAlgebra/Grading
Algebra/MonoidAlgebra/NoZeroDivisors
Algebra/MonoidAlgebra/Support
Data/Polynomial/AlgebraMap
Data/Polynomial/Basic
Data/Polynomial/Eval
Data/Polynomial/Laurent
RingTheory/FiniteType

@@ -57,7 +57,7 @@ Lots is missing!
 --  ```
 --  def trunc : R[T;T⁻¹] →[R] R[X] :=
 --  begin
---    refine (_ : AddMonoidAlgebra R ℕ →[R] R[X]).comp _,
+--    refine (_ : R[ℕ] →[R] R[X]).comp _,
 --    { exact ⟨(toFinsuppIso R).symm, by simp⟩ },
 --    { refine ⟨λ r, comapDomain _ r (Set.injOn_of_injective (λ a b ab, Int.ofNat.inj ab) _), _⟩,
 --      exact λ r f, comapDomain_smul _ _ _ }

This removes redundant field values of the form add := add for smaller terms and less unfolding during unification.

A list of all files containing a structure instance of the form { a1, ... with x1 := val, ... } where some xi is a field of some aj was generated by modifying the structure instance elaboration algorithm to print such overlaps to stdout in a custom toolchain.

Using that toolchain, I went through each file on the list and attempted to remove algebraic fields that overlapped and were redundant, eg add := add and not toFun (though some other ones did creep in). If things broke (which was the case in a couple of cases), I did not push further and reverted.

It is possible that pushing harder and trying to remove all redundant overlaps will yield further improvements.

@@ -579,7 +579,7 @@ instance : Module R[X] R[T;T⁻¹] :=
   Module.compHom _ Polynomial.toLaurent
 
 instance (R : Type*) [Semiring R] : IsScalarTower R[X] R[X] R[T;T⁻¹] where
-  smul_assoc x y z := by simp only [(· • ·), SMul.smul, SMul.comp.smul, map_mul, mul_assoc]
+  smul_assoc x y z := by dsimp; simp_rw [MulAction.mul_smul]
 
 end Semiring
 

@@ -4,6 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 -/
 import Mathlib.Data.Polynomial.AlgebraMap
+import Mathlib.Data.Polynomial.Reverse
+import Mathlib.Data.Polynomial.Inductions
 import Mathlib.RingTheory.Localization.Basic
 
 #align_import data.polynomial.laurent from "leanprover-community/mathlib"@"831c494092374cfe9f50591ed0ac81a25efc5b86"
@@ -71,9 +73,7 @@ Lots is missing!
 -/
 
 
-open Polynomial BigOperators
-
-open Polynomial AddMonoidAlgebra Finsupp
+open Polynomial BigOperators Function AddMonoidAlgebra Finsupp
 
 noncomputable section
 
@@ -86,7 +86,10 @@ abbrev LaurentPolynomial (R : Type*) [Semiring R] :=
   AddMonoidAlgebra R ℤ
 #align laurent_polynomial LaurentPolynomial
 
-local notation:9000 R "[T;T⁻¹]" => LaurentPolynomial R
+@[nolint docBlame]
+scoped[LaurentPolynomial] notation:9000 R "[T;T⁻¹]" => LaurentPolynomial R
+
+open LaurentPolynomial
 
 -- Porting note: `ext` no longer applies `Finsupp.ext` automatically
 @[ext]
@@ -113,7 +116,10 @@ def Polynomial.toLaurentAlg [CommSemiring R] : R[X] →ₐ[R] R[T;T⁻¹] := by
   exact mapDomainAlgHom R R Int.ofNatHom
 #align polynomial.to_laurent_alg Polynomial.toLaurentAlg
 
-@[simp]
+@[simp] lemma Polynomial.coe_toLaurentAlg [CommSemiring R] :
+    (toLaurentAlg : R[X] → R[T;T⁻¹]) = toLaurent :=
+  rfl
+
 theorem Polynomial.toLaurentAlg_apply [CommSemiring R] (f : R[X]) : toLaurentAlg f = toLaurent f :=
   rfl
 #align polynomial.to_laurent_alg_apply Polynomial.toLaurentAlg_apply
@@ -156,6 +162,9 @@ theorem single_eq_C (r : R) : Finsupp.single 0 r = C r := rfl
 set_option linter.uppercaseLean3 false in
 #align laurent_polynomial.single_eq_C LaurentPolynomial.single_eq_C
 
+@[simp] lemma C_apply (t : R) (n : ℤ) : C t n = if n = 0 then t else 0 := by
+  rw [← single_eq_C, Finsupp.single_apply]; aesop
+
 /-- The function `n ↦ T ^ n`, implemented as a sequence `ℤ → R[T;T⁻¹]`.
 
 Using directly `T ^ n` does not work, since we want the exponents to be of Type `ℤ` and there
@@ -166,6 +175,9 @@ def T (n : ℤ) : R[T;T⁻¹] :=
 set_option linter.uppercaseLean3 false in
 #align laurent_polynomial.T LaurentPolynomial.T
 
+@[simp] lemma T_apply (m n : ℤ) : (T n : R[T;T⁻¹]) m = if n = m then 1 else 0 :=
+  Finsupp.single_apply
+
 @[simp]
 theorem T_zero : (T 0 : R[T;T⁻¹]) = 1 :=
   rfl
@@ -220,6 +232,10 @@ theorem _root_.Polynomial.toLaurent_C (r : R) : toLaurent (Polynomial.C r) = C r
 set_option linter.uppercaseLean3 false in
 #align polynomial.to_laurent_C Polynomial.toLaurent_C
 
+@[simp]
+theorem _root_.Polynomial.toLaurent_comp_C : toLaurent (R := R) ∘ Polynomial.C = C :=
+  funext Polynomial.toLaurent_C
+
 @[simp]
 theorem _root_.Polynomial.toLaurent_X : (toLaurent Polynomial.X : R[T;T⁻¹]) = T 1 := by
   have : (Polynomial.X : R[X]) = monomial 1 1 := by simp [← C_mul_X_pow_eq_monomial]
@@ -610,4 +626,34 @@ theorem isLocalization : IsLocalization (Submonoid.closure ({X} : Set R[X])) R[T
 
 end CommSemiring
 
+section Inversion
+
+variable {R : Type*} [CommSemiring R]
+
+/-- The map which substitutes `T ↦ T⁻¹` into a Laurent polynomial. -/
+def invert : R[T;T⁻¹] ≃ₐ[R] R[T;T⁻¹] := AddMonoidAlgebra.domCongr R R <| AddEquiv.neg _
+
+@[simp] lemma invert_T (n : ℤ) : invert (T n : R[T;T⁻¹]) = T (-n) :=
+  AddMonoidAlgebra.domCongr_single _ _ _ _ _
+
+@[simp] lemma invert_apply (f : R[T;T⁻¹]) (n : ℤ) : invert f n = f (-n) := rfl
+
+@[simp] lemma invert_comp_C : invert ∘ (@C R _) = C := by ext; simp
+
+@[simp] lemma invert_C (t : R) : invert (C t) = C t := by ext; simp
+
+lemma involutive_invert : Involutive (invert (R := R)) := fun _ ↦ by ext; simp
+
+@[simp] lemma invert_symm : (invert (R := R)).symm = invert := rfl
+
+lemma toLaurent_reverse (p : R[X]) :
+    toLaurent p.reverse = invert (toLaurent p) * (T p.natDegree) := by
+  nontriviality R
+  induction' p using Polynomial.recOnHorner with p t _ _ ih p hp ih
+  · simp
+  · simp [add_mul, ← ih]
+  · simpa [natDegree_mul_X hp]
+
+end Inversion
+
 end LaurentPolynomial

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).

@@ -511,7 +511,7 @@ set_option linter.uppercaseLean3 false in
 
 theorem degree_C_mul_T_ite (n : ℤ) (a : R) : degree (C a * T n) = ite (a = 0) ⊥ ↑n := by
   split_ifs with h <;>
-    simp only [h, map_zero, MulZeroClass.zero_mul, degree_zero, degree_C_mul_T, Ne.def,
+    simp only [h, map_zero, zero_mul, degree_zero, degree_C_mul_T, Ne.def,
       not_false_iff]
 set_option linter.uppercaseLean3 false in
 #align laurent_polynomial.degree_C_mul_T_ite LaurentPolynomial.degree_C_mul_T_ite
@@ -540,7 +540,7 @@ section DegreeBounds
 
 theorem degree_C_mul_T_le (n : ℤ) (a : R) : degree (C a * T n) ≤ n := by
   by_cases a0 : a = 0
-  · simp only [a0, map_zero, MulZeroClass.zero_mul, degree_zero, bot_le]
+  · simp only [a0, map_zero, zero_mul, degree_zero, bot_le]
   · exact (degree_C_mul_T n a a0).le
 set_option linter.uppercaseLean3 false in
 #align laurent_polynomial.degree_C_mul_T_le LaurentPolynomial.degree_C_mul_T_le

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

This has nice performance benefits.

@@ -77,12 +77,12 @@ open Polynomial AddMonoidAlgebra Finsupp
 
 noncomputable section
 
-variable {R : Type _}
+variable {R : Type*}
 
 /-- The semiring of Laurent polynomials with coefficients in the semiring `R`.
 We denote it by `R[T;T⁻¹]`.
 The ring homomorphism `C : R →+* R[T;T⁻¹]` includes `R` as the constant polynomials. -/
-abbrev LaurentPolynomial (R : Type _) [Semiring R] :=
+abbrev LaurentPolynomial (R : Type*) [Semiring R] :=
   AddMonoidAlgebra R ℤ
 #align laurent_polynomial LaurentPolynomial
 
@@ -138,7 +138,7 @@ def C : R →+* R[T;T⁻¹] :=
 set_option linter.uppercaseLean3 false in
 #align laurent_polynomial.C LaurentPolynomial.C
 
-theorem algebraMap_apply {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A] (r : R) :
+theorem algebraMap_apply {R A : Type*} [CommSemiring R] [Semiring A] [Algebra R A] (r : R) :
     algebraMap R (LaurentPolynomial A) r = C (algebraMap R A r) :=
   rfl
 #align laurent_polynomial.algebra_map_apply LaurentPolynomial.algebraMap_apply
@@ -147,7 +147,7 @@ theorem algebraMap_apply {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R
 (But note that `C` is defined when `R` is not necessarily commutative, in which case
 `algebraMap` is not available.)
 -/
-theorem C_eq_algebraMap {R : Type _} [CommSemiring R] (r : R) : C r = algebraMap R R[T;T⁻¹] r :=
+theorem C_eq_algebraMap {R : Type*} [CommSemiring R] (r : R) : C r = algebraMap R R[T;T⁻¹] r :=
   rfl
 set_option linter.uppercaseLean3 false in
 #align laurent_polynomial.C_eq_algebra_map LaurentPolynomial.C_eq_algebraMap
@@ -562,7 +562,7 @@ end Degrees
 instance : Module R[X] R[T;T⁻¹] :=
   Module.compHom _ Polynomial.toLaurent
 
-instance (R : Type _) [Semiring R] : IsScalarTower R[X] R[X] R[T;T⁻¹] where
+instance (R : Type*) [Semiring R] : IsScalarTower R[X] R[X] R[T;T⁻¹] where
   smul_assoc x y z := by simp only [(· • ·), SMul.smul, SMul.comp.smul, map_mul, mul_assoc]
 
 end Semiring
@@ -571,7 +571,7 @@ section CommSemiring
 
 variable [CommSemiring R]
 
-instance algebraPolynomial (R : Type _) [CommSemiring R] : Algebra R[X] R[T;T⁻¹] :=
+instance algebraPolynomial (R : Type*) [CommSemiring R] : Algebra R[X] R[T;T⁻¹] :=
   { Polynomial.toLaurent with
     commutes' := fun f l => by simp [mul_comm]
     smul_def' := fun f l => rfl }

@@ -605,7 +605,7 @@ theorem isLocalization : IsLocalization (Submonoid.closure ({X} : Set R[X])) R[T
         exact ⟨1, rfl⟩
       · rintro ⟨⟨h, hX⟩, h⟩
         rcases Submonoid.mem_closure_singleton.mp hX with ⟨n, rfl⟩
-        exact mul_X_pow_injective n h }
+        exact (isRegular_X_pow n).left h }
 #align laurent_polynomial.is_localization LaurentPolynomial.isLocalization
 
 end CommSemiring

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
-
-! This file was ported from Lean 3 source module data.polynomial.laurent
-! leanprover-community/mathlib commit 831c494092374cfe9f50591ed0ac81a25efc5b86
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Polynomial.AlgebraMap
 import Mathlib.RingTheory.Localization.Basic
 
+#align_import data.polynomial.laurent from "leanprover-community/mathlib"@"831c494092374cfe9f50591ed0ac81a25efc5b86"
+
 /-!  # Laurent polynomials
 
 We introduce Laurent polynomials over a semiring `R`.  Mathematically, they are expressions of the

Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net>

@@ -93,7 +93,7 @@ local notation:9000 R "[T;T⁻¹]" => LaurentPolynomial R
 
 -- Porting note: `ext` no longer applies `Finsupp.ext` automatically
 @[ext]
-theorem ext [Semiring R] {p q : R[T;T⁻¹]} (h : ∀ a, p a = q a) : p = q :=
+theorem LaurentPolynomial.ext [Semiring R] {p q : R[T;T⁻¹]} (h : ∀ a, p a = q a) : p = q :=
   Finsupp.ext h
 
 /-- The ring homomorphism, taking a polynomial with coefficients in `R` to a Laurent polynomial

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -390,7 +390,7 @@ theorem _root_.Polynomial.toLaurent_ne_zero {f : R[X]} : f ≠ 0 ↔ toLaurent f
   (map_ne_zero_iff _ Polynomial.toLaurent_injective).symm
 #align polynomial.to_laurent_ne_zero Polynomial.toLaurent_ne_zero
 
-theorem exists_T_pow (f : R[T;T⁻¹]) : ∃ (n : ℕ)(f' : R[X]), toLaurent f' = f * T n := by
+theorem exists_T_pow (f : R[T;T⁻¹]) : ∃ (n : ℕ) (f' : R[X]), toLaurent f' = f * T n := by
   refine f.induction_on' ?_ fun n a => ?_ <;> clear f
   · rintro f g ⟨m, fn, hf⟩ ⟨n, gn, hg⟩
     refine' ⟨m + n, fn * X ^ n + gn * X ^ m, _⟩

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: int-y1 <jason_yuen2007@hotmail.com>